QCD Studies in ep Collisions - University of Wisconsin ... · Wesley Smith, U. Wisconsin SLAC...

Wesley Smith, U. Wisconsin SLAC Summer School, August, 1996

Outline: Outline:• Introduction

• HERA & ep scattering• Structure Functions

• Parton Model & Scaling Violation

• F2: Gluons, charm, total γ*P σ

• High Q2 NC & CC

• Jets• Deep Inelastic Scattering (DIS): αs

• Photoproduction

• resolved vs. direct• Diffraction

• Deep Inelastic Scattering

• structure of diffractive exchange• Photoproduction

• σ's & jets

• Vector mesons• Photoproduction & DIS

• Conclusions

QCD Studies in ep CollisionsWesley Smith, U. Wisconsin


Acknowledgements

Appreciation for the help of many people from H1 and ZEUS:

(Advice, slides, etc.)

E. Barberis, V. Boudry, J. Bulmahn,A. Caldwell, R. Cross, J. Dainton, S. Dasu,

R. Eichler, L. Feld, C. Foudas, E. Gallo,G. Grindhammer,G. Iacobucci, S. Magill,

A. Mehta, S. Mattingly, S. Nam, P. Newman, A. Quadt, D. Reeder,

J. Repond, S. Ritz, R. Sacchi,F. Sciulli, B. Surrow, S. Tapprogge,

T. Trefzger, and many others.


Collider:• √s= 300 GeV

• Equivalent to 47 TeV fixed target

Experiments:• 2 general purpose detectors (discussed):

• H1 & Zeus

• Dedicated Fixed Target (not discussed):• HERMES:

• Polarized electrons on polarized H target

• HERA-B• Proton Halo on wire target

H1

ZEUS

p

e

North Hall

South Hall

EastHall

HERMESHERA-B

WestHall

820 GeV p x 27 GeV e±

HERA


Deep Inelastic Scattering

x = the fraction of the proton's momentum carried by the struck parton

y = the fraction of the electron's energy lost in the proton rest frame

s = (k + P)2 = center of mass energy

Q2 = -q2 = -(k-k')2 = (momentum transferred)2

Q2 = sxyy = P•qP•kx = Q2

2P•q

e±(k')e±(k)

(q)xP

p(P)

The DIS process

Measuring DIS at HERA:

electron (27 GeV) proton (820 GeV)

electron

jet

proton remnant

Forward Rear

beampipe

SLAC Summer School, August, 1996Wesley Smith, U. Wisconsin

electronDIS event Q2 = 1600 GeV2

Jet


Photoproduction

photon remnant

Proton Remnant

Jet

Jet

electron goes down the

beampipe (low Q2)

photon remnant

q

q

q

q

Q2 < 4 GeV2

Almost real photon

θ > 170°

Jet

Jet

Proton RemnantProton Remnant

Direct: Resolved:

(Jet)

(Jet)

(Jet)

(Jet)(Jet)

γ γ

gg

(down beampipe)

(towards rear)

Background for DIS

SLAC Summer School, August, 1996Wesley Smith, U. Wisconsin

Photoproduction event

Calorimeter transverse

energy

Jet

Jet

Jet

φη


Major background is beam-gas interactions:Background rejection

Incoming proton

Rear CALorimeterForward

CAL.Mimics electron

Mimics current jet

reject beam gas*vertex cut*timing σt ~ 1 ns

← Cal. timing

(E - Pz) is conservedInitially:EP - PP + Ee -(-Pe) = 2Eeremains same if no energydown rear beam pipe.

True for DISFalse for photoproduction


DIS cross section

DIS differential cross section:

γ* is longitudinally or transversely polarized

F2(x,Q2) = Structure function = interaction btw. transversely polarized photons & spin 1/2 partons = charge weighted sum of the quark distributions.

FL(x,Q2) = Structure function = cross section due to longitudinally polarized photons that interact with the proton. The partons that interact have transverse momentum. (Important at high y).

F3(x,Q2) = Parity-violating structure function from Z0 exchange. (Important at high Q2).

e±(k')e±(k)

p(P)

α

α

γ∗(q)

JetJet

Y± = 1± (1− y)2

dσ NC (e± p)dxdQ2 = 2πα 2

xQ4 Y+ F2 − y2

Y+FL m

Y−

Y+xF3


Kinematic Reconstruction

2 kinematic variables• x,Q2

4 measured quantities• Ee’,θe’,Eh,γh

Any 2 measured variables can be used to reconstruct x,Q2

• Reconstruction may not be optimal.

