Physics at HERA - DESY · D.B. MacFarlane, et al., Z. Phys. C26, 1 (1984) νN scattering. What’s...

DESY Summer Student LecturesAugust 15, 2011

1

Physics at HERA

Roman Kogler Physics at HERA

Roman Kogler (DESY)H1 collaboration

[email protected]

mailto:[email protected]

mailto:[email protected]

Part 2

2Roman Kogler Physics at HERA

A Little Bit Of QCDThe QCD Improved Quark Parton ModelParton Density FunctionsJet Production

What’s Missing?


F2

x

What happens at low x?

Is there a Q2 dependence in F2 ?

D.B. MacFarlane, et al., Z. Phys. C26, 1 (1984)

νN scattering

What’s Missing?


F2

x

What happens at low x?

Is there a Q2 dependence in F2 ?

D.B. MacFarlane, et al., Z. Phys. C26, 1 (1984)

νN scattering

Gluons and QCD!

QCD


Non-abelian gauge theory with SU(3) symmetry, describes the interaction between coloured particles (quarks and gluons).

The Feynman rules can be derived from the QCD Lagrangian

Covariant derivative: Dµ = !µ ! igsTaGaµ

Field strength tensor for spin-1 gluons:

F aµ! = !µGa

! ! !!Gaµ ! gsfabcG

bµGc

!

L = !14F a

µ!Fµ!a +

nf!

j

qj(i!µDµ !mj)qj + Lgauge + Lghost

Very similar to the QED Lagrangian, except for the additional summation over a, which are the 8 colour degree of freedoms (SU(3) instead of U(1))

Non-abelian term, different from QED. Leads to gluon self-interaction.

The QCD Lagrangian


Let’s plug the expressions for and into the Lagrangian:Dµ F aµ!

L =nf!

j

qj(i!µ"µ !mq)qj

! 14("µG!

a ! "!Gµa)("µGa

! ! "!Gaµ)

+ gsGaµ

nf!

j

qj!µTaqj

! gs

2fabc("µG!

a ! "!Gµa)Gb

µGc!

! g2s

4fabcfadeG

µb G!

cGdµGe

!

knownfrom QED

no QEDequivalent

These terms can then be used to obtain the Feynman rules for QCD

Singularities in QCD


Divergencies appear when constructing the first-order corrections to the quark-gluon interaction

leading order vacuum polarisationgraphs

vertex-correction and self energies

Known from QED: redefinition of fields and masses will remove the vertex-correction and self energy divergencies (to all orders)

Integrals are infinite, due to unconstraint loop momenta:ultra-violet (UV) divergencies

finite (?)

Renormalisation


Ultra-violet (UV) divergencies can be interpreted as virtual fluctuations on very small time scales (high energies)

Renormalisation: absorb virtual fluctuations in the definition of the bare coupling, this introduces a new scale parameter μR

μR has the dimension of energy (mass) and defines the point where the subtraction is performed (ultraviolet cut-off scheme)

energy (1/time)

More often used but less intuitive: dimensional regularisation, perform integration in 4-2ε dimensions

Renormalisation Group Equation


The dimensional parameter μR is arbitrary - no general observable Γ(pi, αs) should depend on it. (strong coupling: )

Require:

!s = g2s/4"

!µR

!

!µR+ µR

!"s

!µR

!

!"s+ #!("s)

"!(pi,"s) = 0

⇒ a change in μR has to be compensated by a change in αs

Renormalisation Group Equation (RGE)

Running coupling: αs = αs (μR)

!("s) = µR#"s

#µRThe quantity is known as the QCD beta-function

which can be computed.

QCD cannot predict the absolute value of αs (μR), but its scale dependence.

The Running Coupling


Expansion of the β-function: !("s) = !"s

!!

n=0

!n

""s

4#

#(n+1)

Where the terms βn are known up to four loops:

!0 = 11! 23nf

!1 = 102! 383

nf

!2 =2857

2! 5033

18nf +

32554

n2f

!3 =149753

6+ 3564"3 !

!1078361

162+

650827

"3

"nf

+!

50065162

+647281

"3

"n2

f +1093729

n3f

In Fact...


!as

! lnµR= !"0a

2s ! "1a

3s ! "2a

4s ! "3a

5s +O(a6

s) (as = !s/4")

T. van Ritbergen, et al., Phys. Lett. B400, 379 (1997)

evaluation of ~ 50 000 diagrams

The Running Coupling in QCD


1-loop2-loop3-loop

0 20 40 60 80 1000.10

0.15

0.20

0.25

0.30

0.35

0.40

!R !GeV"

"s#n#lo

op$

The scale dependence αs (μR) of is one of the best known quantities in QCD

Good convergence (expansion parameter as ≈ 0.01)

No visible difference between 3-loop and 4-loop solution

⇒ Possibility for stringent tests of QCD!

