Story of QCD partons: old, recent, new

269
Story of QCD partons: old, recent, new Yuri L. Dokshitzer LPTHE, University Paris VI & VII PNPI, St. Petersburg CERN TH Heidelberg MPI June 23, 2008

Transcript of Story of QCD partons: old, recent, new

Page 1: Story of QCD partons: old, recent, new

Story of QCD partons:

old, recent, new

Yuri L. Dokshitzer

LPTHE, University Paris VI & VII

PNPI, St. Petersburg

CERN TH

Heidelberg MPIJune 23, 2008

Page 2: Story of QCD partons: old, recent, new

Asymptotic Freedom

and

QCD Partons

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Asymptotic Freedom

Running couplingRunning coupling

The strong coupling, αs, runs:

Q2 ∂αs

∂Q2= β(αs) , β(αs) = −α2

s (b0 + b1αs + b2α2s + . . .) ,

b0 =11Nc−2nf

12π, b1 =

17N2c −5Ncnf −3CF nf

24π2;

(

CF = N2c−12Nc

)

Note sign: Asymptotic Freedom, due to gluon to self-interaction

At high scales Q, coupling is weak➥quarks and gluons are almost free, their interactions stay under theperturbation theory control

At low scales, coupling becomes (catastrophically) large➥quarks and gluons interact strongly — they are confined into hadrons.Perturbation theory should fail.

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Asymptotic Freedom

Running couplingRunning coupling

The strong coupling, αs, runs:

Q2 ∂αs

∂Q2= β(αs) , β(αs) = −α2

s (b0 + b1αs + b2α2s + . . .) ,

b0 =11Nc−2nf

12π, b1 =

17N2c −5Ncnf −3CF nf

24π2;

(

CF = N2c−12Nc

)

Note sign: Asymptotic Freedom, due to gluon to self-interaction

At high scales Q, coupling is weak➥quarks and gluons are almost free, their interactions stay under theperturbation theory control

At low scales, coupling becomes (catastrophically) large➥quarks and gluons interact strongly — they are confined into hadrons.Perturbation theory should fail.

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Asymptotic Freedom

Running couplingRunning coupling

The strong coupling, αs, runs:

Q2 ∂αs

∂Q2= β(αs) , β(αs) = −α2

s (b0 + b1αs + b2α2s + . . .) ,

b0 =11Nc−2nf

12π, b1 =

17N2c −5Ncnf −3CF nf

24π2;

(

CF = N2c−12Nc

)

Note sign: Asymptotic Freedom, due to gluon to self-interaction

At high scales Q, coupling is weak➥quarks and gluons are almost free, their interactions stay under theperturbation theory control

At low scales, coupling becomes (catastrophically) large➥quarks and gluons interact strongly — they are confined into hadrons.Perturbation theory should fail.

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Asymptotic Freedom

Running couplingRunning coupling

The strong coupling, αs, runs:

Q2 ∂αs

∂Q2= β(αs) , β(αs) = −α2

s (b0 + b1αs + b2α2s + . . .) ,

b0 =11Nc−2nf

12π, b1 =

17N2c −5Ncnf −3CF nf

24π2;

(

CF = N2c−12Nc

)

Note sign: Asymptotic Freedom, due to gluon to self-interaction

At high scales Q, coupling is weak➥quarks and gluons are almost free, their interactions stay under theperturbation theory control

At low scales, coupling becomes (catastrophically) large➥quarks and gluons interact strongly — they are confined into hadrons.Perturbation theory should fail.

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Asymptotic Freedom

AF and QCD vacuumAsymptotic Freedom : WHY ?

It seems natural to expect the effective interaction strength to decreaseat large distances.

Moreover, it was long thought to be inevitable as corresponding to thephysics of ‘screening’.

The fact that the vacuum fluctuations have to screen the externalcharge, in QFT follows from the first principles: unitarity and crossingsymmetry (= Lorentz invariance + causality)

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Asymptotic Freedom

AF and QCD vacuumAsymptotic Freedom : WHY ?

It seems natural to expect the effective interaction strength to decreaseat large distances.

Moreover, it was long thought to be inevitable as corresponding to thephysics of ‘screening’.

The fact that the vacuum fluctuations have to screen the externalcharge, in QFT follows from the first principles: unitarity and crossingsymmetry (= Lorentz invariance + causality)

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Story of QCD partons (4/54)

Asymptotic Freedom

AF and QCD vacuumAsymptotic Freedom : WHY ?

It seems natural to expect the effective interaction strength to decreaseat large distances.

Moreover, it was long thought to be inevitable as corresponding to thephysics of ‘screening’.

The fact that the vacuum fluctuations have to screen the externalcharge, in QFT follows from the first principles: unitarity and crossingsymmetry (= Lorentz invariance + causality)

Page 10: Story of QCD partons: old, recent, new

Story of QCD partons (4/54)

Asymptotic Freedom

AF and QCD vacuumAsymptotic Freedom : WHY ?

It seems natural to expect the effective interaction strength to decreaseat large distances.

Moreover, it was long thought to be inevitable as corresponding to thephysics of ‘screening’.

The fact that the vacuum fluctuations have to screen the externalcharge, in QFT follows from the first principles: unitarity and crossingsymmetry (= Lorentz invariance + causality)

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Story of QCD partons (4/54)

Asymptotic Freedom

AF and QCD vacuumAsymptotic Freedom : WHY ?

It seems natural to expect the effective interaction strength to decreaseat large distances.

Moreover, it was long thought to be inevitable as corresponding to thephysics of ‘screening’.

The fact that the vacuum fluctuations have to screen the externalcharge, in QFT follows from the first principles: unitarity and crossingsymmetry (= Lorentz invariance + causality) as was understood by

Landau and Pomeranchuk in mid 50’s, after Landau & Co have made asign mistake in calculating the running electromagnetic coupling (andthus, for a couple of weeks, were happy about having discovered‘asymptotic freedom’ in QED)...

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Asymptotic Freedom

AF and QCD vacuumAsymptotic Freedom : WHY ?

It seems natural to expect the effective interaction strength to decreaseat large distances.

Moreover, it was long thought to be inevitable as corresponding to thephysics of ‘screening’.

The fact that the vacuum fluctuations have to screen the externalcharge, in QFT follows from the first principles: unitarity and crossingsymmetry (= Lorentz invariance + causality) as was understood by

Landau and Pomeranchuk in mid 50’s, after Landau & Co have made asign mistake in calculating the running electromagnetic coupling (andthus, for a couple of weeks, were happy about having discovered‘asymptotic freedom’ in QED)...

So, why does this most general argument fail in non-Abelian QFT ?

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

To address questions starting from what or why we better talk physicaldegrees of freedom; use the Hamiltonian language. Then, we have gluonsof two sorts: ‘physical’ transverse gluons and the Coulomb gluon field —mediator of the instantaneous interaction between colour charges.

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

To address questions starting from what or why we better talk physicaldegrees of freedom; use the Hamiltonian language. Then, we have gluonsof two sorts: ‘physical’ transverse gluons and the Coulomb gluon field —mediator of the instantaneous interaction between colour charges.

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

Consider Coulomb interaction between two (colour) charges :

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

Consider Coulomb interaction between two (colour) charges :

��

Instantaneous Coulomb interaction

_13

* *3 2= −Nc

Transverse gluons (and quarks)

−n f

_

screening

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

Consider Coulomb interaction between two (colour) charges :

� � �� �

� � � � �� � � � �� � � � �� � � � �

Instantaneous Coulomb interaction

Vacuum fluctuations of transverse fields

= +N 4*c

ANTI screening

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

Consider Coulomb interaction between two (colour) charges :

� �� �

�� ��

� ��

� � � � �� � � � �� � � � �� � � � �

Instantaneous Coulomb interaction

Instantaneous Coulomb interaction

Vacuum fluctuations of transverse fields

= +N 4*c

_13

* *3 2

Khriplovich (1969)

Gribov (1976)

� �� �� �� �� �

= −Nc

Transverse gluons (and quarks)

−n f

_

ANTI screening

Combine into the QCD β–function:

β(αs) =d

d lnQ24πα−1

s (Q2)

=

[

4 − 1

3

]

∗ Nc −2

3∗ nf

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Asymptotic Freedom

AF and QCD vacuumAutopsy of Asymptotic Freedom

Consider Coulomb interaction between two (colour) charges :

� �� �

�� ��

� ��

� � � � �� � � � �� � � � �� � � � �

Instantaneous Coulomb interaction

Instantaneous Coulomb interaction

Vacuum fluctuations of transverse fields

= +N 4*c

_13

* *3 2

Khriplovich (1969)

Gribov (1976)

� �� �� �� �� �

= −Nc

Transverse gluons (and quarks)

−n f

_

ANTI screening

Combine into the QCD β–function:

β(αs) =d

d lnQ24πα−1

s (Q2)

=

[

4 − 1

3

]

∗ Nc −2

3∗ nf

The origin of antiscreening —

deepening of the ground state under

the 2nd order perturbation in NQM:

∆E0 =∑

n

|〈0|δV |n〉|2E0 − En

< 0.

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other

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Asymptotic Freedom

Running couplingRunning coupling (cont.)

Solve Q2 ∂αs

∂Q2= −b0α

2s ⇒ αs(Q

2) =αs(Q

20 )

1 + b0αs(Q20 ) ln Q2

Q20

=1

b0 ln Q2

Λ2

Λ (aka ΛQCD) —the fundamental QCD scale,at which coupling blows up.

Perturbative calculations validfor large scales Q � Λ.

Not an obvious statement: wedeal with hadrons in nature,while applying QCD to quarksand gluons . . .

“Animalistic” Ideology : someobservables are more equalthan the other jets & shapes 161 GeV

jets & shapes 172 GeV

0.10 0.12 0.14

α (Μ )s Z

τ-decays [LEP]

xF [ν -DIS]F [e-, µ-DIS]

Υ decays

Γ(Z --> had.) [LEP]

e e [σ ]+had

_e e [jets & shapes 35 GeV]+ _

σ(pp --> jets)

pp --> bb X

0

QQ + lattice QCD

DIS [GLS-SR]

2

3

pp, pp --> γ X

DIS [Bj-SR]

e e [jets & shapes 58 GeV]+ _

DIS & pp —> jets

jets & shapes 133 GeV

e e [jets & shapes 22 GeV]+ _

e e [jets & shapes 44 GeV]+ _

e e [σ ]+had

_

jets & shapes 183 GeV

DIS [pol. strct. fctn.]

jets & shapes 189 GeV

e e [scaling. viol.]+ _

jets & shapes 91.2 GeV

e e F+ _2γ

e e [jets & shapes 14 GeV]+ _

e e [4-jet rate]+ _

jets & shapes 195 GeV jets & shapes 201 GeVjets & shapes 206 GeV

DIS [ep —> jets]

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Hard Processes

Large momentum transferHard QCD interactions

Hit hard to see what is it there inside (a childish but productive idea)

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Hard Processes

Large momentum transferHard QCD interactions

Hit hard to see what is it there inside

Heat the Vacuum

e+e− annihilation into hadrons : e+e− → qq → hadrons.

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Hard Processes

Large momentum transferHard QCD interactions

Hit hard to see what is it there inside

Hit the proton (with an electromagnetic/electroweak probe)

e+e− annihilation into hadrons : e+e− → qq → hadrons.

Deep Inelastic lepton-hadron Scattering (DIS) : e−p → e− + X .

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Hard Processes

Large momentum transferHard QCD interactions

Hit hard to see what is it there inside

Make two hadrons hit each other hard

e+e− annihilation into hadrons : e+e− → qq → hadrons.

Deep Inelastic lepton-hadron Scattering (DIS) : e−p → e− + X .

Hadron–hadron collisions

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Hard Processes

Large momentum transferHard QCD interactions

Hit hard to see what is it there inside

Make two hadrons hit each other hard

e+e− annihilation into hadrons : e+e− → qq → hadrons.

Deep Inelastic lepton-hadron Scattering (DIS) : e−p → e− + X .

Hadron–hadron collisions : production of

massive “sterile” objects :

➥ lepton pairs (µ+µ−, the Drell-Yan process),

➥ electroweak vector bosons (Z 0, W±),

➥ Higgs boson(s)

hadrons/photons with large transverse momenta wrt to the collision axis.

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Hard Processes

Large momentum transferHard QCD interactions

Hit hard to see what is it there inside

Make two hadrons hit each other hard

e+e− annihilation into hadrons : e+e− → qq → hadrons.

Deep Inelastic lepton-hadron Scattering (DIS) : e−p → e− + X .

Hadron–hadron collisions : production of

massive “sterile” objects :

➥ lepton pairs (µ+µ−, the Drell-Yan process),

➥ electroweak vector bosons (Z 0, W±),

➥ Higgs boson(s)

hadrons/photons with large transverse momenta wrt to the collision axis.