PT method

• Best performance for full kinematic range

• Uses (Ee’,θe’,Eh,γh ), E-Pz conservation, and PT balance between the electron and current jet

E’e,θ’e

Eh,γh


Experiments - High Q2

←pe→

H1:

ZEUS:

e→ ←p


Experiments - Low Q2

+e

BPC

Zeus Beampipe Calorimeter:

H1 & Zeus Shifted Vertex:

H1 & Zeus Initial State Radiation


Experimental Kinematic Range


Proton is made up of non-interacting partons.

Bjorken scaling, i.e., Q2 independence of structure functions holds. SLAC-MIT experiments obseved approximate scaling in data.

Structure function is given by the charge weighted sum of parton momentum densities

For spin-half partons

For spin-zero partons

The parton densities fi(x) are not calculable in the model and are to be derived from experiment.

Deep inelastic scattering provides a good laboratory for parton density extraction because the electromagnetic probe is well understood.

F2 (x) = ei2xf i (x)

i∑

FL = 0

FL = F2

Parton model


α

α

αs

QCD Compton

γ∗

αsα

αγ∗

Boson-Gluon Fusion

electron

gluon

gluon

qq

q

Quark transverse momentum from quark-gluon in-teractions causes scaling violation: F2(x) →F2(x,Q2).

Splitting functions, probablities for these interac-tions, are calculated in 2nd order perturbative QCD.

These interactions drive F2(x) to grow with decreasing x:

Scaling violations

electron

10-4

10-3

10-2

10-1

1

1

2

MRSD-

MRSD0

Q 2 = 25 GeV 2Q 2 = 25 GeV 2Q 2 = 25 GeV 2

ZEUS 1993

NMC

x

F2

P

small x


Perturbative QCD

Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations describe evolution of parton densities to higher Q2

Next-to-leading order splitting functions, P, are now available.

The structure function F2 is given by,

Calculation of DIS cross section requires FL:

Parameterization of gluon density can be deter-mined by fitting QCD evolution to DIS data.

dqi (x,Q2 )

d lnQ2 = αs (Q2 )2π

dwwx

1∫ qi (w,Q2 )Pqq

xw

+ g(w,Q2 )Pqg

xw

dg(x,Q2 )d lnQ2 = αs (Q2 )

2πdwwx

1∫ qi (w,Q2 )

i∑ Pgq

xw

+ g(w,Q2 )Pgg

xw

F2 (x,Q2 ) = ei2xqi (x,Q2 )

i∑

FL (x,Q2 ) = αs (Q2 )π

dww

xw

2

x

1∫

43

F2 (w,Q2 ) + 2 ei2

i∑ 1− x

w

wg(w,Q2 )

Given an empirical parameterization for parton densities at Q2=Q0

2 ,e.g.:

xg(x) = Agxδg (1− x)

ηg (1+ γ gx)


Expected low-x behavior of F2• Regge Approach

• Donnachie-Landshoff (DL)

• Martin-Roberts-Stirling (MRS)

• Assume g(x,Q02) ~ xγ1 & F2(x,Q0

2) ~ xγ2

• Evolve in Q2 according to QCD• Gluck-Reya-Vogt (GRV)

• Use "valence-like" distributions at low Q2

• Evolve in Q2 according to QCD

• Empically produces γ << -0.08

• Balitsky-Fadin-Kuraev-Lipatov (BFKL)• Summation of many QCD graphs in

powers of ln(1/x)

since :

but at

and at low

Therefore : lim

Q2

FQ

p

Q p C W

x WQ

xp C Q X

F x Q f Q x

2

2

2

2 2 0 08

22

2 0 08

02

2 2 0 08

4

0

=

= =

= → = ′

=

−

−

→

−

πασ γ

σ γ

σ γ

( * )

: ( * ) ( )

: ( * ) ( )

( , ) ( )

.

.

.

g x Q x s( , ) ~ln( )

~ .02 12 2

0 5γ γπ

α and = − −


F2 Results Extraction:

• Bin data in x, Q2

• Subtract background

• Cross section multiplied by QCD FL

calculation using parameterizations of q(x,Q2) and G(x,Q2)

• Acceptance estimated from Monte Carlo

• F2 unfolded iteratively until MC matches data

• Estimate Systematic Error Issues:

• Does rise at low x continue?• Over what kinematic range is rise

observed?• Agreement with fixed target

experiments?