Asymptotically free for μR → ∞

4-loop

Another Challenge


The small values of αs (μR) at large scales allows the application of perturbation theory

But as μR → 0, αs (μR) becomes large and higher order corrections become increasingly important ⇒ diagram techniques fail for bound states in QCD

How can we calculate anything with hadrons in the initial / final state involved?

Another Challenge


The small values of αs (μR) at large scales allows the application of perturbation theory

But as μR → 0, αs (μR) becomes large and higher order corrections become increasingly important ⇒ diagram techniques fail for bound states in QCD

How can we calculate anything with hadrons in the initial / final state involved?

Answer: different time / length scales!

Timescale of proton fluctuation: t =1

!E! k2

T

2xP

Timescale of interaction: ! =1

E!=

2xP

Q2

t

!! k2

T

Q2" 1 proton is ‘frozen’ during the interaction

Factorisation


Absorb long time (small scale) effects in the proton structuree(k) e(k!)

p(P) X

!i

fi

µfμF

Hard scattering, calculable in perturbative QCD

Parton density function (PDF), Soft interactions

The factorisation scale μF gives the separation between long and short time physics

• PDFs acquire a scale dependence

• PDFs can not be predicted by QCD

Parton Evolution


q

P

small Q 2 large Q 2

Drawing from A. Pich, arXiv:hep-ph/9505231 (1995)

Intuitive picture: the number of partons changes with scale μF = Q2

The virtual photon as probe with resolving power Q2 ~ 1 / λ

many partons with large x we ‘see’ parton radiation, branchings

⇒ many partons with small x

Scaling Violations


Large x Small x

With increasing Q2, the valence quarks radiate more and more gluons, so the studied x decreases

F2 decreases with increasing Q2

Gluons split into sea quarks, which can be resolved with increasing Q2, more quarks become visible

F2 increases with increasing Q2

DGLAP Equations


It is possible to calculate the evolution of partons in QCD: DGLAP equations (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi)

!

! lnµ2F

!qi(x, µ2

F )g(x, µ2

F )

"=

"s(µR)2#

#

j

1$

x

d$

$

!Pqiqj (

x! ) Pqig(

x! )

Pgqj (x! ) Pgg(x

! )

"!qj($, µ2

F )g($, µ2

F )

"

Splitting functions Pab(x/ξ): meaning (in LO) of an emission probability:

!x

a

g!

xa

b!

xg

b

!x

g

g

P(0)

abx! P

(0)

agx! P

(0)gb

x! P

(0)gg

x!

We can predict the scale dependence of the quark q(x, μF) and gluon g(x, μF) distributions!

F2 Revisited


In the QPM we had: F2(x) = x!

i

e2i qi(x)

Now we have (MS-scheme used)

F2(x,Q2) = x!

q,q

e2q

1"

x

d!

!q(!, Q2)

#"

$1! x

!

%+

#s

2$CMS

q

$x

!

%+ . . .

&

+ x!

q,q

e2q

1"

x

d!

!g(!, Q2)

##s

2$CMS

g

$x

!

%+ . . .

&

• In leading order (LO) we get back to the QPM

• F2 obtained an explicit Q2 dependence

• In next-to-leading order (NLO) F2 is sensitive to the gluon component

(Cq and Cg are scheme-dependent coefficient functions)MS MS

µF = Q2(in DIS use )

Structure Functions and PDFs


A common misconception:

Parton Distribution Functions ≠ Structure Functions

e(k) e(k!)

p(P) XSF

Process-dependent structure functions Universal PDFs

Convolution integral

e(k) e(k!)

p(P) X

!i

fi

µf

fi p

σ

Hard partonic cross sections

(matrix elements)

F2 From HERA


H1 and ZEUS

HE

RA

In

clu

sive

Work

ing G

rou

pA

ugu

st 2

010

x = 0.00005, i=21x = 0.00008, i=20

x = 0.00013, i=19x = 0.00020, i=18

x = 0.00032, i=17

x = 0.0005, i=16

x = 0.0008, i=15

x = 0.0013, i=14

x = 0.0020, i=13

x = 0.0032, i=12

x = 0.005, i=11

x = 0.008, i=10

x = 0.013, i=9

x = 0.02, i=8

x = 0.032, i=7

x = 0.05, i=6

x = 0.08, i=5

x = 0.13, i=4

x = 0.18, i=3

x = 0.25, i=2

x = 0.40, i=1

x = 0.65, i=0

Q2/ GeV

2

!r,

NC

(x,Q

2)

x 2

i

+

HERA I+II NC e+p (prel.)