Momentum transfer = measure of “hardness”

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2)

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2)

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

Measure of inelasticity – Bjorken variable x = − q2

2(Pq) (0 ≤ x ≤ 1)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2)

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

Measure of inelasticity – Bjorken variable x = − q2

2(Pq) (0 ≤ x ≤ 1)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2)

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

q

P + q

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P = 0

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

Measure of inelasticity – Bjorken variable x = − q2

2(Pq) (0 ≤ x ≤ 1)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2) · δ(1 − x) dx

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

Measure of inelasticity – Bjorken variable x = − q2

2(Pq) (0 ≤ x ≤ 1)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2) · δ(1 − x) dx

dσinelastic

dq2=

(

dq2

)

point

· F 2inelastic(q

2, x) · dx

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Hard Processes

DISDeep Inelastic lepton-proton Scattering

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Bit of kinematics: invariant mass of final hadrons

W 2 − M2P = (P + q)2 − M2

P

= 2(Pq)

(

1 − −q2

2(Pq)

)

≡ 2(Pq) · (1−x)

Measure of inelasticity – Bjorken variable x = − q2

2(Pq) (0 ≤ x ≤ 1)

dσelastic

dq2=

(

dq2

)

point

· F 2elastic(q

2)

dσinelastic

dq2=

(

dq2

)

point

· F 2inelastic(q

2, x) · dx

What to expect for elastic and inelastic proton Form Factors F 2(q2) ?

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Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 41: Story of QCD partons: old, recent, new

Story of QCD partons (9/54)

Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 42: Story of QCD partons: old, recent, new

Story of QCD partons (9/54)

Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 43: Story of QCD partons: old, recent, new

Story of QCD partons (9/54)

Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 44: Story of QCD partons: old, recent, new

Story of QCD partons (9/54)

Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 45: Story of QCD partons: old, recent, new

Story of QCD partons (9/54)

Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 46: Story of QCD partons: old, recent, new

Story of QCD partons (9/54)

Hard Processes

DISFree quarks

Two plausible and one crazy scenarios for the |q2| → ∞ (Bjorken) limit

1). Smooth electric charge distribution: (classical picture)

F 2elastic(q

2) ∼ F 2inelastic(q

2) � 1

– external probe penetrates the proton as knife thru butter.

2). Tightly bound point charges inside the proton: (quarks?)

F 2elastic(q

2) ∼ 1; F 2inelastic(q

2) � 1

– excitation of one quark gets redistributed inside the proton via the confinement

“springs” that bind quarks together and don’t let them fly away.

3). Now look at this: (Mother Nature)

F 2elastic(q

2) � 1; F 2inelastic(q

2) ∼ 1

– there are points (quarks) inside proton, but the hit quark behaves as a free

particle that flies away without caring about confinement.

Page 47: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system (of 3 quarks + glue + · · · )

Page 48: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system

P

p p’

qP + q

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Equate

Inelastic electron–proton scattering

=elastic electron–quark scattering

Page 49: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Equate

Inelastic electron–proton scattering

=elastic electron–quark scattering

Page 50: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Let the parton carry a finite fraction of theproton momentum k ' z · P (k2 ' 0)

(k ′)2 = (zP + q)2

' 2(Pq) · (z−x) ' 0 .

Page 51: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Let the parton carry a finite fraction of theproton momentum k ' z · P (k2 ' 0)

(k ′)2 = (zP + q)2

' 2(Pq) · (z−x) ' 0 .DIS selects a quark with momentum x · P

Page 52: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Let the parton carry a finite fraction of theproton momentum k ' z · P (k2 ' 0)

(k ′)2 = (zP + q)2

' 2(Pq) · (z−x) ' 0 .DIS selects a quark with momentum x · P

Bjorken x has the meaning of parton momentum fraction; F 2inelastic

becomes the probability of finding a parton with given momentum.

Page 53: Story of QCD partons: old, recent, new

Story of QCD partons (10/54)

Hard Processes

DISBjorken scaling: Partons

Conclusion: Proton is a loosely bound system

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Let the parton carry a finite fraction of theproton momentum k ' z · P (k2 ' 0)

(k ′)2 = (zP + q)2

' 2(Pq) · (z−x) ' 0 .DIS selects a quark with momentum x · P

Bjorken x has the meaning of parton momentum fraction; F 2inelastic

becomes the probability of finding a parton with given momentum.Existence of the limiting distribution

F 2inelastic(q

2, x) = DqP(x) ; |q2| → ∞, x = const

constitutes the Bjorken scaling hypothesis.

Page 54: Story of QCD partons: old, recent, new

Story of QCD partons (11/54)

QCD Partons

Collinear SingularitiesViolation of scaling is inevitable in QFT

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Particle virtualities/transverse momenta inQFT are not limited. In particular, in a DISprocess, “partons” (quarks and gluons) mayhave transverse momenta up to

k2⊥ � Q2 = |q2|.

Page 55: Story of QCD partons: old, recent, new

Story of QCD partons (11/54)

QCD Partons

Collinear SingularitiesViolation of scaling is inevitable in QFT

P

q

k

kB

A

kC

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

Particle virtualities/transverse momenta inQFT are not limited. In particular, in a DISprocess, “partons” (quarks and gluons) mayhave transverse momenta up to

k2⊥ � Q2 = |q2|.

As a result, the number of particles turns outto be large in spite of small coupling :

dw ∝∫ Q2

αs

π

dk2⊥

k2⊥

∼ αs

πlnQ2 = O(1) .

Page 56: Story of QCD partons: old, recent, new

Story of QCD partons (11/54)

QCD Partons

Collinear SingularitiesViolation of scaling is inevitable in QFT

P

q

k

kB

A

kC

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

Particle virtualities/transverse momenta inQFT are not limited. In particular, in a DISprocess, “partons” (quarks and gluons) mayhave transverse momenta up to

k2⊥ � Q2 = |q2|.

As a result, the number of particles turns outto be large in spite of small coupling :

dw ∝∫ Q2

αs

π

dk2⊥

k2⊥

∼ αs

πlnQ2 = O(1) .

Such – “collinear” – enhancement is typical for QFTs with dimensionlesscoupling – “logarithmic” Field Theories.

Page 57: Story of QCD partons: old, recent, new

Story of QCD partons (11/54)

QCD Partons

Collinear SingularitiesViolation of scaling is inevitable in QFT

P

q

k

kB

A

kC

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

Particle virtualities/transverse momenta inQFT are not limited. In particular, in a DISprocess, “partons” (quarks and gluons) mayhave transverse momenta up to

k2⊥ � Q2 = |q2|.

As a result, the number of particles turns outto be large in spite of small coupling :

dw ∝∫ Q2

αs

π

dk2⊥

k2⊥

∼ αs

πlnQ2 = O(1) .

Such – “collinear” – enhancement is typical for QFTs with dimensionlesscoupling – “logarithmic” Field Theories.

Physically, a QFT particle is surrounded by a virtual coat; its visiblecontent depends on the resolution power of the probe λ = 1

Q= 1√

−q2

Page 58: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution, Q2

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

Page 59: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution,

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

Page 60: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution,

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

Page 61: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution,

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

Page 62: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution,

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

Page 63: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution,

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

αs =⇒ αs · lnQ2

Page 64: Story of QCD partons: old, recent, new

Story of QCD partons (12/54)

QCD Partons

Parton cascadesPartons in QFT?

Thus we learned that in QCD the probability to find a parton q inside thetarget h must depend on the resolution,

Dqh = Dq

h (x , ln Q2) .

Moreover,

the Feynman–Bjorken picture of partons employedthe classical (probabilistic) language:

σh = σq ⊗ Dqh .

However, as we see, quarks and gluons multiply willingly, w = O(1).

Is there any chance to rescue probabilistic interpretationof quark–gluon cascades, to speak of “QCD partons”?

The question may sound silly, since in QFT the number of Feynmangraphs grows as (n!)2 with the number n of participating particles . . .

However, which are the most probable parton fluctuations?

(αs)n =⇒ (αs · lnQ2)n

Page 65: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

p p’

q

k

k’

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

Page 66: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' x · P , kA ' x

z· P

Page 67: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' x · P , kA ' x

z· P

Page 68: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

Page 69: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B |z

=|k2

A|1

+k2C

1 − z+

k2⊥

z(1 − z)

Page 70: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥ k2

(k2B)2

Page 71: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥ k2

(k2B)2

∝ αs

π

dk2⊥

k2⊥

,

Page 72: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥

k2⊥

(k2B)2

∝ αs

π

dk2⊥

k2⊥

,

|k2B |z

' k2⊥

z(1−z)� |k2

A|1

(

as well ask2C

1 − z

)

.

Page 73: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥

k2⊥

(k2B)2

∝ αs

π

dk2⊥

k2⊥

,

|k2B |z

' k2⊥

z(1−z)� |k2

A|1

(

as well ask2C

1 − z

)

.

This inequality has a transparent physical meaning:

z · EA

|k2B |

� EA

|k2A|

Page 74: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥

k2⊥

(k2B)2

∝ αs

π

dk2⊥

k2⊥

,

|k2B |z

' k2⊥

z(1−z)� |k2

A|1

(

as well ask2C

1 − z

)

.

This inequality has a transparent physical meaning:

EB

|k2B |

=z · EA

|k2B |

� EA

|k2A|

Page 75: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥

k2⊥

(k2B)2

∝ αs

π

dk2⊥

k2⊥

,

|k2B |z

' k2⊥

z(1−z)� |k2

A|1

(

as well ask2C

1 − z

)

.

This inequality has a transparent physical meaning:

tB ≡ EB

|k2B |

=z · EA

|k2B |

� EA

|k2A|

≡ tA

Page 76: Story of QCD partons: old, recent, new

Story of QCD partons (13/54)

QCD Partons

Parton cascadesLong-living partons fluctuations

P

q

k

kB

A

kC

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

Kinematics of the parton splitting A → B +C

kB ' zkA , kC ' (1 − z)kA

|k2B|

z=

|k2A|

1 +k2C

1−z+

k2⊥

z(1−z)

Probability of the splitting process :

dw ∝ αs

π

dk2⊥

k2⊥

(k2B)2

∝ αs

π

dk2⊥

k2⊥

,

|k2B |z

' k2⊥

z(1−z)� |k2

A|1

(

as well ask2C

1 − z

)

.

This inequality has a transparent physical meaning:

tB ≡ EB

|k2B |

=z · EA

|k2B |

� EA

|k2A|

≡ tA

strongly ordered lifetimes of successive parton fluctuations !

Page 77: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

P

q

k

kB

A

kC

� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �� � � � �

So long as probability of one extra partonemission is large, one has to consider andtreat arbitrary number of parton splittings

Page 78: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

P

µ2� t1 � t2 � t3 � t4 � t5 � P

Q2

Page 79: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

P

µ2� t1 � t2 � t3 � t4 � t5 � P

Q2

Four basic splitting processes :

Page 80: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

P

µ2� t1 � t2 � t3 � t4 � t5 � P

Q2

Four basic splitting processes :q → q(z) +g z = k5/k4

Φqq(z) = CF · 1 + z2

1 − z,

Page 81: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

P

µ2� t1 � t2 � t3 � t4 � t5 � P

Q2

Four basic splitting processes :q → g(z) +q z = k2/k1

Φqq(z) = CF · 1 + z2

1 − z,

Φgq(z) = CF · 1 + (1−z)2

z,

Page 82: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

P

µ2� t1 � t2 � t3 � t4 � t5 � P

Q2

Four basic splitting processes :g → q(z) +q z = k4/k3

Φqq(z) = CF · 1 + z2

1 − z,

Φgq(z) = CF · 1 + (1−z)2

z,

Φqg (z) = TR ·

[

z2 + (1−z)2]

,

Page 83: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

P

µ2� t1 � t2 � t3 � t4 � t5 � P

Q2

Four basic splitting processes :g → g(z) +g z = k3/k2

Φqq(z) = CF · 1 + z2

1 − z,

Φgq(z) = CF · 1 + (1−z)2

z,

Φqg (z) = TR ·

[

z2 + (1−z)2]

,

Φgg (z) = Nc ·

1 + z4 + (1−z)4

z(1 − z)

Page 84: Story of QCD partons: old, recent, new

Story of QCD partons (14/54)

QCD Partons

Parton cascadesquark–gluon cascades

q

P

2

3

4

5

1

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �� � � �

µ2 � k21⊥ � k2

2⊥ � k23⊥ � k2

4⊥ � k25⊥ � Q2

Four basic splitting processes :

“Hamiltonian” for parton cascades

Φqq(z) = CF · 1 + z2

1 − z,

Φgq(z) = CF · 1 + (1−z)2

z,

Φqg (z) = TR ·

[

z2 + (1−z)2]

,

Φgg (z) = Nc ·

1 + z4 + (1−z)4

z(1 − z)

Logarithmic “evolution time” dξ = αs

dk2⊥

k2⊥

Page 85: Story of QCD partons: old, recent, new

Story of QCD partons (15/54)

QCD Partons

Parton dynamicsEvolution

Nowadays we cannot predict, from the first principles, parton content (B)of a hadron (h). However, perturbative QCD tells us how it changes withthe resolution of the DIS process – momentum transfer Q2.