DGLAP describes down to x ~ 10-4, Q2 ~ 1.5 GeV2

No need to resum ln(1/x) terms (BFKL)

Scaling violations → Gluons

Overlap with FT: good agreement


Scaling Violation - Gluon sensitivity

0.6

0.8

1

1.2

1.4

1.6

10 102

Q2

F2

ZEUS 1994, x = 0.0016

ZEUS 1993, x = 0.0016

0.6

0.8

1

1.2

1.4

1.6

10 102

Q2

F2

ZEUS 1994, x = 0.0025

ZEUS 1993, x = 0.0027

0.8

1

1.2

1.4

1.6

1.8

6 7 8 9 10 20Q2

F2

ZEUS 1994, x = 0.0004

ZEUS 1993, x = 0.00042

0.6

0.8

1

1.2

1.4

1.6

10 102

Q2

F2

ZEUS 1994, x = 0.004

ZEUS 1993, x = 0.0047

Sensitivity to the gluon distribution is in the slope of F2 versus logQ2 plots. 1994 and 1993 ZEUS F2 data is shown above. It is seen that 94 data constrains dF2/dlogQ2 with high precision.


Example: fit to ZEUS 1994 F2 data:

• Used NMC data to constrain fit at larger values of x.

• Assumed momentum sum rule to constrain gluon density.

• Assumed quark and gluon density functional forms.

• Assumed (SLAC/BCDMS) αs(MZ2)=0.113

and evolved to higher Q2.• Evolved the distributions using GLAP

eq'ns to measured Q2 bins to calculate F2.• In computation of χ2 for agreement with

the fit only the statistical errors were included.

• Performed nonlinear minimization of χ2 to find fit parameters for assumed functional forms of quarks and gluons.

• Systematic uncertainty estimated separately by varying each of the 31 different systematic effects individually and performing a new fit.

Extraction of gluon density


Gluon results

A significant improvement in the uncertainty and in the validity range in kinematic plane is seen in the gluon density extracted from the 1994 H1 and ZEUS DIS data. Agreement with 1993 extraction is remarkable.

H1 1994

ZEUS 1994 (preliminary)

H1 1993

ZEUS 1993

NMC

by A.Quadt

NLO QCD fit Q2 = 20 GeV2

x

x g(

x)

0

5

10

15

20

25

30

35

40

45

10-4

10-3

10-2

10-1

10

5

10

15

20

25

30

35

40

45

10-4

10-3

10-2

10-1

1

δg = 0.24 ± 0.02

Momentum sum @ Q2=7 GeV2

0.555 quarks + 0.445 gluons


Impact of FL uncertainty (FL: 0 → F2) on F2 and dF2/dlnQ2

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1y

(F2H

i - F 2Lo

) / F

2Lo (

%)

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1y

|dF 2H

i - dF

2Lo| /

dF 2Lo

(%

)

Q2=5 GeV2

Q2=10

Q2=20

Q2=30

0

10

20

30

40

50

60

70

80

90

100

10-4

10-3

10-2

x

(F2H

i - F 2Lo

) / F

2Lo (

%)

Q2=5 GeV2

Q2=10

Q2=20

Q2=30

0

10

20

30

40

50

60

70

80

90

100

10-4

10-3

10-2

x

|dF 2H

i - dF

2Lo| /

dF 2Lo

(%

)

Q2=5 GeV2

Q2=10

Q2=20

Q2=30

Caveats on F2 & Gluons ZEUS F

2 extraction, as is true with most world F

2 data, involved

apriori assumptions for αs and quark-gluon parameterizations in

computing FL and F

3 corrections for DIS cross section.

The extracted F2 is sensitive to these assumptions, particularly

for high y kinematic range data, which is sensitive to the gluon. Therefore, an assumption independent analysis needs to be done by fitting directly to the cross section data.

The results of such analysis can yield consistent values for αs,

quark and gluon parameterizations.


Analyze components of F2

• Identify Flavor in the final state• Justify NLO QCD assumptions• Further understand the rise in F2

Evolution of charm from the sea:• Boson Gluon Fusion:

• Small Contribution from framentation• Higher sensitivity to gluon density

than F2

Charm F2

-c

c

P

g

k

k'

γ


Identifying open charm/D* signals

Mass(K,π)

D* → ( K π ) πS in DIS

0

10

20

30

40

50

60

1.4 1.6 1.8 2 2.2 2.4

GeV

Eve

nts

/ 20

MeV

Signal Region

Control Region

ZEUS 1994 Preliminary

Bck. Control Reg.

Bck. Side Band

Fit: Exp + Gauss

M(Do) = 1.859 ± 0.004 GeV

Delta M

0

20

40

60

80

100

135 140 145 150 155 160 165 170 175 180

MeV

Eve

nts

/ 1 M

eV Side BandsSignal Region Control Region

ZEUS 1994 Preliminary

Bck. Control Reg.

Fit: A ( x - mπ)B + Gauss

M(D*) - M(Do) = 145.57 ± 0.11 MeV


H1 Result:

QCD Studies in ep Collisions - University of Wisconsin ... · Wesley Smith, U. Wisconsin SLAC...

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Transcript of QCD Studies in ep Collisions - University of Wisconsin ... · Wesley Smith, U. Wisconsin SLAC...