Fixed Target

HERAPDF1.5

10-3

10-2

10-1

1

10

102

103

104

105

106

107

1 10 102

103

104

105

fixed target

HERA data cover 5 orders in Q2 and 4 orders in x

Clear scaling violations at small and large x

Approximate scaling at intermediate x

DGLAP works!

Huge success of QCD

! F2(x,Q2)

!+r,NC(x,Q2) =

d2!e+pNC

dQ2dx

xQ4

2"#2Y+

F2 From H1 and ZEUS: Combination


Combination of H1 and ZEUS data

• improved statistics

• cross-calibration helps to reduce the systematic uncertainty

Scaling violations on a linear scale, some example regions

H1 and ZEUS

Q2 / GeV

2

!r,

NC

(x,Q

2)

x=0.0002x=0.002

x=0.008

x=0.032

x=0.08

x=0.25

HERA I NC e+p

ZEUS

H1

+

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 10 102

103

104

What Happens At Low x?


K. Nakamura, et al. (PDG), J. Phys. G37, 075021 (2010)

Early HERA data compared to fixed-target experiments

Strong rise of F2 towards small x, becoming steeper with increasing Q2

x

F 2(x,Q2)

H1ZEUSBCDMSNMCSLACE665

0.2

0.4

0.6

0.8

1

1.2

1.4

10 -4 10 -3 10 -2 10 -1 1

Strong Rise Of F2 Versus x


0

1

0

1

0

1

0

1

0

1

H1 and ZEUS

Q2 = 2 GeV

2

!r,

NC

(x,Q

2)

+

Q2 = 2.7 GeV

2Q

2 = 3.5 GeV

2Q

2 = 4.5 GeV

2

Q2 = 6.5 GeV

2Q

2 = 8.5 GeV

2Q

2 = 10 GeV

2Q

2 = 12 GeV

2

Q2 = 15 GeV

2Q

2 = 18 GeV

2Q

2 = 22 GeV

2Q

2 = 27 GeV

2

Q2 = 35 GeV

2Q

2 = 45 GeV

2

10-3

10-1

Q2 = 60 GeV

2

10-3

10-1

Q2 = 70 GeV

2

xH

ER

A I

ncl

usi

ve

Work

ing G

rou

pA

ugu

st 2

010

Q2 = 90 GeV

2

10-3

10-1

Q2 = 120 GeV

2

10-3

10-1

x


HERAPDF1.5

0

1

2

0

1

0

1

0

0.5

0

0.2

H1 and ZEUS

Q2 = 150 GeV

2

!r,

NC

(x,Q

2)

+

Q2 = 200 GeV

2Q

2 = 250 GeV

2Q

2 = 300 GeV

2

Q2 = 400 GeV

2Q

2 = 500 GeV

2Q

2 = 650 GeV

2Q

2 = 800 GeV

2

Q2 = 1000 GeV

2Q

2 = 1200 GeV

2Q

2 = 1500 GeV

2Q

2 = 2000 GeV

2

Q2 = 3000 GeV

2Q

2 = 5000 GeV

2Q

2 = 8000 GeV

2

10-2

10-1

Q2 = 12000 GeV

2

10-2

10-1

x

HE

RA

In

clu

sive

Work

ing G

rou

pA

ugu

st 2

010

Q2 = 20000 GeV

2

10-2

10-1

Q2 = 30000 GeV

2

10-2

10-1

x


HERAPDF1.5

Strong rise of F2 towards small x, becoming steeper with increasing Q2

Parton Distribution Functions (PDFs)


Modify the simple QPM picture, where the proton was only made up of two up and one down quark

The up- and down-quark distributions obtain contributions from the valence quarks and the virtual sea quarks

u(x) = uv(x) + us(x) d(x) = dv(x) + ds(x)and

u(x) = us(x)anti-quarks originate only from the sea

d(x) = ds(x)and

The proton consists of two up quarks and one down quark:! 1

0uv(x)dx = 2

! 1

0dv(x)dx = 1and

No a-priori expectation for the number of sea quarks and gluons.

