Hard Processes in ep-Scattering

Hans-Christian Schultz-CoulonUniversität Dortmund

[representing the H1 and Z

EUS

Collaborations]

PIC 2003, Zeuthen, June 2003

Inclusive DIS

Jet Physics

Searches at HERA

The HERA ep-Collider

@ DESY/Hamburg

ep

HERA I

[1994 –2000]

e

+

p Scattering: L ~ 100 pb

-1

e

-

p Scattering: L ~ 15 pb

-1

HERA II

[2003++]

Int. Luminosity: 1000 pb

-1

e

±

-Polarisation ~50%

[+ low energy ep-data]

[27.6 GeV]

[920 GeV]

s 320 GeV=

Hard Process[Calculable]

Proton Structure[Parameterized]

Electron Electron

ProtonProtonRemnant

µµµµ

2

µ

2

: Scale

[defines spatial resolution ~ 1/

µ]

[should be greater

Λ

QCD

for pQCD]

Q

2

: photon virtualityE

t

2

: trans. momentum of final state part./jets

Selected Topics

I. Inclusive DIS

Proton Structure Parton Distributions

II. Jet Physics

QCD Tests,

α

s

Parton Dynamics

III. Searches

High P

t

Leptons Multi-Leptons

?

Inclusive Deep-Inelastic Scattering

Proton

Q2

x

Electron (e±) Electron (e±)

Quark

Proton Remnant

γ

Q

2

: four-momentum transferQ

2

:

[spatial resolution ~ 1/Q]

x: fractional momentum x: of the struck quark

y = Q

2

/sx: Inelasticityy =

[√s: cms energy]

d

2

σ

dxdQ

2

------------------

=

2

πα

2

xQ

4

-------------

1 1 y

–

( )

2

–

[ ]

F

2

x Q

2

,

( )

y

2

F

L

x Q

2

,

( )

–

{ }

Contribution only @ high yRelated to gluon density

[LO: F

L

=0]

Typical DIS-Event

[as seen by the H1 detector] Calorimeters

Backward

Forward

Q

2

Trackers

ϑ

Electrons

Protons

Jet

(scattered Quark)

ElectronScattered

Q

2

= 4E

e

E

e

cos

2

(ϑ/2)

’

Precision: 2-3% (bulk region)

Scaling violations at low x < 10

-2

dF

2

/dlogQ

2

~ g(x,Q

2

) .

α

s

(Q

2

)

From NLO QCD Fits:

Quark densitiesGluon densityStrong coupling constant

10-3

10-2

10-1

1

10

102

103

104

105

106

1 10 102

103

104

105

x = 0.65, i = 0

x = 0.40, i = 1

x = 0.25, i = 2

x = 0.18, i = 3

x = 0.13, i = 4

x = 0.080, i = 5

x = 0.050, i = 6

x = 0.032, i = 7

x = 0.020, i = 8

x = 0.013, i = 9

x = 0.0080, i = 10

x = 0.0050, i = 11

x = 0.0032, i = 12

x = 0.0020, i = 13

x = 0.0013, i = 14

x = 0.00080, i = 15

x = 0.00050, i = 16

x = 0.00032, i = 17

x = 0.00020, i = 18

x = 0.00013, i = 19

x = 0.000080, i = 20x = 0.000050, i = 21 H1 e+p high Q2

94-00

H1 e+p low Q2

96-97

BCDMS

NMC

H1 PDF 2000extrapolation

F

2

(x,Q

2

)

Q

2

[GeV

2

]

F2 x Q2,( ) eq2xq x Q2,( )∑=

HERA [& Fixed Target]

F2-Measurements

Determination of PDFsfitting DIS data from HERA and Fixed Target Experiments

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-3

10-2

10-1

1

ZEUS NLO QCD fitαs(MZ

2) = 0.118

tot. error

uncorr. error

Q2=10 GeV2

xuv

xdv

xg(× 0.05)

xS(× 0.05)

x

xf

CTEQ 6M

MRST2001

Procedure:

• Assume parametric formof parton distribution functions at starting scale Q0

2~O(5 GeV2). [H1: 4 GeV2; ZEUS: 7 GeV2].[# Parameters: O(10)]

• Fit all data by evolving the PDFs to higher Q2

Parametric Forms:

• xg(x) = axb(1-x)c ζ(x)• xu(x) = a’xb’(1-x)c’ ξ(x)

...e.g.: H1 → ζ(x) = 1+d +ex

ZEUS → ζ(x) = 1x

xg(x,Q2) — Comparison of Results

0

5

10

15

20

10-4

10-3

10-2

10-1

xg(x,Q2)

x

Q2=5 GeV2

Q2=20 GeV2

Q2=200 GeV2

H1 NLO-QCD fitxg=a.xb.(1-x)c.(1+d√x+ex)

FFN heavy-quark scheme

total uncert.exp. uncert.

ZEUS NLO-QCD fitxg=a.xb.(1-x)c

RT-VFN heavy-quark scheme

exp. uncert.

Independent fitsExperimental errors only

Different approachesDifferent goals[H1: g(x) & αs, Zeus: PDFs]

Parametric forms:Influence of choiceto be investigated

theoretical uncertainty

experimental uncertainty

S. Bethke: World Average [hep-ex/0211012]

J. Santiago, F.J. Yndurain [hep-ph/0102247]

ZEUS: NLO QCD fit [Phys. Rev. D 67 (2003) 012007]

H1: NLO QCD fit [Eur. Phys. J. C 21 (2001) 33]

0.1 0.12 0.14

αs(MZ)0.16 0.18

theoretical errordominated by scale uncertainty

NNLO αs from F2moment analysis based on Bernstein polynomials

systematic error includes: NNNLO correction estimate higher twist effects NNLO (and still improved precision)

promises world beating αsfrom HERA

ZEUS:αs = 0.1166 + 0.0052 - 0.0052 ± 0.004

H1:αs = 0.1150 + 0.0019 - 0.0018 ± 0.005

renorm. scaleuncertainty

exp. & modeluncertainty

[World average: 0.1183 ± 0.0027]S. Bethke: hep-ph/0211012

Determination of FL

d2σdxdQ2------------------ = 2πα2

xQ4------------- 1 1 y–( )2–[ ] F2 x Q2,( ) y2F

Lx Q2,( )–{ }

DIS cross section:

FL ~ αsg(x) → constrains xg(x)Provides important QCD test

Direct measurement requiresdata at different cms-energies

Indirect determination possible assuming F2 to be known

Contributes only @ high y

Reduced Cross Section

F2

FL ~ F2 – σrextrapolation methodalso: derivative method

shape method

FL at fixed y=0.75W2 ≈ ys

[γp cms-energy]

New low Q2 results provide additional constraints.Data in basic agreement with NLO QCD Fit to F2 data.

Direct FL-Measurementusing radiative deep-inelastic scattering data

ISR reducesep cms-energy

ElectronElectronγ

Proton

Quark

Remnant

Errors largeData prefer small FL

DIS Cross Section @ High Q2

F2 x qi qi+[ ]i

∑∼

xF3 x qi qi–[ ]i

∑∼

Neutral Current:

Proton

γ ,Z0

(W±)

e± e± (ν,ν-)

q

q

SF Remnant

d2σ e±( )

dxdQ2------------------- ξF2 ζxF3 ηy2FL–+−∼

Influenceonly @ high y

d2σ e+( ) x d u+[ ]∼

d2σ e– ( ) x u d+[ ]∼

Charged Current:

Use e+p/e–p data to extract xF3Sensitivity to valence quark density

Use e+p/e–p data to disentangleup-/down-quark content at high x

different contribution from xF3 for different lepton charge

NC and CC Cross Sections

10-7

10-5

10-3

10-1

10

103

104

H1 e+p

NC 94-00CC 94-00

H1 e–p

NC 98-99CC 98-99

√s = 319 GeV

y < 0.9

H1 PDF 2000

Q2 [GeV2]

dσ/d

Q2

[pb/

GeV2 ]