Page 86: Story of QCD partons: old, recent, new

Story of QCD partons (15/54)

QCD Partons

Parton dynamicsEvolution

Nowadays we cannot predict, from the first principles, parton content (B)of a hadron (h). However, perturbative QCD tells us how it changes withthe resolution of the DIS process – momentum transfer Q2. Evolution ofparton distribution reminds the Schrodinger equation:

d

d lnQ2DB

h (x ,Q2) =αs(Q

2)

A=q,q,g

∫ 1

x

dz

zΦB

A(z) · DAh (

x

z,Q2)

Page 87: Story of QCD partons: old, recent, new

Story of QCD partons (15/54)

QCD Partons

Parton dynamicsEvolution

Nowadays we cannot predict, from the first principles, parton content (B)of a hadron (h). However, perturbative QCD tells us how it changes withthe resolution of the DIS process – momentum transfer Q2. Evolution ofparton distribution reminds the Schrodinger equation:

d

d lnQ2DB

h (x ,Q2) =αs(Q

2)

A=q,q,g

∫ 1

x

dz

zΦB

A(z) · DAh (

x

z,Q2)

“wave function”

Page 88: Story of QCD partons: old, recent, new

Story of QCD partons (15/54)

QCD Partons

Parton dynamicsEvolution

Nowadays we cannot predict, from the first principles, parton content (B)of a hadron (h). However, perturbative QCD tells us how it changes withthe resolution of the DIS process – momentum transfer Q2. Evolution ofparton distribution reminds the Schrodinger equation:

d

d lnQ2DB

h (x ,Q2) =αs(Q

2)

A=q,q,g

∫ 1

x

dz

zΦB

A(z) · DAh (

x

z,Q2)

“time derivative”

Page 89: Story of QCD partons: old, recent, new

Story of QCD partons (15/54)

QCD Partons

Parton dynamicsEvolution

Nowadays we cannot predict, from the first principles, parton content (B)of a hadron (h). However, perturbative QCD tells us how it changes withthe resolution of the DIS process – momentum transfer Q2. Evolution ofparton distribution reminds the Schrodinger equation:

d

d lnQ2DB

h (x ,Q2) =αs(Q

2)

A=q,q,g

∫ 1

x

dz

zΦB

A(z) · DAh (

x

z,Q2)

“Hamiltonian”

Page 90: Story of QCD partons: old, recent, new

Story of QCD partons (15/54)

QCD Partons

Parton dynamicsEvolution

Nowadays we cannot predict, from the first principles, parton content (B)of a hadron (h). However, perturbative QCD tells us how it changes withthe resolution of the DIS process – momentum transfer Q2. Evolution ofparton distribution reminds the Schrodinger equation:

d

d lnQ2DB

h (x ,Q2) =αs(Q

2)

A=q,q,g

∫ 1

x

dz

zΦB

A(z) · DAh (

x

z,Q2)

Parton Dynamics turned out to be extremely simple.

Hidden symmetries of the QCD evolutionmay eventually allow one to “exactly solve”

the major part of parton dynamics

Page 91: Story of QCD partons: old, recent, new

Hadron Jets

and

QCD Radiophysics

Page 92: Story of QCD partons: old, recent, new

Story of QCD partons (17/54)

Hadron Jets Quarks → jets of hadrons

DALI_F1 ECM=206.7 Pch=83.0 Efl=194. Ewi=124. Eha=35.9 BEHOLD

Nch=28 EV1=0 EV2=0 EV3=0 ThT=0 00−06−14 2:32 Detb= E3FFFFALEPH5 Gev EC5 Gev HC

Aleph Higgs event:

Claim: it corresponds toZH → qqbb.

But actually just bunches (‘jets’)of hadrons.

Page 93: Story of QCD partons: old, recent, new

Story of QCD partons (17/54)

Hadron Jets Quarks → jets of hadrons

DALI_F1 ECM=206.7 Pch=83.0 Efl=194. Ewi=124. Eha=35.9 BEHOLD

Nch=28 EV1=0 EV2=0 EV3=0 ThT=0 00−06−14 2:32 Detb= E3FFFFALEPH5 Gev EC5 Gev HC

Aleph Higgs event:

Claim: it corresponds toZH → qqbb.

But actually just bunches (‘jets’)of hadrons.

Can they be related?And How?

Page 94: Story of QCD partons: old, recent, new

Story of QCD partons (17/54)

Hadron Jets Quarks → jets of hadrons

DALI_F1 ECM=206.7 Pch=83.0 Efl=194. Ewi=124. Eha=35.9 BEHOLD

Nch=28 EV1=0 EV2=0 EV3=0 ThT=0 00−06−14 2:32 Detb= E3FFFFALEPH5 Gev EC5 Gev HC

Aleph Higgs event:

Claim: it corresponds toZH → qqbb.

But actually just bunches (‘jets’)of hadrons.

Can they be related?And How?

Need understanding of QCD

Page 95: Story of QCD partons: old, recent, new

Story of QCD partons (18/54)

Hadron Jets Jet as a ‘string’ of hadrons

Existence of Jets was envisaged from “parton models” in the late 1960’s.

Kogut–Susskind vacuum breaking picture :

Page 96: Story of QCD partons: old, recent, new

Story of QCD partons (18/54)

Hadron Jets Jet as a ‘string’ of hadrons

Existence of Jets was envisaged from “parton models” in the late 1960’s.

Kogut–Susskind vacuum breaking picture :

In a DIS a green quark in the proton is hit by a virtual photon;

virtual photon

proton

Page 97: Story of QCD partons: old, recent, new

Story of QCD partons (18/54)

Hadron Jets Jet as a ‘string’ of hadrons

Existence of Jets was envisaged from “parton models” in the late 1960’s.

Kogut–Susskind vacuum breaking picture :

In a DIS a green quark in the proton is hit by a virtual photon;The quark leaves the stage and the colour field starts to build up;

colour field

Page 98: Story of QCD partons: old, recent, new

Story of QCD partons (18/54)

Hadron Jets Jet as a ‘string’ of hadrons

Existence of Jets was envisaged from “parton models” in the late 1960’s.

Kogut–Susskind vacuum breaking picture :

In a DIS a green quark in the proton is hit by a virtual photon;The quark leaves the stage and the colour field starts to build up;A green–anti-green quark pair pops up from the vacuum, splitting thesystem into two globally blanched sub-systems.

Vacuum break−upin the external field

colour field

colour field

Page 99: Story of QCD partons: old, recent, new

Story of QCD partons (18/54)

Hadron Jets Jet as a ‘string’ of hadrons

Existence of Jets was envisaged from “parton models” in the late 1960’s.

Kogut–Susskind vacuum breaking picture :

In a DIS a green quark in the proton is hit by a virtual photon;The quark leaves the stage and the colour field starts to build up;A green–anti-green quark pair pops up from the vacuum, splitting thesystem into two globally blanched sub-systems.

Vacuum break−upin the external field

colour field

colour field

Repeating, one gets the “Feynman Plateau” :

“One” hadron per∆ω

ω; Hadron multiplicity ∝ lnQ .

Page 100: Story of QCD partons: old, recent, new

Story of QCD partons (19/54)

Hadron Jets qq → hadrons

Near ‘perfect’ 2-jet event

2 well-collimated jets of particles.

Page 101: Story of QCD partons: old, recent, new

Story of QCD partons (19/54)

Hadron Jets qq → hadrons

Near ‘perfect’ 2-jet event

2 well-collimated jets of particles.

HOWEVER :

Transverse momenta increase with Q;

Jets become “fatter” in k⊥(though narrower in angle).

Page 102: Story of QCD partons: old, recent, new

Story of QCD partons (19/54)

Hadron Jets qq → hadrons

Near ‘perfect’ 2-jet event

2 well-collimated jets of particles.

HOWEVER :

Transverse momenta increase with Q;

Jets become “fatter” in k⊥(though narrower in angle).

Moreover,

In 10% of e+e− annihilationevents

— striking fluctuations !

Page 103: Story of QCD partons: old, recent, new

Story of QCD partons (20/54)

Hadron Jets

Gluon jetThird jet

By eye, can make out 3-jet structure.

Page 104: Story of QCD partons: old, recent, new

Story of QCD partons (20/54)

Hadron Jets

Gluon jetThird jet

By eye, can make out 3-jet structure.

No surprise : (Kogut & Susskind, 1974)

Hard gluon bremsstrahlung offthe qq pair may be expected togive rise to 3-jet events . . .

Page 105: Story of QCD partons: old, recent, new

Story of QCD partons (20/54)

Hadron Jets

Gluon jetThird jet

By eye, can make out 3-jet structure.

No surprise : (Kogut & Susskind, 1974)

Hard gluon bremsstrahlung offthe qq pair may be expected togive rise to 3-jet events . . .

The first QCD analysis was done byJ.Ellis, M.Gaillard & G.Ross (1976)

Planar events with large k⊥ ;

How to measure gluon spin ;

Gluon jet – softer, more populated.

Page 106: Story of QCD partons: old, recent, new

Story of QCD partons (21/54)

Hadron Jets

Gluon jetGluon → hadrons

QCD possesses N2c − 1 gauge fields — vector gluons g .

At large distances, they are supposed to “glue” quarks together.At small distances (space-time intervals) g is as legitimate a parton as q is.

Page 107: Story of QCD partons: old, recent, new

Story of QCD partons (21/54)

Hadron Jets

Gluon jetGluon → hadrons

QCD possesses N2c − 1 gauge fields — vector gluons g .

At large distances, they are supposed to “glue” quarks together.At small distances (space-time intervals) g is as legitimate a parton as q is.The first indirect evidence in favour of gluons came from DIS where it was found

that the electrically charged partons (quarks) carry, on aggregate, less than 50%

of the proton’s energy–momentum.

Page 108: Story of QCD partons: old, recent, new

Story of QCD partons (21/54)

Hadron Jets

Gluon jetGluon → hadrons

QCD possesses N2c − 1 gauge fields — vector gluons g .

At large distances, they are supposed to “glue” quarks together.At small distances (space-time intervals) g is as legitimate a parton as q is.The first indirect evidence in favour of gluons came from DIS where it was found

that the electrically charged partons (quarks) carry, on aggregate, less than 50%

of the proton’s energy–momentum.

Now, we see a gluon emitted as a “real” particle.What sort of final hadronic state will it produce?

Page 109: Story of QCD partons: old, recent, new

Story of QCD partons (21/54)

Hadron Jets

Gluon jetGluon → hadrons

QCD possesses N2c − 1 gauge fields — vector gluons g .

At large distances, they are supposed to “glue” quarks together.At small distances (space-time intervals) g is as legitimate a parton as q is.The first indirect evidence in favour of gluons came from DIS where it was found

that the electrically charged partons (quarks) carry, on aggregate, less than 50%

of the proton’s energy–momentum.

Now, we see a gluon emitted as a “real” particle.What sort of final hadronic state will it produce?

B.Andersson, G.Gustafson & C.Peterson, Lund Univ., Sweden (1977)

Gluon ' quark-antiquark pair:3 ⊗ 3 = N2

c = 9 ' 8 = N2c − 1.

Relative mismatch : O(1/N2c ) � 1 (the large-Nc limit)

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Hadron Jets

Gluon jetGluon → hadrons

QCD possesses N2c − 1 gauge fields — vector gluons g .

At large distances, they are supposed to “glue” quarks together.At small distances (space-time intervals) g is as legitimate a parton as q is.The first indirect evidence in favour of gluons came from DIS where it was found

that the electrically charged partons (quarks) carry, on aggregate, less than 50%

of the proton’s energy–momentum.

Now, we see a gluon emitted as a “real” particle.What sort of final hadronic state will it produce?

B.Andersson, G.Gustafson & C.Peterson, Lund Univ., Sweden (1977)

Gluon ' quark-antiquark pair:3 ⊗ 3 = N2

c = 9 ' 8 = N2c − 1.

Relative mismatch : O(1/N2c ) � 1 (the large-Nc limit)

Lund model interpretation of a gluon —

Gluon – a “kink” on the “string” (colour tube)that connects the quark with the antiquark

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Hadron Jets

Gluon jetColour “drag”

Look at hadrons produced in a qq+photone+e− annihilation event.

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Hadron Jets

Gluon jetColour “drag”

PhotonLook at hadrons produced in a qq+photone+e− annihilation event.The hot-dog of hadrons that was “cylindric” inthe cms, is now lopsided [boosted string]

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Hadron Jets

Gluon jetColour “drag”

Photon

Gluon

Look at hadrons produced in a qq+photone+e− annihilation event.

Now substitute a gluon for the photon in the samekinematics.

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Hadron Jets

Gluon jetColour “drag”

Photon

Gluon

Look at hadrons produced in a qq+photone+e− annihilation event.

The gluon carries “double” colour charge;quark pair is repainted into octet colour state.

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Hadron Jets

Gluon jetColour “drag”

Photon

Gluon

Look at hadrons produced in a qq+photone+e− annihilation event.

The gluon carries “double” colour charge;quark pair is repainted into octet colour state.

Lund: hadrons = the sum of two independent(properly boosted) colorless substrings, made of

q + 12g and q + 1

2g .

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Hadron Jets

Gluon jetColour “drag”

Photon

Gluon

Look at hadrons produced in a qq+photone+e− annihilation event.

The gluon carries “double” colour charge;quark pair is repainted into octet colour state.

Lund: hadrons = the sum of two independent(properly boosted) colorless substrings, made of

q + 12g and q + 1

2g .

The first immediate consequence :

Double Multiplicity of hadronsin fragmentation of the gluon

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Hadron Jets

Gluon jetComparing hadron multiplicities

5

10

15

20

25

10 102

Ecm [GeV]

Nch

Gluon-Gluon

DELPHI: 3-Jetssym. evts.all evts.

OPAL: leading OPAL: 3-Jets

CLEO: Y DecaysTRISTAN: 3-Jets

Prediction (Eden et al.)

Quark-AntiquarkLEPPETRA

TRISTAN PEPFit (Webber et al.)

Look at experimental findings

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Hadron Jets

Gluon jetComparing hadron multiplicities

5

10

15

20

25

10 102

Ecm [GeV]

Nch

Gluon-Gluon

DELPHI: 3-Jetssym. evts.all evts.