(quark number sum rules)

Constituents Of The Proton


In general we have 10 quark and anti-quark densities and the gluon:

Distinguish only between up-type and down-type quarks:

U = u (+ c), D = d + s (+b)U = u (+ c), D = d + s (+b)

Then the valence quark distributions are

uv = U − U, dv = D − D

u, u, d, d, s, s, c, c, (b, b) , g

The total sea distribution is often expressed as

S = 2(U + D)

! 1

0

"#

i

(qi(x) + qi(x)) + g(x)$xdx = 1

and the momentum sum rule has to be fulfilled

From F2 To PDFs


QCD (DGLAP) predicts scale dependence of quark and gluon densities

x-dependence can not be calculated in perturbative QCD (reminder: renormalisation of the bare quark and gluon densities - soft, long-range effects are absorbed in the PDF)

› Parametrise qi(x), g(x) at a starting scale Q0

› Use DGLAP to evolve F2 to a higher scale ( and calculate σr(x,Q2) )› Determine the parameters from a fit to data

Need to obtain the x-dependence from experiment!

Note: Q2 has to be smaller than the lowest value of Q2 in the data0

Only limited number of free parameters possible

Use physical constraints for PDFs

A Note On Fits


Naïve definition:

Fit (in physics): ‘Minimise the difference between data and theoretical predictions by adjusting free parameters.’

Quantify the difference with a single variable: χ2(d, t(x))

!2 =!

i

(di ! ti(x))2

"2i

! 1! 1 ! 1

Obs [GeV]0 1 2 3 4 5 6

[pb]

σ

0

0.5

1

1.5

2

Obs [GeV]0 1 2 3 4 5 6

[pb]

σ

0

0.5

1

1.5

2

Obs [GeV]0 1 2 3 4 5 6

[pb]

σ

0

0.5

1

1.5

2

χ2/n.d.f χ2/n.d.f χ2/n.d.fa + sin(bx)a + bx pol. 6th order

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

HERAPDF1.5 (prel.)

exp. uncert.

model uncert.

parametrization uncert.

x

xf

2 = 2 GeV2Q

vxu

vxd

xS

xg

HE

RA

Str

uct

ure

Fu

nct

ion

s W

ork

ing G

rou

pJu

ly 2

010

H1 and ZEUS HERA I+II Combined PDF Fit

0.2

0.4

0.6

0.8

1

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

HERAPDF1.5 (prel.)

exp. uncert.

model uncert.


HERAPDF1.0

xx

f

2 = 10000 GeV2Q

vxu

vxd

xS

xg

HE

RA

Str

uct

ure

Fu

nct

ion

s W

ork

ing G

rou

pJu

ly 2

010

H1 and ZEUS HERA I +II Combined PDF Fit

0.2

0.4

0.6

0.8

1

HERAPDF


10 free parameters, about 1000 data points entered the fit, χ2/n.d.f ≈ 0.94

DGLAP

uv ≈ 2dv , gluon starts to dominate around x ~ 0.2

Disentangling uv From dv


In the extraction of PDFs, how can we distinguish between uv and dv?

Disentangling uv From dv


In the extraction of PDFs, how can we distinguish between uv and dv?

Charged Current Interactions

W− W+

e− νe

p u (c)d (s)

e+ νe

p d (s)u (c)

d2!!CC

dxdQ2=

G2F

2"

!M2

W

M2W + Q2

"2 #u(x) + c(x) + (1! y)2(d(x) + s(x))

$

d2!+CC

dxdQ2=

G2F

2"

!M2

W

M2W + Q2

"2 #u(x) + c(x) + (1! y)2(d(x) + s(x))

$

]2

[p

b/G

eV

2/d

Q!

d

-710

-510

-310

-110

10

]2

[GeV2

Q

310 410

p CC (prel.)+

H1 e

p CC (prel.)-

H1 e

p CC 06-07 (prel.)+

ZEUS e

p CC 04-06-

ZEUS e

p CC (HERAPDF 1.0)+

SM e

p CC (HERAPDF 1.0)-

SM e

p NC (prel.)+

H1 e

p NC (prel.)-

H1 e

p NC 06-07 (prel.)+

ZEUS e

p NC 05-06-

ZEUS e

p NC (HERAPDF 1.0)+

SM e

p NC (HERAPDF 1.0)-

SM e

y < 0.9

= 0eP

HERA

The NC and CC Cross Sections


e+p → νe + X cross section only half as big as e−p → νe + X

NC and CC cross sections become comparable at Q2 !M2

W ! 6500 GeV2

]2

[p

b/G

eV

2/d

Q!

d

-710

-510

-310

-110

10

]2

[GeV2

Q

310 410

p CC (prel.)+

H1 e

p CC (prel.)-

H1 e

p CC 06-07 (prel.)+

ZEUS e

p CC 04-06-

ZEUS e

p CC (HERAPDF 1.0)+

SM e

p CC (HERAPDF 1.0)-

SM e

p NC (prel.)+

H1 e

p NC (prel.)-

H1 e

p NC 06-07 (prel.)+

ZEUS e

p NC 05-06-

ZEUS e

p NC (HERAPDF 1.0)+

SM e

p NC (HERAPDF 1.0)-

SM e

y < 0.9

= 0eP

HERA

The NC and CC Cross Sections


e+p → νe + X cross section only half as big as e−p → νe + X

NC and CC cross sections become comparable at Q2 !M2

W ! 6500 GeV2

Why is there a difference in the NC cross sections for e+p

and e−p scattering?

Z0 Exchange


At Q2 ≈ MZ effects from Z0 exchange cannot be neglected anymore2

d2!±NC

dxdQ2=

2"#2

Q4x

!Y+F2(x,Q2)! Y!xF3(x,Q2)

"Y± = 1± (1! y)2( )

Parity violating structure function

e+ e+

Xp

e+ e+

Xp

Z0γ

2

d2!±NC

dxdQ2! ! 1

q2 + M2Z

! 1q2

F2(x,Q2) = F !2 ! a!Z!ZF !Z

2 + aZ!2ZFZ

2

xF3(x,Q2) = !xb!Z!ZF !Z3 + xbZ!2

ZFZ3

!Z =Q2

Q2 + M2Z

1sin2 2"W

0.2 0.4 0.60

0.2

0.4

0.6

0.8

1

HE

RA

I +

II

2 = 1500 GeV2transformed to Q Z!

3xF

x

H1 Preliminary

H1 (prel.)

HERAPDF 1.0

High Q2 NC Cross Section and xF3


H1 and ZEUS

HE

RA

In

clu

siv

e W

ork

ing

Gro

up

Au

gu

st 2

01

0

x = 0.02 (x300.0)

x = 0.032 (x170.0)

x = 0.05 (x90.0)

x = 0.08 (x50.0)

x = 0.13 (x20.0)

x = 0.18 (x8.0)

x = 0.25 (x2.4)

x = 0.40 (x0.7)

x = 0.65

Q2/ GeV

2

!r,

NC

(x,Q

2)


HERA I+II NC e-p (prel.)

HERAPDF1.5 e+p

HERAPDF1.5 e-p

!

10-2

10-1

1

10

102

103

102

103

104

105

e−p scattering:positive interference between γ and Z0

e+p scattering:negative interference

Polarisation at HERA


At the upgrade HERA has been equipped with spin rotators

Transverse polarisation builds up due to synchrotron radiation (Sokolov-Ternov effect)

Spin rotator: flips transverse → longitudinal spin before the experiments and back afterwards

Positive or negative helicity states can be achieved!

Pe =NRH !NLH

NRH + NLHBeam polarisation:



Polarisation [%] -60 -40 -20 0 20 40 60

] -1

Lu

min

os

ity

[n

b

0

2000

4000

6000

8000

10000p+e

The CC cross section depends on the longitudinal polarisation Pe:

At HERA polarisation of ~30-55% were achieved

Example of polarisation: HERA-2 running with positrons

d2!±CC(Pe)dxdQ2

= (1± Pe)d2!±CC

dxdQ2



Polarisation [%] -60 -40 -20 0 20 40 60

] -1

Lu

min

os

ity

[n

b

0

2000

4000

6000

8000

10000p+e




d2!±CC(Pe)dxdQ2

= (1± Pe)d2!±CC

dxdQ2Why?



Polarisation [%] -60 -40 -20 0 20 40 60

] -1

Lu

min

os

ity

[n

b

0

2000

4000

6000

8000

10000p+e




d2!±CC(Pe)dxdQ2

= (1± Pe)d2!±CC

dxdQ2

Jz = 0 Jz = 1 No right-handed neutrinos (left-handed anti-neutrinos) in the SM!

Why?

Polarised CC Cross Section


eP-1 -0.5 0 0.5 1

[p

b]

CC

!

0

20

40

60

80

100

120

p Scattering!HERA Charged Current e

2 > 400 GeV2Q

y < 0.9

X" #p +e

X" #p -e

HERAPDF 1.0

H1 HERA IH1 HERA II (prel.)

ZEUS 98-06

H1 HERA IH1 HERA II (prel.)

ZEUS 06-07ZEUS HERA I

eP-1 -0.5 0 0.5 1

[p

b]

CC

!