OPAL: leading OPAL: 3-Jets

CLEO: Y DecaysTRISTAN: 3-Jets

Prediction (Eden et al.)

Quark-AntiquarkLEPPETRA

TRISTAN PEPFit (Webber et al.)

Look at experimental findings

Lessons :

N increases faster than lnE(=⇒ Feynman was wrong)

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Hadron Jets

Gluon jetComparing hadron multiplicities

5

10

15

20

25

10 102

Ecm [GeV]

Nch

Gluon-Gluon

DELPHI: 3-Jetssym. evts.all evts.

OPAL: leading OPAL: 3-Jets

CLEO: Y DecaysTRISTAN: 3-Jets

Prediction (Eden et al.)

Quark-AntiquarkLEPPETRA

TRISTAN PEPFit (Webber et al.)

Look at experimental findings

Lessons :

N increases faster than lnE(=⇒ Feynman was wrong)

Ng/Nq < 2

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Hadron Jets

Gluon jetComparing hadron multiplicities

5

10

15

20

25

10 102

Ecm [GeV]

Nch

Gluon-Gluon

DELPHI: 3-Jetssym. evts.all evts.

OPAL: leading OPAL: 3-Jets

CLEO: Y DecaysTRISTAN: 3-Jets

Prediction (Eden et al.)

Quark-AntiquarkLEPPETRA

TRISTAN PEPFit (Webber et al.)

Look at experimental findings

Lessons :

N increases faster than lnE(=⇒ Feynman was wrong)

Ng/Nq < 2 however

dNg

dNq= Nc

CF= 2N2

c

N2c−1

= 94 ' 2

(=⇒ bremsstrahlung gluons

add to the hadron yield; QCD

respecting parton cascades)

Page 121: Story of QCD partons: old, recent, new

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Hadron Jets

Gluon jetComparing hadron multiplicities

5

10

15

20

25

10 102

Ecm [GeV]

Nch

Gluon-Gluon

DELPHI: 3-Jetssym. evts.all evts.

OPAL: leading OPAL: 3-Jets

CLEO: Y DecaysTRISTAN: 3-Jets

Prediction (Eden et al.)

Quark-AntiquarkLEPPETRA

TRISTAN PEPFit (Webber et al.)

Look at experimental findings

Lessons :

N increases faster than lnE(=⇒ Feynman was wrong)

Ng/Nq < 2 however

dNg

dNq= Nc

CF= 2N2

c

N2c−1

= 94 ' 2

(=⇒ bremsstrahlung gluons

add to the hadron yield; QCD

respecting parton cascades)

Now let’s look at a more subtleconsequence of Lund wisdom

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Radiophysics of Colour

Hadrons between JetsInter-Jet QCD coherence

Lund: final hadrons are given by the sumof two independent substrings made of

q + 12g and q + 1

2g .

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Radiophysics of Colour

Hadrons between JetsInter-Jet QCD coherence

Lund: final hadrons are given by the sumof two independent substrings made of

q + 12g and q + 1

2g .

Let’s look into the inter-quark valley andcompare the hadron yield with that in theqq γ event.

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Radiophysics of Colour

Hadrons between JetsInter-Jet QCD coherence

Lund: final hadrons are given by the sumof two independent substrings made of

q + 12g and q + 1

2g .

Let’s look into the inter-quark valley andcompare the hadron yield with that in theqq γ event.The overlay results in a magnificent“String effect” — depletion of particleproduction in the qq valley !

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Radiophysics of Colour

Hadrons between JetsInter-Jet QCD coherence

Lund: final hadrons are given by the sumof two independent substrings made of

q + 12g and q + 1

2g .

Let’s look into the inter-quark valley andcompare the hadron yield with that in theqq γ event.The overlay results in a magnificent“String effect” — depletion of particleproduction in the qq valley !

Destructive interferencefrom the QCD point of view

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Radiophysics of Colour

Hadrons between JetsInter-Jet QCD coherence

QCD prediction :

dN(qqγ)qq

dN(qqg)qq

' 2(N2c − 1)

N2c − 2

=16

7

(experiment: 2.3 ± 0.2)

Lund: final hadrons are given by the sumof two independent substrings made of

q + 12g and q + 1

2g .

Let’s look into the inter-quark valley andcompare the hadron yield with that in theqq γ event.The overlay results in a magnificent“String effect” — depletion of particleproduction in the qq valley !

Destructive interferencefrom the QCD point of view

Ratios of hadron flows between jets invarious multi-jet processes — example ofnon-trivial CIS (collinear-and-infrared-safe)

QCD observable

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Radiophysics of Colour

Parton CascadesQuantum Mechanics strikes back

Rediscovery of the quantum-mechanical nature of gluon radiation playedthe major role in understanding the internal structure of jets as well.

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Radiophysics of Colour

Parton CascadesQuantum Mechanics strikes back

Rediscovery of the quantum-mechanical nature of gluon radiation playedthe major role in understanding the internal structure of jets as well.

Why “rediscovery”?

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Radiophysics of Colour

Parton CascadesQuantum Mechanics strikes back

Rediscovery of the quantum-mechanical nature of gluon radiation playedthe major role in understanding the internal structure of jets as well.

Why “rediscovery”?Because, under the spell of the probabilistic parton cascade picture,theorists managed to make serious mistakes in the late 70’s when theyindiscriminately applied it to parton multiplication in jets.

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Radiophysics of Colour

Parton CascadesQuantum Mechanics strikes back

Rediscovery of the quantum-mechanical nature of gluon radiation playedthe major role in understanding the internal structure of jets as well.

Why “rediscovery”?Because, under the spell of the probabilistic parton cascade picture,theorists managed to make serious mistakes in the late 70’s when theyindiscriminately applied it to parton multiplication in jets.

Subtlety: When gauge fields (conserved currents) are concerned,

born later (time ordering)

does not meanbeing born independently

Page 131: Story of QCD partons: old, recent, new

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Radiophysics of Colour

Parton CascadesQuantum Mechanics strikes back

Rediscovery of the quantum-mechanical nature of gluon radiation playedthe major role in understanding the internal structure of jets as well.

Why “rediscovery”?Because, under the spell of the probabilistic parton cascade picture,theorists managed to make serious mistakes in the late 70’s when theyindiscriminately applied it to parton multiplication in jets.

Subtlety: When gauge fields (conserved currents) are concerned,

born later (time ordering)

does not meanbeing born independently

=⇒Coherence in radiation

of soft gluons (photons) with x � 1— the ones that determine the bulk

of secondary parton multiplicity!

Page 132: Story of QCD partons: old, recent, new

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Radiophysics of Colour

Parton CascadesQuantum Mechanics strikes back

Rediscovery of the quantum-mechanical nature of gluon radiation playedthe major role in understanding the internal structure of jets as well.

Why “rediscovery”?Because, under the spell of the probabilistic parton cascade picture,theorists managed to make serious mistakes in the late 70’s when theyindiscriminately applied it to parton multiplication in jets.

Subtlety: When gauge fields (conserved currents) are concerned,

born later (time ordering)

does not meanbeing born independently

=⇒Coherence in radiation

of soft gluons (photons) with x � 1— the ones that determine the bulk

of secondary parton multiplicity!

Recall an amazing historical example: Cosmic ray physics (mid 50’s);

conversion of high energy photons into e+e− pairs in the emulsion

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

Photon converts into two electric charges : γ → e+e−.

e+e− track (expected)

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

Photon converts into two electric charges : γ → e+e−.

e+e− track (expected)

Why then do we see this ?

e+e− (observed)

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

Photon converts into two electric charges : γ → e+e−.

e+e− track (expected)

Why then do we see this ?

e+e− (observed)

Transverse distance between two charges(size of the e+e− dipole) is

ρ⊥ ' c t · ϑeϑ e

k

pϑp+kphoton

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

Photon converts into two electric charges : γ → e+e−.

e+e− track (expected)

Why then do we see this ?

e+e− (observed)

Transverse distance between two charges(size of the e+e− dipole) is

ρ⊥ ' c t · ϑeϑ e

k

pϑp+kphoton

The photon is emitted after the time (lifetime of the virtual p + k state)

t ' (p + k)0(p + k)2

' p0

2p0k0(1 − cos ϑ)' 1

k0ϑ2' 1

k⊥· 1

ϑ= λ⊥ · 1

ϑ

Page 138: Story of QCD partons: old, recent, new

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

Photon converts into two electric charges : γ → e+e−.

e+e− track (expected)

Why then do we see this ?

e+e− (observed)

Transverse distance between two charges(size of the e+e− dipole) is

ρ⊥ ' c t · ϑe = λ⊥ · ϑe

ϑ. Angular Ordering

ϑ < ϑe – independent radiation off e− & e+ ϑ e

k

pϑp+kphoton

The photon is emitted after the time (lifetime of the virtual p + k state)

t ' (p + k)0(p + k)2

' p0

2p0k0(1 − cos ϑ)' 1

k0ϑ2' 1

k⊥· 1

ϑ= λ⊥ · 1

ϑ

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Radiophysics of Colour

Parton CascadesChudakov effect

Charged particle leaves a track of ionized atoms in photo-emulsion.

electron track

Photon converts into two electric charges : γ → e+e−.

e+e− track (expected)

Why then do we see this ?

e+e− (observed)

Transverse distance between two charges(size of the e+e− dipole) is

ρ⊥ ' c t · ϑe = λ⊥ · ϑe

ϑ. Angular Ordering

ϑ < ϑe – independent radiation off e− & e+

ϑ > ϑe – no emission ! (ρ⊥ < λ⊥)

ϑ e

k

pϑp+kphoton

The photon is emitted after the time (lifetime of the virtual p + k state)

t ' (p + k)0(p + k)2

' p0

2p0k0(1 − cos ϑ)' 1

k0ϑ2' 1

k⊥· 1

ϑ= λ⊥ · 1

ϑ

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Radiophysics of Colour

Parton CascadesintRA-jet coherence

Angular Ordering is more restrictive than the fluctuation time ordering:

ϑ ≤ ϑe versus ϑ ≤ ϑe ·√

p0

k0that follows from (DGLAP)

tγ =p0

p2⊥

' 1

p0ϑe2

<1

k0ϑ2' k0

k2⊥

= te

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Radiophysics of Colour

Parton CascadesintRA-jet coherence

Angular Ordering is more restrictive than the fluctuation time ordering:

ϑ ≤ ϑe versus ϑ ≤ ϑe ·√

p0

k0.

Significant difference when k0/p0 = x � 1 (soft radiation).

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Radiophysics of Colour

Parton CascadesintRA-jet coherence

Angular Ordering is more restrictive than the fluctuation time ordering:

ϑ ≤ ϑe versus ϑ ≤ ϑe ·√

p0

k0.

Significant difference when k0/p0 = x � 1 (soft radiation).

Coherence in large-angle gluon emission not only affected (suppressed) totalparton multiplicity but had dramatic consequences for the structure of theenergy distribution of secondary partons in jets.

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Radiophysics of Colour

Parton CascadesintRA-jet coherence

Angular Ordering is more restrictive than the fluctuation time ordering:

ϑ ≤ ϑe versus ϑ ≤ ϑe ·√

p0

k0.

Significant difference when k0/p0 = x � 1 (soft radiation).

Coherence in large-angle gluon emission not only affected (suppressed) totalparton multiplicity but had dramatic consequences for the structure of theenergy distribution of secondary partons in jets.

It was predicted that, due to coherence, “Feynman plateau” dN/d ln xmust develop a hump at

(ln k)max =

(

1

2− c ·

αs(Q) + . . .

)

· lnQ , kmax ' Q0.35

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Radiophysics of Colour

Parton CascadesintRA-jet coherence

Angular Ordering is more restrictive than the fluctuation time ordering:

ϑ ≤ ϑe versus ϑ ≤ ϑe ·√

p0

k0.

Significant difference when k0/p0 = x � 1 (soft radiation).

Coherence in large-angle gluon emission not only affected (suppressed) totalparton multiplicity but had dramatic consequences for the structure of theenergy distribution of secondary partons in jets.

It was predicted that, due to coherence, “Feynman plateau” dN/d ln xmust develop a hump at

(ln k)max =

(

1

2− c ·

αs(Q) + . . .

)

· lnQ , kmax ' Q0.35 ,

while the softest particles (that seem to be the easiest to produce)

should not multiply at all !

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Radiophysics of Colour

Parton CascadesHump-backed plateau

First confronted withtheory in e+e− → h+X .

CDF (Tevatron)

pp → 2 jets

Charged hadron yield asa function of ln(1/x) fordifferent values of jethardness, versus (MLLA)

QCD prediction.

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Radiophysics of Colour

Parton CascadesHump-backed plateau

First confronted withtheory in e+e− → h+X .

CDF (Tevatron)

pp → 2 jets

Charged hadron yield asa function of ln(1/x) fordifferent values of jethardness, versus (MLLA)

QCD prediction.