0

20

40

60

80

100

120Standard Model Expectation:

!!CC(Pe = +1) = 0

!+CC(Pe = !1) = 0

Observed (H1):

± 1.9(sys) ± 1.9(pol) pb−0.9 ± 2.9(stat)!!CC(+1) =

−3.9 ± 2.3(stat)

± 0.7(sys) ± 0.8(pol) pb

!+CC(!1) =

The Longitudinal Structure Function FL


In the QPM we found 2xF1 = F2

The longitudinal structure function FL is defined as FL = F2 ! 2xF1

FL is non-zero in the QCD improved QPM, since partons can have non-negligible PT

FL describes the scattering of longitudinally polarised photons off a proton

FL = 0⇒

The NC cross section in its most general Form:

FL is directly proportional to the gluon density: FL ! “!sq + !sg”

d2!±NC

dxdQ2=

2"#2

Q4x

!Y+F2(x,Q2)! Y!xF3(x,Q2)" y2FL(x,Q2)

"

Measurement of FL


Rewrite the NC cross section, neglecting xF3 (contributes only at high Q2)

d2!NC

dxdQ2=

2"#2

Q4x

!1 + (1! y)2

" #F2(x,Q2)! y2

1 + (1! y)2FL(x,Q2)

$

or in terms of the reduced cross section:

!r(x,Q2) = F2(x,Q2)! y2

1 + (1! y)2FL(x,Q2)

Measurement of FL



d2!NC

dxdQ2=

2"#2

Q4x

!1 + (1! y)2

" #F2(x,Q2)! y2

1 + (1! y)2FL(x,Q2)

$


!r(x,Q2) = F2(x,Q2)! y2

1 + (1! y)2FL(x,Q2) How could we measure it?

Measurement of FL



d2!NC

dxdQ2=

2"#2

Q4x

!1 + (1! y)2

" #F2(x,Q2)! y2

1 + (1! y)2FL(x,Q2)

$


!r(x,Q2) = F2(x,Q2)! y2

1 + (1! y)2FL(x,Q2) How could we measure it?

Measure σr at the same x and Q2, but at different values of y0.8

1

1.2

x=0.00012

Q2=6.5 GeV

2

!r x=0.00014 x=0.00015

H1 Collaboration

0.8

1

1.2

0 0.5 1

x=0.00017

0.5 1

x=0.00020

0.5 1

x=0.00026

y2/(1+(1-y)

2)

Ep=920 GeV

Ep=575 GeV

Ep=460 GeV

Linear fit

0.8

1

1.2

x=0.00012

Q2=6.5 GeV

2

!r x=0.00014 x=0.00015

H1 Collaboration

0.8

1

1.2

0 0.5 1

x=0.00017

0.5 1

x=0.00020

0.5 1

x=0.00026

y2/(1+(1-y)

2)

Ep=920 GeV

Ep=575 GeV

Ep=460 GeV

Linear fit

σr

Only possible with different s, since Q2 = xys

Determine FL from the slope

⇒ Measure at different beam energies!

The Longitudinal Structure Function


FL consistent with expectation from PDF fits and pQCD

-0.2

0

0.2

0.4

2 10 50

0.2

8

0.4

3

0.5

9

0.8

8

1.2

9

1.6

9

2.2

4

3.1

9

4.0

2

5.4

0

6.8

6

10

.3

14

.6

x 1

04

H1

ZEUS

HERAPDF1.0 NLO

CT10 NLO JR09 NNLO

ABKM09 NNLONNPDF2.1 NLO

MSTW08 NNLO

H1 Collaboration

Q2 / GeV

2

FL

More precise information on gluon from scaling violations

Exclusive Measurements


So far we have only looked at inclusive measurements - we measured the scattered electron and integrated over the final state XLet’s try to be a bit more exclusive and try to measure

e+p → e+ + q + g + X

We will have to consider contributions like

e+ e+

qqg g

XX

We can not measure these processes since quarks and gluons cannot be observed as free particles: we only see hadrons, leptons, photons...

We can not calculate these processes because of divergent integrals

But:

What Can We Measure?


q, gπ0 2γ

2γn0

π0

π −

KS0

π +

π +

π −

pK−

Hadronisation Particle decaysTrack

DetectorEM

CaloHADCalo

MuonChambers

What Can We Measure?


q, gπ0 2γ

2γn0

π0

π −

KS0

π +

π +

π −

pK−

Hadronisation Particle decaysTrack

DetectorEM

CaloHADCalo

MuonChambers

After the hadronisation and the detector effects it is virtually impossible to reconstruct all particles which originated from a single quark or gluon

The total deposited energy can be well measured

What Can We Calculate?


Timelike branching:

⇒ Infrared (IR) divergences

ab

c

θ

Gluon splitting on outgoing line b: p2a = EbEc(1! cos !)

Propagator 1/pa diverges when emitted gluon is soft (Eb or Ec → 0) or2

when b and c are collinear (θ → 0)

› Infrared and collinear (IRC) safe observables

Possible solutions:

› Factorisable quantities

◊ total cross sections ◊ event shape variables◊ jets

Jets


A jet algorithm combines objects (partons, hadrons, detector deposits) which are “close” together

IRC safety: Observables insensitive to soft and/or collinear emissions

Divergences from virtual contributions (loops) cancel with divergent contributions from real emissions - KLN theorem

Different choices for IRC safe jet algorithms exist, with different distance definitions (lectures from T. Schörner and G. Steinbrück)

Jets can be defined on parton, hadron and detector level - one requirement is good correspondence between these levels

= =

Jets help us to understand the underlying parton dynamics!

Jet Production In DIS

Only hard QCD processes generate considerable PT in the Breit framen-jet production in LO ∝ αsn-1

Q2

e

q

e'

p

xBj·P

q

g!·P

q

q

!·P

Boost to Breit frame,PT

only EW coupling

2xP + q = 0

∝αs

Momentum fraction of struck parton (in LO):

∝αs

! = x

!1 +

M212

Q2

"

42Roman Kogler

!!s !

!s

Physics at HERA

!njet =!!!

i=q,q,g

1"""

0

dx fi(x, µf) !i(x, "n!1s (µr), µr, µf) (1 + #had)

fi(x, µf)

!i

: PDF of parton i in proton ⇒ test universality of PDFs

: partonic cross section, calculable in pQCD up to NLO

3-jet cross sections in NLO: O(!3s)

µf = Q µr =!

(Q2 + P 2T )/2choice of scales:


Jet Production In DIS

2-jet cross sections in LO: and in NLO: O(!2s)O(!s)

(1 + !had) : hadronisation corrections, obtained from different models

or µr = !PT "

!"#$%&'()

*'+

,-.

/%0!0

12113

1213

123

3

31

12113

1213

123

3

31

31 41 51 61 71 81

12113

1213

123

3

31

!"&'()*'+

,-./

31 41 51 61 71 81

!)!3

9/:;!"5<6!#$

*'+!'='>?@!ABCD'!E=B'>+CF=+@

19

!G"HC0>

!G"IJK4*'+

,-./L4

MNO

4!

4MN

O

4!4*'+

,-./MO

4!

4!P!471!&'(4

347!P!N4

!P!711!&'(4

471!P!N

4!P!3111!&'(4

711!P!N4

!P!4111!&'(4

3111!P!N

4!P!7111!&'(4

4111!P!N4

!P!41111!&'(4

7111!P!N

9/:;Dijet Cross Sections

44Roman Kogler Jets At High Q2 and Determination of αs

Data are well described by NLO calculations over large range in Q2 and PT

Experimental uncertainty of 4-8% about half the theoretical uncertainty

Stringent test of PDFs and perturbative QCD

Measurement spans about three orders of magnitude

Trijet Cross Sections

45Roman Kogler Jets At High Q2 and Determination of αs

H1 Preliminary

Trijet Cross Section ]

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b G

eVT

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Q2

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> [GeV]T<P8 9 10 20

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H1 Preliminary

Trijet Cross Section

H1 Preliminary


]-3

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H1 Preliminary


]-3

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H1 Preliminary


]-3

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H1 Preliminary


Double-differential trijet cross section measurement at high Q2

Experimental uncertainty of 6% (low <PT>) and 15% (high <PT>)

H1 Preliminary

Trijet Cross Section ]

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eVT

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Q2

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H1 Data (prel.)0 Z⊗ h c⊗NLO

HERAPDF 1.5

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!"#$%!&'(!)#$**!+',(-$.*!-.!/0+*!!!

!1!2'3!!!!!!!!!!!!#!

45 645

5745

5748

5765

5768

!1!2'3!!!!!!!!!!!!#!

45 645

!*

5745

5748

5765

5768

6!9!455!2'36:4!;<(<!"$#!8!9!=6!>!485!2'36:4!;<(<!"$#!=

!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!

)'.(#<?!@<?A'!<.;!'BC7!A.,7

D/E!A.,7"FG'$#H

!I(G7J!K!57554L!ID/EJ!5755M5N5755OLK!57555P!I'BC7J!!Q!5744LR!*!!!!

!S<#T-@U5V5O7MRP5W6!>!485!2'36E-(!"#$%!=

αs Determination From Jets


Running of αs(μR) measured over a large range by a single experiment

μR [GeV]

αs(MZ) = 0.1168± 0.0007 (exp)

± 0.0038 (th.)

± 0.0016 (pdf)

)Z

(Msα0.11 0.12 0.13

)Z

(Msα0.11 0.12 0.13

uncertaintyexp.th.