One free parameter –overall normalization(the number of final π’sper extra gluon)

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Radiophysics of Colour

Parton CascadesHump (continued)

10 1001

2

3

4

5

CDF Data Fit:

Qeff=223 20 MeV+_

Mjj sin(�c) GeV/c2

ξ 0=

log(1

/x0)

CDF, �c =0.28

CDF, �c =0.47CDF, �c =0.36

ee Data, �c =1.57ep Data, �c =1.57

Inco

here

nt F

ragm

enta

tion

Leading Log Approximatio

n

Position of the Hump asa function ofQ = Mjj sinΘc

(hardness of the jet)

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Radiophysics of Colour

Parton CascadesHump (continued)

10 1001

2

3

4

5

CDF Data Fit:

Qeff=223 20 MeV+_

Mjj sin(�c) GeV/c2

ξ 0=

log(1

/x0)

CDF, �c =0.28

CDF, �c =0.47CDF, �c =0.36

ee Data, �c =1.57ep Data, �c =1.57

Inco

here

nt F

ragm

enta

tion

Leading Log Approximatio

n

Position of the Hump asa function ofQ = Mjj sinΘc

(hardness of the jet)

is the parameter-freeQCD prediction.

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Radiophysics of Colour

Parton CascadesHump (continued)

10 1001

2

3

4

5

CDF Data Fit:

Qeff=223 20 MeV+_

Mjj sin(�c) GeV/c2

ξ 0=

log(1

/x0)

CDF, �c =0.28

CDF, �c =0.47CDF, �c =0.36

ee Data, �c =1.57ep Data, �c =1.57

Inco

here

nt F

ragm

enta

tion

Leading Log Approximatio

n

Position of the Hump asa function ofQ = Mjj sinΘc

(hardness of the jet)

is the parameter-freeQCD prediction.

Yet another calculable –CIS – quantity.

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Radiophysics of Colour

Parton CascadesHump (continued)

10 1001

2

3

4

5

CDF Data Fit:

Qeff=223 20 MeV+_

Mjj sin(�c) GeV/c2

ξ 0=

log(1

/x0)

CDF, �c =0.28

CDF, �c =0.47CDF, �c =0.36

ee Data, �c =1.57ep Data, �c =1.57

Inco

here

nt F

ragm

enta

tion

Leading Log Approximatio

n

Position of the Hump asa function ofQ = Mjj sinΘc

(hardness of the jet)

is the parameter-freeQCD prediction.

Yet another calculable –CIS – quantity.

Mark Universality:same behaviour seenin e+e−, DIS (ep),hadron–hadron coll.

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.Should we proudly claim the victory ? I would think NOT.

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.Should we proudly claim the victory ? I would think NOT.We should rather feel puzzled than satisfied.

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.The strange thing is, these phenomena reveal themselves at present-dayexperiments via hadrons (pions) with extremely small momenta k⊥, wherewe were expecting to hit the non-perturbative domain — large couplingαs(k⊥) — and potential failure of the quark–gluon language as such.

Page 155: Story of QCD partons: old, recent, new

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.The strange thing is, these phenomena reveal themselves at present-dayexperiments via hadrons (pions) with extremely small momenta k⊥, wherewe were expecting to hit the non-perturbative domain — large couplingαs(k⊥) — and potential failure of the quark–gluon language as such.

The fact that the underlying physics of colour is being impressed upon“junky” pions with 100–300 MeV momenta, could not be a priori expected.

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.The strange thing is, these phenomena reveal themselves at present-dayexperiments via hadrons (pions) with extremely small momenta k⊥, wherewe were expecting to hit the non-perturbative domain — large couplingαs(k⊥) — and potential failure of the quark–gluon language as such.

The fact that the underlying physics of colour is being impressed upon“junky” pions with 100–300 MeV momenta, could not be a priori expected.At the same time, it sends us a powerful message: confinement –transformation of quarks and gluons into hadrons – has a non-violentnature: there is no visible reshuffling of energy–momentum at thehadronization stage.

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LPHD Soft Confinement

So, the ratios of particle flows between jets (intERjet radiophysics),as well as the shape of the inclusive energy spectra of secondary particles(intRAjet cascades) turn out to be formally calculable (CIS) quantities.Moreover, these perturbative QCD predictions actually work.The strange thing is, these phenomena reveal themselves at present-dayexperiments via hadrons (pions) with extremely small momenta k⊥, wherewe were expecting to hit the non-perturbative domain — large couplingαs(k⊥) — and potential failure of the quark–gluon language as such.

The fact that the underlying physics of colour is being impressed upon“junky” pions with 100–300 MeV momenta, could not be a priori expected.At the same time, it sends us a powerful message: confinement –transformation of quarks and gluons into hadrons – has a non-violentnature: there is no visible reshuffling of energy–momentum at thehadronization stage. Known under the name of the Local Parton-HadronDuality hypothesis (LPHD), explaining this phenomenon remainsa challenge for the future quantitative theory of colour confinement.

Page 158: Story of QCD partons: old, recent, new

Screwing Non-Perturbative QCD

with

Perturbative Tools

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Non-perturbative effects in Jets

Event ShapesEvent Shape observables

There is a specific (though not too narrow a) class of QCD observables thattaught us a thing or two about genuine non-perturbative effects inmultiple production of hadrons in hard processes. Among them — the socalled event shapes which measure global properties of final states (jetprofiles) in an inclusive manner.

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Non-perturbative effects in Jets

Event ShapesEvent Shape observables

There is a specific (though not too narrow a) class of QCD observables thattaught us a thing or two about genuine non-perturbative effects inmultiple production of hadrons in hard processes. Among them — the socalled event shapes which measure global properties of final states (jetprofiles) in an inclusive manner. In e+e−, for example, one defines

thrust T = max~n

i |~pi .~n|∑

i |~pi |,

C -param. C =3

2

i ,j |~pi ||~pj | sin2 θij

(∑

i |~pi |)2,

jet-mass ρ =

(

i∈hemisphere pi

)2

(∑

i Ei )2 , broadening BT =

i pti∑

i |~pi |.

right hemisphereleft hemisphere

~nT

Page 161: Story of QCD partons: old, recent, new

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Non-perturbative effects in Jets

Event ShapesEvent Shape observables

There is a specific (though not too narrow a) class of QCD observables thattaught us a thing or two about genuine non-perturbative effects inmultiple production of hadrons in hard processes. Among them — the socalled event shapes which measure global properties of final states (jetprofiles) in an inclusive manner. In e+e−, for example, one defines

thrust T = max~n

i |~pi .~n|∑

i |~pi |,

C -param. C =3

2

i ,j |~pi ||~pj | sin2 θij

(∑

i |~pi |)2,

jet-mass ρ =

(

i∈hemisphere pi

)2

(∑

i Ei )2 , broadening BT =

i pti∑

i |~pi |.

right hemisphereleft hemisphere

~nT

They are formally calculable in pQCD (being collinear and infrared safe)

but possess large non-perturbative 1/Q–suppressed corrections.

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Non-perturbative effects in Jets

Event Shapes1/Q Confinement effects in mean shapes

Mark JTASSODELCOMark II

JADE

AMY

DELPHI

L3

ALEPH

OPAL

SLD

GeV

⟨1−

T⟩

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 20 40 60 80 100 120 140 160 180

QMean Thrust

JADE

ALEPH

DELPHI

L3

OPAL

SLD

GeV

⟨C⟩

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100 120 140 160 180

QMean C -parameter

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Non-perturbative effects in Jets

Event Shapes1/Q Confinement effects in mean shapes

Mark JTASSODELCOMark II

JADE

AMY

DELPHI

L3

ALEPH

OPAL

SLD

GeV

⟨1−

T⟩

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 20 40 60 80 100 120 140 160 180

QMean Thrust

JADE

ALEPH

DELPHI

L3

OPAL

SLD

GeV

⟨C⟩

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100 120 140 160 180

QMean C -parameter

〈1−T 〉hadron ≈ 〈1−T 〉parton + 1 GeV/Q

〈C 〉hadron ≈ 〈C 〉parton + 4 GeV/Q

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Non-perturbative effects in Jets

Event Shapes1/Q Confinement effects in mean shapes

Mark JTASSODELCOMark II

JADE

AMY

DELPHI

L3

ALEPH

OPAL

SLD

GeV

⟨1−

T⟩

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 20 40 60 80 100 120 140 160 180

QMean Thrust

JADE

ALEPH

DELPHI

L3

OPAL

SLD

GeV

⟨C⟩

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100 120 140 160 180

QMean C -parameter

〈1−T 〉hadron ≈ 〈1−T 〉parton + 1 GeV/Q

〈C 〉hadron ≈ 〈C 〉parton + 4 GeV/Q

“p”QCDtheory

8 years old

and

running

{

4

1=⇒ 3π

2

Page 165: Story of QCD partons: old, recent, new

Story of QCD partons (34/54)

Non-perturbative effects in Jets

WDMNon-perturbative Games

The origin of power-suppressed corrections to Collinear and InfraRed Safe(CIS) observables can be linked with the mathematical property of badlyconvergent perturbative series, typical for field theories, known under thename of “renormalons”.

Page 166: Story of QCD partons: old, recent, new

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Non-perturbative effects in Jets

WDMNon-perturbative Games

The origin of power-suppressed corrections to Collinear and InfraRed Safe(CIS) observables can be linked with the mathematical property of badlyconvergent perturbative series, typical for field theories, known under thename of “renormalons”.The renormalon-based analysis is perfectly capable of controlling the ratiosof power terms, mentioned above, but can say next to nothing about theabsolute magnitude of such a correction.

Page 167: Story of QCD partons: old, recent, new

Story of QCD partons (34/54)

Non-perturbative effects in Jets

WDMNon-perturbative Games

The origin of power-suppressed corrections to Collinear and InfraRed Safe(CIS) observables can be linked with the mathematical property of badlyconvergent perturbative series, typical for field theories, known under thename of “renormalons”.The renormalon-based analysis is perfectly capable of controlling the ratiosof power terms, mentioned above, but can say next to nothing about theabsolute magnitude of such a correction.To address the latter issue, an additional hypothesis had to be invokednamely, that of the existence of an InfraRed-finite QCD coupling(whatever this might mean).

Page 168: Story of QCD partons: old, recent, new

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Non-perturbative effects in Jets

WDMNon-perturbative Games

The origin of power-suppressed corrections to Collinear and InfraRed Safe(CIS) observables can be linked with the mathematical property of badlyconvergent perturbative series, typical for field theories, known under thename of “renormalons”.The renormalon-based analysis is perfectly capable of controlling the ratiosof power terms, mentioned above, but can say next to nothing about theabsolute magnitude of such a correction.To address the latter issue, an additional hypothesis had to be invokednamely, that of the existence of an InfraRed-finite QCD coupling(whatever this might mean).

In 1996 the Wise Dispersive Methodfor quantifying non-perturbative effects in CIS observables,

and in Event Shapes in particular, has been developed.

Page 169: Story of QCD partons: old, recent, new

Story of QCD partons (34/54)

Non-perturbative effects in Jets

WDMNon-perturbative Games

The origin of power-suppressed corrections to Collinear and InfraRed Safe(CIS) observables can be linked with the mathematical property of badlyconvergent perturbative series, typical for field theories, known under thename of “renormalons”.The renormalon-based analysis is perfectly capable of controlling the ratiosof power terms, mentioned above, but can say next to nothing about theabsolute magnitude of such a correction.To address the latter issue, an additional hypothesis had to be invokednamely, that of the existence of an InfraRed-finite QCD coupling(whatever this might mean).

In 1996 the Wise Dispersive Methodfor quantifying non-perturbative effects in CIS observables,

and in Event Shapes in particular, has been developed.

Let’s have a brief NP look at these

Page 170: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δVp =2CF

π

∫ µI

0

dm

m·(

m

Q

)p

·(

αs(m2)−αPT

s (m2))

· cV

Page 171: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δVp =2CF

π

∫ µI

0

dm

m·(

m

Q

)p

·(

αs(m2)−αPT

s (m2))

· cV

PT controlled observable dependent coefficient cV ;

Page 172: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δVp =2CF

π

∫ µI

0

dm

m·(

m

Q

)p

·(

αs(m2)−αPT

s (m2))

· cV

PT controlled observable dependent coefficient cV ;sensitivity of a given observable to the IR momentum scales;

Page 173: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δV =2CF

π

∫ µI

0

dm

m· m

Q·(

αs(m2)−αPT

s (m2))

· cV

PT controlled observable dependent coefficient cV ;linear damping, p = 1, for the vast majority of event shapes;

Page 174: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δV =2CF

π

∫ µI

0

dm

m· m

Q·(

αs(m2)−αPT

s (m2))

· cV

PT controlled observable dependent coefficient cV ;linear damping, p = 1, for the vast majority of event shapes;

One subtracts off αPTs , the fixed-order perturbative expansion

of the coupling in order to avoid double counting:

Page 175: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δV =2CF

π

∫ µI

0

dm

m· m

Q·(

αs(m2)−αPT

s (m2))

· cV

PT controlled observable dependent coefficient cV ;linear damping, p = 1, for the vast majority of event shapes;

One subtracts off αPTs to avoid double counting:

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

with α0 the first moment of the coupling in the InfraRed:

α0 =1

µI

∫ µI

0dm αs(m

2), 〈αPTs 〉µI

= αs(Q2) + β0

α2s

(

ln QµI

+ Kβ0

+ 1)

Page 176: Story of QCD partons: old, recent, new

Story of QCD partons (35/54)

Non-perturbative effects in Jets

WDMNP power corrections

This “industry-standard” way of fitting event-shape power correctionsexploits the idea that the power correction is driven by the NPmodification of the QCD coupling in the InfraRed:

δV =2CF

π

∫ µI

0

dm

m· m

Q·(

αs(m2)−αPT

s (m2))

· cV

PT controlled observable dependent coefficient cV ;linear damping, p = 1, for the vast majority of event shapes;

One subtracts off αPTs to avoid double counting:

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

with α0 the first moment of the coupling in the InfraRed:

α0 =1

µI

∫ µI

0dm αs(m

2), 〈αPTs 〉µI

= αs(Q2) + β0

α2s

(

ln QµI

+ Kβ0

+ 1)

to be fitted simultaneously

Page 177: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

Page 178: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

Page 179: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

Page 180: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

Page 181: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

Page 182: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

NLO PT numbers A, B (known; no messing around)

Page 183: Story of QCD partons: old, recent, new

Story of QCD partons (36/54)

Non-perturbative effects in Jets

UniversalityUniversality hypothesis

V = Aαs + Bα2s + cV

2CF

π

µI

Q

(

α0 − 〈αPTs 〉µI

)

Thus, one has to compare next-to-leading PT + NP predictions to data,fitting for αs(Q

2) and α0 (IR-average coupling), in a hope to see that bothαs and α0 will turn out to be independent of the observable.