World averageS. Bethke, Eur. Phys. J. C64, 689 (2009)

D0 incl. midpoint cone jetsPhys. Rev. D80, 111107 (2009)

Aleph Event Shapes, NNLO+NLLAJHEP 08, 036 (2009)

Aleph 3−jet rate, NNLOPhys. Rev. Lett. 104, 072002 (2010)

jets, NLOTZEUS incl. anti−kPhys. Lett. B691, 127 (2010)

jets, NLOTZEUS incl. kPhys. Lett. B 649, 12 (2007)

multijets, NLOT k2H1 low QEur. Phys. J. C67, 1 (2010)

multijets, NLOT norm. k2H1 high QEur. Phys. J. C65, 363 (2010)

H1+ZEUS NC, CC and jet QCD fits, NLOH1−prelim−11−034

trijet, NLO2H1 high QH1−prelim−11−032

dijet, NLO2H1 high QH1−prelim−11−032

inclusive jet, NLO2H1 high QH1−prelim−11−032

αs From Jet Measurements


Jets And PDF Determinations


In PDF fits the gluon is constrained through scaling violations

The gluon is always multiplied by αs, F2 = “q + !sg”

⇒ Strong correlation between gluon and value of αs

Usually one keeps the value of αs fixed in PDF determinations, then the gluon can be well constrained.

50 On the Feasibility of a QCD Analysis of Jet Production in DIS

-2 0 -2 0 -2 0 -2 0

log10

(xpdf

)

the xpdf

-range covered by the inclusive jet cross section

cross section

(arbitrary

normalization)

gluon induced total jet cross section

Q2

ET

Figure 3.6: The next-to-leading order prediction for the inclusive jet cross section. Displayed

is the total jet cross section (in arbitrary normalization) and the gluon induced contribution

as a function of the proton momentum fraction x carried by the parton in the Q2 and ET

bins of the analysis.

0

In the present work we use the next-to-leading order calculation as implemented in the

program DISENT which includes neither contributions from Z0 exchange nor the QCDmatrix elements for massive quarks. To estimate the size of these e!ects we use the leadingorder calculation as implemented in the program MEPJET and calculate the dijet cross

section for the inclusive k! algorithm with and without these e!ects.

In Fig. 3.7 we show the ratios of these calculations as a function of Q2. The e!ects from

Z0 contributions (shown on the left hand side) reduce the dijet cross section at large Q2. AtQ2 < 2500GeV2 these corrections are, however, below 2%. Integrated over the highest Q2

bin chosen in our analysis (600 < Q2 < 5000GeV2) the e!ect is already negligible.

The e!ects of quark masses in the leading order dijet cross section (shown on the righthand side) are 2.5% at Q2 = 10GeV2 and are decreasing towards higher Q2. At Q2 >

150GeV2 the e!ect is below 1.5%. Massive NLO calculations are not available for jet crosssections, but given the small size of the e!ect we consider it safe to neglect this influence.

Jets can decorrelate the gluon and αs:low Q2:

high Q2:

!jet ! “"sg”

!jet ! “"sq”

PDFs With αs(MZ) As Free Parameter


0

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HE

RA

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re F

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vxd

0.05)!xS (

0.05)!xg (

HE

RA

PD

F S

tru

ctu

re F

un

ctio

n W

ork

ing G

rou

pM

arc

h 2

011

H1 and ZEUS HERA I+II PDF Fit

0

0.2

0.4

0.6

0.8

1

No jet data With jet data

Uncertainty of gluon PDF becomes large when αs(MZ) is left free in fit

Jet data helps to decorrelate the gluon from αs during the fit

PDF Fit: χ2 Versus αs


dashed line: PDF determination with αs as free parameter, no jet data

)Z

(MS

!

0.114 0.116 0.118 0.12 0.122 0.124 0.126

min

2"

-

2"

0

5

10

15

20

H1 and ZEUS (prel.)

HERAPDF1.5f

HERAPDF1.6

HE

RA

PD

F S

tru

ctu

re F

un

cti

on

Wo

rkin

g G

rou

p M

arc

h 2

011

solid line: same as above, but including jet data in the fit

Turn the argument around: how well can we determine αs(MZ) when the gluon is left free?

αs is well constrained in a simultaneous fit

χ2 / n.d.f ≈ 1.04min

HERA Physics


The structure of the proton

QCD

Electroweak Physics

Searches for physics beyond the standard model

Diffraction

› Structure functions, parton density functions (PDFs), spin...

› Jets, αs, heavy quark production, hadron production...

› Charged current interactions, EW unification...

› SUSY, leptoquarks, contact interactions...

› Diffractive structure functions, diffractive particle production...

The structure of the photon

› γ*p scattering, photoproduction...

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Physics at HERA - DESY · D.B. MacFarlane, et al., Z. Phys. C26, 1 (1984) νN scattering. What’s...

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