This Universality Hypothesis is the key ingredient of the game: the new NPparameter α0 must inherit the universal nature of the QCD coupling itself.

The power-corrections-to-event-shapes business underwent quite anevolution. Its dramatic element was laregly due to impatience ofexperimenters who were too fast to feast on theoretical predictions beforethose could possibly reach a “well-done” cooking status.

The general PT + NP equation for mean values of event shapeobservables V contains (apart from philosophy)

NLO PT numbers A, B (known; no messing around)

new (PT-obtainable) coefficients cV

Page 184: Story of QCD partons: old, recent, new

Story of QCD partons (37/54)

Non-perturbative effects in Jets

UniversalityNP effects in means and distributions

This is as far as event shape mean values 〈V〉 go, plus similar – andconsistent – results from (theoretical and experimental) DIS jet studies.

The same technology is applicable to event shape distributions, dN/dV.Here the genuine NP physics manifests itself, basically, in shifting the PTspectra, in V variable, by an amount propotional to 1/Q (D & Webber 1997)

Distributions turned out to be an important addition to the menu.

☛ Firstly, functions are more informative and revealing than numbers.

☛ Secondly, it was the studies of event shape distributions that allowedtheorists to better understand what the hell they’ve been doing, thanksto pedagogical lessons theorists were taught by those impatientcolleagues experimenters (P. Movilla Fernandez, JADE 1998)

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Story of QCD partons (37/54)

Non-perturbative effects in Jets

UniversalityNP effects in means and distributions

This is as far as event shape mean values 〈V〉 go, plus similar – andconsistent – results from (theoretical and experimental) DIS jet studies.

The same technology is applicable to event shape distributions, dN/dV.Here the genuine NP physics manifests itself, basically, in shifting the PTspectra, in V variable, by an amount propotional to 1/Q (D & Webber 1997)

Distributions turned out to be an important addition to the menu.

☛ Firstly, functions are more informative and revealing than numbers.

☛ Secondly, it was the studies of event shape distributions that allowedtheorists to better understand what the hell they’ve been doing, thanksto pedagogical lessons theorists were taught by those impatientcolleagues experimenters (P. Movilla Fernandez, JADE 1998)

Page 186: Story of QCD partons: old, recent, new

Story of QCD partons (37/54)

Non-perturbative effects in Jets

UniversalityNP effects in means and distributions

This is as far as event shape mean values 〈V〉 go, plus similar – andconsistent – results from (theoretical and experimental) DIS jet studies.

The same technology is applicable to event shape distributions, dN/dV.Here the genuine NP physics manifests itself, basically, in shifting the PTspectra, in V variable, by an amount propotional to 1/Q (D & Webber 1997)

Distributions turned out to be an important addition to the menu.

☛ Firstly, functions are more informative and revealing than numbers.

☛ Secondly, it was the studies of event shape distributions that allowedtheorists to better understand what the hell they’ve been doing, thanksto pedagogical lessons theorists were taught by those impatientcolleagues experimenters (P. Movilla Fernandez, JADE 1998)

Page 187: Story of QCD partons: old, recent, new

Story of QCD partons (37/54)

Non-perturbative effects in Jets

UniversalityNP effects in means and distributions

This is as far as event shape mean values 〈V〉 go, plus similar – andconsistent – results from (theoretical and experimental) DIS jet studies.

The same technology is applicable to event shape distributions, dN/dV.Here the genuine NP physics manifests itself, basically, in shifting the PTspectra, in V variable, by an amount propotional to 1/Q (D & Webber 1997)

Distributions turned out to be an important addition to the menu.

☛ Firstly, functions are more informative and revealing than numbers.

☛ Secondly, it was the studies of event shape distributions that allowedtheorists to better understand what the hell they’ve been doing, thanksto pedagogical lessons theorists were taught by those impatientcolleagues experimenters (P. Movilla Fernandez, JADE 1998)

Page 188: Story of QCD partons: old, recent, new

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Non-perturbative effects in Jets

UniversalityNP effects in distributions

parton level

hadron level

The Jet Broadening distribution has a rich structure exhibiting lnBQ

andlnQQ

non-perturbative corrections.

Page 189: Story of QCD partons: old, recent, new

Story of QCD partons (38/54)

Non-perturbative effects in Jets

UniversalityNP effects in distributions

parton level

hadron level

The Jet Broadening distribution has a rich structure exhibiting lnBQ

andlnQQ

non-perturbative corrections.

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Story of QCD partons (38/54)

Non-perturbative effects in Jets

UniversalityNP effects in distributions

parton level

hadron level

The Jet Broadening distribution has a rich structure exhibiting lnBQ

andlnQQ

non-perturbative corrections.

E.g., squeezing at the hadron-level (!!), uncovered by the JADE gang

Page 191: Story of QCD partons: old, recent, new

Story of QCD partons (39/54)

Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α 0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

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Story of QCD partons (40/54)

Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

Theory + Phenomenology of 1/Q effectsin event shape observables, both in e+e−

annihilation and Deep Inelastic Scatteringsystematically points at the average valueof the infrared coupling

α0 ≡ 1

2 GeV

∫ 2 GeV

0dk αs(k

2) ∼ 0.5

The value turned out to be

Universal

Reasonably small

Comfortably above the Gribov’s critical value (π · 0.137 ' 0.4)

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Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

Theory + Phenomenology of 1/Q effectsin event shape observables, both in e+e−

annihilation and Deep Inelastic Scatteringsystematically points at the average valueof the infrared coupling

α0 ≡ 1

2 GeV

∫ 2 GeV

0dk αs(k

2) ∼ 0.5

The value turned out to be

Universal

Reasonably small

Comfortably above the Gribov’s critical value (π · 0.137 ' 0.4)

Page 194: Story of QCD partons: old, recent, new

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Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

Theory + Phenomenology of 1/Q effectsin event shape observables, both in e+e−

annihilation and Deep Inelastic Scatteringsystematically points at the average valueof the infrared coupling

α0 ≡ 1

2 GeV

∫ 2 GeV

0dk αs(k

2) ∼ 0.5

The value turned out to be

Universal(as the coupling should be)

Reasonably small

Comfortably above the Gribov’s critical value (π · 0.137 ' 0.4)

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Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

Theory + Phenomenology of 1/Q effectsin event shape observables, both in e+e−

annihilation and Deep Inelastic Scatteringsystematically points at the average valueof the infrared coupling

α0 ≡ 1

2 GeV

∫ 2 GeV

0dk αs(k

2) ∼ 0.5

The value turned out to be

Universal holds to within ±15%

Reasonably small

Comfortably above the Gribov’s critical value (π · 0.137 ' 0.4)

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Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

Theory + Phenomenology of 1/Q effectsin event shape observables, both in e+e−

annihilation and Deep Inelastic Scatteringsystematically points at the average valueof the infrared coupling

α0 ≡ 1

2 GeV

∫ 2 GeV

0dk αs(k

2) ∼ 0.5

The value turned out to be

Universal holds to within ±15%

Reasonably small (which opens intriguing possibilities . . . )

Comfortably above the Gribov’s critical value (π · 0.137 ' 0.4)

Page 197: Story of QCD partons: old, recent, new

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Non-perturbative effects in Jets

UniversalityPhenomenology of the QCD coupling

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.110 0.120 0.130

α0

αs(MZ)

BW

BT

C

T

ρh

ρτtE

ρE

CE

τzE

BzE

p-scheme

e+e- mean valuesH1 distributions (Q > 30 GeV)

Theory + Phenomenology of 1/Q effectsin event shape observables, both in e+e−

annihilation and Deep Inelastic Scatteringsystematically points at the average valueof the infrared coupling

α0 ≡ 1

2 GeV

∫ 2 GeV

0dk αs(k

2) ∼ 0.5

The value turned out to be

Universal holds to within ±15%

Reasonably small

Comfortably above the Gribov’s critical value (π · 0.137 ' 0.4)

Page 198: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets,☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 199: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets,☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 200: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets,☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 201: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets,☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 202: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets,☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 203: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets,☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 204: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets, and☛ soft hadron multiplicity flows IN-BETWEEN Jets

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 205: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets, and☛ soft hadron multiplicity flows IN-BETWEEN Jets

taught us an important lesson, or rather are sending us a hint, aboutnon-violent nature of hadronization – “Soft Confinement”.

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 206: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets, and☛ soft hadron multiplicity flows IN-BETWEEN Jets

taught us an important lesson, or rather are sending us a hint, aboutnon-violent nature of hadronization – “Soft Confinement”.

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 207: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets, and☛ soft hadron multiplicity flows IN-BETWEEN Jets

taught us an important lesson, or rather are sending us a hint, aboutnon-violent nature of hadronization – “Soft Confinement”.

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory

the existence of light u and d quarks is likely to play a crucial role.

Page 208: Story of QCD partons: old, recent, new

Story of QCD partons (41/54)

Conclusions Resume

pQCD, talking quarks and gluons, did the job it has been asked toperform namely,

☛ to measure quark and gluon spins,☛ to establish SUc(3) as the true QCD gauge group (colour charges),☛ to verify Asymptotic Freedom.

Moreover, comparing theoretical predictions concerning multiplication ofpartons, with production of hadrons in jets,

☛ inclusive energy spectra of (relatively soft) hadrons INSIDE Jets, and☛ soft hadron multiplicity flows IN-BETWEEN Jets

taught us an important lesson, or rather are sending us a hint, aboutnon-violent nature of hadronization – “Soft Confinement”.

First semi-quantitative understanding of the geniune Non-Perturbativephysics of the Hard–Soft Interface has been gained.

Confinement of Colour remains a challenge for the QCD as anon-Abelian Quantum Field Theory, and

the existence of light u and d quarks is likely to play a crucial role.

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Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]

Page 210: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]

Page 211: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]

Page 212: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]To understand the essence of what we experience in hadron interactions,we need to study messier phenomena, i.e. those involving scattering offand of nuclei.

Page 213: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]To understand the essence of what we experience in hadron interactions,we need to study messier phenomena, i.e. those involving scattering offand of nuclei.

a probe for internal structure of hadron projectile: diffractionfiltering out strongly interacting components (colour transparency)

Page 214: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]To understand the essence of what we experience in hadron interactions,we need to study messier phenomena, i.e. those involving scattering offand of nuclei.

a probe for internal structure of hadron projectile: diffractionfiltering out strongly interacting components (colour transparency)

new phenomena in strong colour fields (stopping, strangeness, ...)

Page 215: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]To understand the essence of what we experience in hadron interactions,we need to study messier phenomena, i.e. those involving scattering offand of nuclei.

a probe for internal structure of hadron projectile: diffractionfiltering out strongly interacting components (colour transparency)

new phenomena in strong colour fields (stopping, strangeness, ...)

How does the vacuum break up in stronger than usual colour fields?

Page 216: Story of QCD partons: old, recent, new

Story of QCD partons (42/54)

Conclusions What is phenomenology?

Google:

Phenomenologists tend tooppose the acceptance ofunobservable matters andgrand systems erected inspeculative thinking;

[Center for advanced

research in phenomenology]

WikipediA:

Phenomenology is a current in philosophythat takes intuitive experience of phenom-ena (what presents itself to us in consciousexperience) as its starting point and tries toextract the essential features of experiencesand the essence of what we experience.

[early 20th century philosophers: Husserl,

Merleau-Ponty, Heidegger]To understand the essence of what we experience in hadron interactions,we need to study messier phenomena, i.e. those involving scattering offand of nuclei.

a probe for internal structure of hadron projectile: diffractionfiltering out strongly interacting components (colour transparency)

new phenomena in strong colour fields (stopping, strangeness, ...)

How does the vacuum break up in stronger than usual colour fields?Surprises to be expected. Mind your head.

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Conclusions QCD in the Medium

Plenty of New Interesting Phenomena in the Medium ...

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Story of QCD partons (43/54)

Conclusions QCD in the Medium

Plenty of New Interesting Phenomena in the Medium ...

Page 219: Story of QCD partons: old, recent, new

A RECENT IDEA

Page 220: Story of QCD partons: old, recent, new

A RECENT IDEA

Employ N =4 Super-Symmetrical Yang–Mills QFTto simplify QCD !

Page 221: Story of QCD partons: old, recent, new

EXTRAS

Page 222: Story of QCD partons: old, recent, new

Story of QCD partons (46/54)

Light quark confinement Coulomb instability and Hadronization

What happens with the Coulomb field when the sources move apart?

Page 223: Story of QCD partons: old, recent, new

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Light quark confinement Coulomb instability and Hadronization

What happens with the Coulomb field when the sources move apart?

Bearing in mind that virtual quarkslive in the background of gluons(zero fluctuations of A⊥ gluon fields)

Page 224: Story of QCD partons: old, recent, new

Story of QCD partons (46/54)

Light quark confinement Coulomb instability and Hadronization

What happens with the Coulomb field when the sources move apart?

u d

Colorless systems (sub) (jets)

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

��������

��������

��� ��

� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �

���

� �� �� �

� �� �� �

u dπ

Bearing in mind that virtual quarkslive in the background of gluons(zero fluctuations of A⊥ gluon fields)

what we look for is a mechanismfor binding (negative energy) vacuumquarks into colorless hadrons (positive

energy physical states of the theory)

Page 225: Story of QCD partons: old, recent, new

Story of QCD partons (46/54)

Light quark confinement Coulomb instability and Hadronization

What happens with the Coulomb field when the sources move apart?

u d

Colorless systems (sub) (jets)

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

��������

��������

��� ��

� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �

���

� �� �� �

� �� �� �

u dπ

Bearing in mind that virtual quarkslive in the background of gluons(zero fluctuations of A⊥ gluon fields)

what we look for is a mechanismfor binding (negative energy) vacuumquarks into colorless hadrons (positive

energy physical states of the theory)

V.Gribov suggested such a mechanism — the supercritical bindingof light fermions subject to a Coulomb-like interaction.

Page 226: Story of QCD partons: old, recent, new

Story of QCD partons (46/54)

Light quark confinement Coulomb instability and Hadronization

What happens with the Coulomb field when the sources move apart?

u d

Colorless systems (sub) (jets)

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

� � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � �

��������

��������

��� ��

� � � � � �� � � � � �� � � � � �

� � � � �� � � � �� � � � �� � � � �

���

� �� �� �

� �� �� �

u dπ

Bearing in mind that virtual quarkslive in the background of gluons(zero fluctuations of A⊥ gluon fields)

what we look for is a mechanismfor binding (negative energy) vacuumquarks into colorless hadrons (positive

energy physical states of the theory)

V.Gribov suggested such a mechanism — the supercritical bindingof light fermions subject to a Coulomb-like interaction. It develops whenthe coupling constant hits a definite “critical value” (Gribov 1990)

α

π>

αcrit

π= C−1

F

[

1 −√

2

3

]

' 0.137(

CF = N2c−12Nc

= 43

)

Page 227: Story of QCD partons: old, recent, new

Story of QCD partons (47/54)

Light quark confinement

InfraRed InstabilityHeritage or Handicap?

An amazing success of the relativistic theory of electron and photon fields— quantum electrodynamics (QED) — has produced a long-lastingnegative impact: it taught the generations of physicists that came into thebusiness in/after the 70’s to “not to worry”.Indeed, today one takes a lot of things for granted:

One rarely questions whether the alternative roads to constructing QFT— secondary quantization, functional integral and the Feynman diagramapproach — really lead to the same quantum theory of interacting fields

One feels ashamed to doubt an elegant powerful, but potentiallydeceiving, technology of translating the dynamics of quantum fields intothat of statistical systems

One takes the original concept of the “Dirac sea ” — the picture of thefermionic content of the vacuum — as an anachronistic model

Page 228: Story of QCD partons: old, recent, new

Story of QCD partons (47/54)

Light quark confinement

InfraRed InstabilityHeritage or Handicap?

An amazing success of the relativistic theory of electron and photon fields— quantum electrodynamics (QED) — has produced a long-lastingnegative impact: it taught the generations of physicists that came into thebusiness in/after the 70’s to “not to worry”.Indeed, today one takes a lot of things for granted:

One rarely questions whether the alternative roads to constructing QFT— secondary quantization, functional integral and the Feynman diagramapproach — really lead to the same quantum theory of interacting fields

One feels ashamed to doubt an elegant powerful, but potentiallydeceiving, technology of translating the dynamics of quantum fields intothat of statistical systems

One takes the original concept of the “Dirac sea ” — the picture of thefermionic content of the vacuum — as an anachronistic model

Page 229: Story of QCD partons: old, recent, new

Story of QCD partons (47/54)

Light quark confinement

InfraRed InstabilityHeritage or Handicap?

An amazing success of the relativistic theory of electron and photon fields— quantum electrodynamics (QED) — has produced a long-lastingnegative impact: it taught the generations of physicists that came into thebusiness in/after the 70’s to “not to worry”.Indeed, today one takes a lot of things for granted:

One rarely questions whether the alternative roads to constructing QFT— secondary quantization, functional integral and the Feynman diagramapproach — really lead to the same quantum theory of interacting fields

One feels ashamed to doubt an elegant powerful, but potentiallydeceiving, technology of translating the dynamics of quantum fields intothat of statistical systems

One takes the original concept of the “Dirac sea ” — the picture of thefermionic content of the vacuum — as an anachronistic model

Page 230: Story of QCD partons: old, recent, new

Story of QCD partons (47/54)

Light quark confinement

InfraRed InstabilityHeritage or Handicap?

An amazing success of the relativistic theory of electron and photon fields— quantum electrodynamics (QED) — has produced a long-lastingnegative impact: it taught the generations of physicists that came into thebusiness in/after the 70’s to “not to worry”.Indeed, today one takes a lot of things for granted:

One rarely questions whether the alternative roads to constructing QFT— secondary quantization, functional integral and the Feynman diagramapproach — really lead to the same quantum theory of interacting fields

One feels ashamed to doubt an elegant powerful, but potentiallydeceiving, technology of translating the dynamics of quantum fields intothat of statistical systems

One takes the original concept of the “Dirac sea ” — the picture of thefermionic content of the vacuum — as an anachronistic model

Page 231: Story of QCD partons: old, recent, new

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Light quark confinement

InfraRed InstabilityHeritage or Handicap?

An amazing success of the relativistic theory of electron and photon fields— quantum electrodynamics (QED) — has produced a long-lastingnegative impact: it taught the generations of physicists that came into thebusiness in/after the 70’s to “not to worry”.Indeed, today one takes a lot of things for granted:

One rarely questions whether the alternative roads to constructing QFT— secondary quantization, functional integral and the Feynman diagramapproach — really lead to the same quantum theory of interacting fields

One feels ashamed to doubt an elegant powerful, but potentiallydeceiving, technology of translating the dynamics of quantum fields intothat of statistical systems

One takes the original concept of the “ Dirac sea ” — the picture of thefermionic content of the vacuum — as an anachronistic model

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Light quark confinement

InfraRed InstabilityHeritage or Handicap?

An amazing success of the relativistic theory of electron and photon fields— quantum electrodynamics (QED) — has produced a long-lastingnegative impact: it taught the generations of physicists that came into thebusiness in/after the 70’s to “not to worry”.Indeed, today one takes a lot of things for granted:

One rarely questions whether the alternative roads to constructing QFT— secondary quantization, functional integral and the Feynman diagramapproach — really lead to the same quantum theory of interacting fields

One feels ashamed to doubt an elegant powerful, but potentiallydeceiving, technology of translating the dynamics of quantum fields intothat of statistical systems

One takes the original concept of the “Dirac sea ” — the picture of thefermionic content of the vacuum — as an anachronistic model

One was taught to look upon the problems that arise with field-theoreticaldescription of point-like objects and their interactions at very smalldistances (ultraviolet divergences) as purely technical: renormalize it andforget it.

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Light quark confinement

InfraRed InstabilityGribov Copies

Covariant derivative

D [A⊥] . = ∇ . + igs [A⊥ .]

The Coulomb field “propagator”

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Light quark confinement

InfraRed InstabilityGribov Copies

Covariant derivative

D [A⊥] . = ∇ . + igs [A⊥ .]

The Coulomb field “propagator” (Abelian)

G (x − y) = − 1

∇2

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Light quark confinement

InfraRed InstabilityGribov Copies

Covariant derivative

D [A⊥] . = ∇ . + igs [A⊥ .]

The Coulomb field “propagator”

G (x− y) = −⟨

1

D[A⊥] · ∇ ∇2 1

D[A⊥] · ∇

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Light quark confinement

InfraRed InstabilityGribov Copies

Covariant derivative

D [A⊥] . = ∇ . + igs [A⊥ .]

The Coulomb field “propagator”

G (x− y) = −⟨

1

D[A⊥] · ∇ ∇2 1

D[A⊥] · ∇

averageover transverse vacuum fields A⊥

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Light quark confinement

InfraRed InstabilityGribov Copies

Covariant derivative

D [A⊥] . = ∇ . + igs [A⊥ .]

The Coulomb field “propagator”

G (x− y) = −⟨

1

D[A⊥] · ∇ ∇2 1

D[A⊥] · ∇

Estimate of non-linearity :

gsA⊥/∇ ∼ gs · |A⊥| L

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Light quark confinement

InfraRed InstabilityGribov Copies

Covariant derivative

D [A⊥] . = ∇ . + igs [A⊥ .]

The Coulomb field “propagator”

G (x− y) = −⟨

1

D[A⊥] · ∇ ∇2 1

D[A⊥] · ∇

Estimate of non-linearity :

gsA⊥/∇ ∼ gs · |A⊥| L ∼ 1

Appearance of Zero Modes of the operator D[A⊥] · ∇ signals

a failure of extracting physical d.o.f. (gauge fixing);

Gribov horizon C0 (gauge fixing condition has multiple solutions);

Fundamental Domain in the functional integral over gluon fields

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Light quark confinement

THE ConfinementGribov Confinement: setting up the Problem

The question of interest isThe confinement in the real world (with 2 very light u and d quarks),rather than a confinement.

No mechanism for binding massless bosons (gluons) seems to exist inQuantum Field Theory (QFT), while the Pauli exclusion principle mayprovide means for binding together massless fermions (light quarks).

The problem of ultraviolet regularization may be more than a technicaltrick in a QFT with apparently infrared-unstable dynamics: theultraviolet and infrared regimes of the theory may be closely linked.

The Feynman diagram technique has to be reconsidered in QCD if onegoes beyond trivial perturbative correction effects.Feynman’s famous iε prescription was designed for (and applies only to)the theories with stable perturbative vacua.

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Light quark confinement

THE ConfinementGribov Confinement: setting up the Problem

The question of interest isThe confinement in the real world (with 2 very light u and d quarks),rather than a confinement.

No mechanism for binding massless bosons (gluons) seems to exist inQuantum Field Theory (QFT), while the Pauli exclusion principle mayprovide means for binding together massless fermions (light quarks).

The problem of ultraviolet regularization may be more than a technicaltrick in a QFT with apparently infrared-unstable dynamics: theultraviolet and infrared regimes of the theory may be closely linked.

The Feynman diagram technique has to be reconsidered in QCD if onegoes beyond trivial perturbative correction effects.Feynman’s famous iε prescription was designed for (and applies only to)the theories with stable perturbative vacua.

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Light quark confinement

THE ConfinementGribov Confinement: setting up the Problem

The question of interest isThe confinement in the real world (with 2 very light u and d quarks),rather than a confinement.

No mechanism for binding massless bosons (gluons) seems to exist inQuantum Field Theory (QFT), while the Pauli exclusion principle mayprovide means for binding together massless fermions (light quarks).

The problem of ultraviolet regularization may be more than a technicaltrick in a QFT with apparently infrared-unstable dynamics: theultraviolet and infrared regimes of the theory may be closely linked.

The Feynman diagram technique has to be reconsidered in QCD if onegoes beyond trivial perturbative correction effects.Feynman’s famous iε prescription was designed for (and applies only to)the theories with stable perturbative vacua.

Page 242: Story of QCD partons: old, recent, new

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Light quark confinement

THE ConfinementGribov Confinement: setting up the Problem

The question of interest isThe confinement in the real world (with 2 very light u and d quarks),rather than a confinement.

No mechanism for binding massless bosons (gluons) seems to exist inQuantum Field Theory (QFT), while the Pauli exclusion principle mayprovide means for binding together massless fermions (light quarks).

The problem of ultraviolet regularization may be more than a technicaltrick in a QFT with apparently infrared-unstable dynamics: theultraviolet and infrared regimes of the theory may be closely linked.

The Feynman diagram technique has to be reconsidered in QCD if onegoes beyond trivial perturbative correction effects.Feynman’s famous iε prescription was designed for (and applies only to)the theories with stable perturbative vacua.

Page 243: Story of QCD partons: old, recent, new

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Light quark confinement

THE ConfinementGribov Confinement: setting up the Problem

The question of interest isThe confinement in the real world (with 2 very light u and d quarks),rather than a confinement.

No mechanism for binding massless bosons (gluons) seems to exist inQuantum Field Theory (QFT), while the Pauli exclusion principle mayprovide means for binding together massless fermions (light quarks).

The problem of ultraviolet regularization may be more than a technicaltrick in a QFT with apparently infrared-unstable dynamics: theultraviolet and infrared regimes of the theory may be closely linked.

The Feynman diagram technique has to be reconsidered in QCD if onegoes beyond trivial perturbative correction effects.Feynman’s famous iε prescription was designed for (and applies only to)the theories with stable perturbative vacua.

Page 244: Story of QCD partons: old, recent, new

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Light quark confinement

THE ConfinementGribov Confinement: setting up the Problem

The question of interest isThe confinement in the real world (with 2 very light u and d quarks),rather than a confinement.

No mechanism for binding massless bosons (gluons) seems to exist inQuantum Field Theory (QFT), while the Pauli exclusion principle mayprovide means for binding together massless fermions (light quarks).

The problem of ultraviolet regularization may be more than a technicaltrick in a QFT with apparently infrared-unstable dynamics: theultraviolet and infrared regimes of the theory may be closely linked.

The Feynman diagram technique has to be reconsidered in QCD if onegoes beyond trivial perturbative correction effects.Feynman’s famous iε prescription was designed for (and applies only to)the theories with stable perturbative vacua.

To understand and describe a physical process in a confining theory, it isnecessary to take into consideration the response of the vacuum, whichleads to essential modifications of the quark and gluon Green functions.

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Light quark confinement

THE ConfinementVacuum instability and supercritical binding

QED: physical objets — electrons and photons — are in one-to-onecorrespondence with the fundamental fields that one puts into the localLagrangian of the theory.

QCD: the Vacuum changes the bare fields beyond recognition.

A known QFT example of such a violent response of the vacuum —screening of super-charged ions with Z > 137.

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Light quark confinement

THE ConfinementVacuum instability and supercritical binding

QED: physical objets — electrons and photons — are in one-to-onecorrespondence with the fundamental fields that one puts into the localLagrangian of the theory.

The role of the QED Vacuum is “trivial”: it makes αe.m. (and the electronmass operator) run, but does not affect the nature of the interacting fields.

QCD: the Vacuum changes the bare fields beyond recognition.

A known QFT example of such a violent response of the vacuum —screening of super-charged ions with Z > 137.

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Light quark confinement

THE ConfinementVacuum instability and supercritical binding

QED: physical objets — electrons and photons — are in one-to-onecorrespondence with the fundamental fields that one puts into the localLagrangian of the theory.

The role of the QED Vacuum is “trivial”: it makes αe.m. (and the electronmass operator) run, but does not affect the nature of the interacting fields.

QCD: the Vacuum changes the bare fields beyond recognition.

A known QFT example of such a violent response of the vacuum —screening of super-charged ions with Z > 137.

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Light quark confinement

THE ConfinementVacuum instability and supercritical binding

QED: physical objets — electrons and photons — are in one-to-onecorrespondence with the fundamental fields that one puts into the localLagrangian of the theory.

The role of the QED Vacuum is “trivial”: it makes αe.m. (and the electronmass operator) run, but does not affect the nature of the interacting fields.

QCD: the Vacuum changes the bare fields beyond recognition.

A known QFT example of such a violent response of the vacuum —screening of super-charged ions with Z > 137.

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Light quark confinement

THE ConfinementSupercritical binding by over-charged nuclei

The expression for Dirac energy levels of an electron in an external staticfield created by the point-like electric charge Z containsε ∝

1 − (αe.m.Z )2.For Z > 137 the energy becomes complex. This means instability.

Classically, the electron “falls onto the centre”.

Quantum-mechanically, it also “falls”, but into the Dirac sea.

In QFT the instability develops when the energy ε of an empty atomicelectron level drops, with increase of Z , below −mec

2.

An e+e− pair pops up from the vacuum, with the vacuum electronoccupying the level: the super-critically charged ion decays into an“atom” (the ion with the smaller positive charge, Z − 1) and a realpositron:

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Light quark confinement

THE ConfinementSupercritical binding by over-charged nuclei

The expression for Dirac energy levels of an electron in an external staticfield created by the point-like electric charge Z containsε ∝

1 − (αe.m.Z )2.For Z > 137 the energy becomes complex. This means instability.

Classically, the electron “falls onto the centre”.

Quantum-mechanically, it also “falls”, but into the Dirac sea.

In QFT the instability develops when the energy ε of an empty atomicelectron level drops, with increase of Z , below −mec

2.

An e+e− pair pops up from the vacuum, with the vacuum electronoccupying the level: the super-critically charged ion decays into an“atom” (the ion with the smaller positive charge, Z − 1) and a realpositron:

Page 251: Story of QCD partons: old, recent, new

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Light quark confinement

THE ConfinementSupercritical binding by over-charged nuclei

The expression for Dirac energy levels of an electron in an external staticfield created by the point-like electric charge Z containsε ∝

1 − (αe.m.Z )2.For Z > 137 the energy becomes complex. This means instability.

Classically, the electron “falls onto the centre”.

Quantum-mechanically, it also “falls”, but into the Dirac sea.

In QFT the instability develops when the energy ε of an empty atomicelectron level drops, with increase of Z , below −mec

2.

An e+e− pair pops up from the vacuum, with the vacuum electronoccupying the level: the super-critically charged ion decays into an“atom” (the ion with the smaller positive charge, Z − 1) and a realpositron:

Page 252: Story of QCD partons: old, recent, new

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Light quark confinement

THE ConfinementSupercritical binding by over-charged nuclei

The expression for Dirac energy levels of an electron in an external staticfield created by the point-like electric charge Z containsε ∝

1 − (αe.m.Z )2.For Z > 137 the energy becomes complex. This means instability.

Classically, the electron “falls onto the centre”.

Quantum-mechanically, it also “falls”, but into the Dirac sea.

In QFT the instability develops when the energy ε of an empty atomicelectron level drops, with increase of Z , below −mec

2.

An e+e− pair pops up from the vacuum, with the vacuum electronoccupying the level: the super-critically charged ion decays into an“atom” (the ion with the smaller positive charge, Z − 1) and a realpositron:

AZ =⇒ AZ−1 + e+ , for Z > Zcrit.

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Light quark confinement

THE ConfinementSupercritical binding by over-charged nuclei

The expression for Dirac energy levels of an electron in an external staticfield created by the point-like electric charge Z containsε ∝

1 − (αe.m.Z )2.For Z > 137 the energy becomes complex. This means instability.

Classically, the electron “falls onto the centre”.

Quantum-mechanically, it also “falls”, but into the Dirac sea.

In QFT the instability develops when the energy ε of an empty atomicelectron level drops, with increase of Z , below −mec

2.

An e+e− pair pops up from the vacuum, with the vacuum electronoccupying the level: the super-critically charged ion decays into an“atom” (the ion with the smaller positive charge, Z − 1) and a realpositron:

AZ =⇒ AZ−1 + e+ , for Z > Zcrit.

Thus, the ion becomes unstable and gets rid of an excessive electric chargeby emitting a positron (Pomeranchuk & Smorodinsky 1945)

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Light quark confinement

THE ConfinementBinding “massless” fermions

In the QCD context, the increase of the running quark-gluon coupling atlarge distances replaces the large Z of the QED problem.Gribov generalised the problem of supercritical binding in the field of aninfinitely heavy source to the case of two massless fermions interacting viaCoulomb-like exchange. He found that in this case the supercriticalphenomenon develops much earlier.

Namely, a pair of light fermions developssupercritical behaviour if the coupling hitsa definite critical value

α

π>

αcrit

π= 1 −

2

3.

With account of the QCD colour Casimir operator, the value of thecoupling above which restructuring of the perturbative vacuum leads tochiral symmetry breaking and, likely, to confinement, translates into

αcrit

π= C−1

F

[

1 −√

2

3

]

' 0.137(

CF = N2c−12Nc

)

= 43

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Light quark confinement

THE ConfinementBinding “massless” fermions

In the QCD context, the increase of the running quark-gluon coupling atlarge distances replaces the large Z of the QED problem.Gribov generalised the problem of supercritical binding in the field of aninfinitely heavy source to the case of two massless fermions interacting viaCoulomb-like exchange. He found that in this case the supercriticalphenomenon develops much earlier.

Namely, a pair of light fermions developssupercritical behaviour if the coupling hitsa definite critical value

α

π>

αcrit

π= 1 −

2

3.

With account of the QCD colour Casimir operator, the value of thecoupling above which restructuring of the perturbative vacuum leads tochiral symmetry breaking and, likely, to confinement, translates into

αcrit

π= C−1

F

[

1 −√

2

3

]

' 0.137(

CF = N2c−12Nc

)

= 43

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Light quark confinement

THE ConfinementBinding “massless” fermions

In the QCD context, the increase of the running quark-gluon coupling atlarge distances replaces the large Z of the QED problem.Gribov generalised the problem of supercritical binding in the field of aninfinitely heavy source to the case of two massless fermions interacting viaCoulomb-like exchange. He found that in this case the supercriticalphenomenon develops much earlier.

Namely, a pair of light fermions developssupercritical behaviour if the coupling hitsa definite critical value

α

π>

αcrit

π= 1 −

2

3.

With account of the QCD colour Casimir operator, the value of thecoupling above which restructuring of the perturbative vacuum leads tochiral symmetry breaking and, likely, to confinement, translates into

αcrit

π= C−1

F

[

1 −√

2

3

]

' 0.137(

CF = N2c−12Nc

)

= 43

Page 257: Story of QCD partons: old, recent, new

Story of QCD partons (52/54)

Light quark confinement

THE ConfinementBinding “massless” fermions

In the QCD context, the increase of the running quark-gluon coupling atlarge distances replaces the large Z of the QED problem.Gribov generalised the problem of supercritical binding in the field of aninfinitely heavy source to the case of two massless fermions interacting viaCoulomb-like exchange. He found that in this case the supercriticalphenomenon develops much earlier.

Namely, a pair of light fermions developssupercritical behaviour if the coupling hitsa definite critical value

α

π>

αcrit

π= 1 −

2

3.

With account of the QCD colour Casimir operator, the value of thecoupling above which restructuring of the perturbative vacuum leads tochiral symmetry breaking and, likely, to confinement, translates into

αcrit

π= C−1

F

[

1 −√

2

3

]

' 0.137(

CF = N2c−12Nc

)

= 43

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Light quark confinement

Open ProblemsGluon sector

In the analysis of the quark Green function, behaviour of αs was implied.

An open problem:

To construct and to analyse an equation for the gluonsimilar to that for the quark Green function. From thisanalysis a consistent picture of the coupling g(q) risingabove gcrit in the IR momentum region should emerge.

Difficulty:To learn to separate the running coupling effects from anunphysical gauge dependent phase that are both presentin the gluon Green function.

V.G. gave the solution of the problem in the Abelian theory (QED)

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Light quark confinement

Open ProblemsGluon sector

In the analysis of the quark Green function, behaviour of αs was implied.

An open problem:

To construct and to analyse an equation for the gluonsimilar to that for the quark Green function. From thisanalysis a consistent picture of the coupling g(q) risingabove gcrit in the IR momentum region should emerge.

Difficulty:To learn to separate the running coupling effects from anunphysical gauge dependent phase that are both presentin the gluon Green function.

V.G. gave the solution of the problem in the Abelian theory (QED)

Page 260: Story of QCD partons: old, recent, new

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Light quark confinement

Open ProblemsGluon sector

In the analysis of the quark Green function, behaviour of αs was implied.

An open problem:

To construct and to analyse an equation for the gluonsimilar to that for the quark Green function. From thisanalysis a consistent picture of the coupling g(q) risingabove gcrit in the IR momentum region should emerge.

Difficulty:To learn to separate the running coupling effects from anunphysical gauge dependent phase that are both presentin the gluon Green function.

V.G. gave the solution of the problem in the Abelian theory (QED)

Page 261: Story of QCD partons: old, recent, new

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Light quark confinement

Open ProblemsGluon sector

In the analysis of the quark Green function, behaviour of αs was implied.

An open problem:

To construct and to analyse an equation for the gluonsimilar to that for the quark Green function. From thisanalysis a consistent picture of the coupling g(q) risingabove gcrit in the IR momentum region should emerge.

Difficulty:To learn to separate the running coupling effects from anunphysical gauge dependent phase that are both presentin the gluon Green function.

V.G. gave the solution of the problem in the Abelian theory (QED)

Page 262: Story of QCD partons: old, recent, new

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Light quark confinement

Open ProblemsGluon sector

In the analysis of the quark Green function, behaviour of αs was implied.

An open problem:

To construct and to analyse an equation for the gluonsimilar to that for the quark Green function. From thisanalysis a consistent picture of the coupling g(q) risingabove gcrit in the IR momentum region should emerge.

Difficulty:To learn to separate the running coupling effects from anunphysical gauge dependent phase that are both presentin the gluon Green function.

V.G. gave the solution of the problem in the Abelian theory (QED)

Phasis Publishing HouseMoscow (2002)

www.prospero.hu/gribov.html

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

Page 265: Story of QCD partons: old, recent, new

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

∝ dz

z

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

Page 266: Story of QCD partons: old, recent, new

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

∝ dz

z

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

Ain’t any “catastrophe” but a simple consequence of the fact that anycharged particle is always surrounded by a long-range Coulomb field whichgets shaken off when the charge is accelerated.As a result,

wA ∼ CAαs

πln2 Q2 . [ parton multiplicities, form factors, etc. ]

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

An important remark :soft gluon radiation has a classical nature (celebrated F.Low theorem).

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Light quark confinement

Ifrared (‘soft’) SingularitiesSoft gluons

We spoke about the Collinear enhancement in 1 → 2 parton splittings.Radiation of gluons is enhanced even stronger :

dw [A → A + g(z)] ∝ CA · dz

[

2(1 − z)

z+ O(z)

]

We are facing an additional Soft (infra-red) enhancement which ischaracteristic for small-energy vector fields (photons, gluons), z � 1.

Divergence of the total emission probability at z → 0 is known (from thegood old QED times) under the catchy name of “Infra-Red catastrophe”.

An important remark :soft gluon radiation has a classical nature.

This statement has rather dramatic consequences which still remain to beproperly digested by the theoretical community . . .