Standard Model describes cross sections over large range of Q2

Electroweak ‘unification’at large Q2 ~ MZ

2

e+p/e–p cross sections differ due to different

quark contributions

helicity structure of EW interactions

~Q-4

NC

CC

NC Reduced Cross Section

10-3

10-2

10-1

1

10

10 2

10 3

103

104

Q2 (GeV2)

σ∼ ZEUS e−p 98−99 √s=318 GeV

ZEUS e+p 96−97 √s=300 GeV

e−p ZEUS-S √s=318 GeV

e+p ZEUS-S √s=300 GeV

xF312-- ζ

1–

σ̃NC e–( ) σ̃NC e+( )–[ ]=

σ̃NC e+( ) ξF2

ζxF3

–=

σ̃NC e–( ) ξF2

ζxF3

+=

ZEUSAt high Q2: sensitivity to valence quark densities

xF̃3

˜Σ q x Q2,( ) q– x Q2,( )[ ]∼

1/(xQ4)-dependence removed

xF3 Extraction:

down to x ~ 10-2

0

0.4

0.8

1.2

0

0.4

0.8

0.1 0.2 0.3 0.4 0.5 0.6

xF3 γ Z

Data H1 PDF 2000

Q2 = 1500 GeV2

5000 GeV2

12000 GeV2

x

xF3 γ Z

transformed to Q2 = 1500 GeV2

H1

H1 PDF 2000

xF3γγγγZ

Q2 dependencecalculated to be small

Average overdifferent Q2-ranges

Valence like

Uncertainty dominated by statistical errorsNeeds more luminosity from HERA II

Jet Physics

αs

Et

ProtonStructure

Jet Physics

αs

Et

ProtonStructure

PhotonStructure

xγ[Q2 small]

Dijets in PhotoproductionThe Structure of Real Photons (Q2≈0)

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

(σ-σ

Th

eory

) /σ

Th

eory

-0.20

0.20.4

-0.20

0.20.4

0.2 0.4 0.6 0.8 1xγ

H1 dataNLO (1+δhadr)

GRVAFG

photonPDF

data: correlated uncert.

NLO: 0.5< µ f,r /ET < 2

25<ET,max<35 GeV

0

100

200

300

400

500

0.2 0.4 0.6 0.8 1xγ

H1 dataNLONLO (1+δhadr)

25 <ET,max< 35 GeV

d σ

dije

t /dx γ (

pb

)ep

• NLO describes data well• Variation due to γ-PDF small• Large scale uncertainty

Further progress with reduction of experimental and theoretical uncertainties

Inclusive γγγγp Jet Cross Section

σ jetpert α s

n Ci n, pdfi⊗i g q,=∑

n∑=

Sensitivity to αs

Sensitivity top- and γ-structure

10-3

10-2

10-1

1

10

10 2ZEUS 98-00•NLO QCDLO QCD

-1 < ηjet < 2.5 142 < Wγp < 243 GeV d

σ/d

ET jet (

pb/G

eV)

-1

-0.5

0

0.5

20 30 40 50 60 70 80 90

jet energy scale uncertainty

NLO uncertainty

ET jet (GeV)

(dat

a-N

LO

)/N

LO

Coefficient functions

Q2=0Coefficient functions:NLO calculation available

PDFs from global fits

Allows αs extractionby fitting cross section data

αs Result from Jets

0.1

0.12

0.14

0.16

0.18

0.2

20 30 40 50 60 70

Bethke 2002

from αs(MZ) = 0.1224 ± 0.0001 –0.0019+0.0022

–0.0042+0.0054

ZEUS 98-00

ET jet (GeV)

ααααs

αs(MZ) = 0.1224 + 0.0022– 0.0019

+ 0.0054– 0.0042

+ 0.0001– 0.0001

stat.

exp.

theo.

from jets @ HERABest value of αs

theoretical uncertainty

experimental uncertainty

S. Bethke: World Average [hep-ex/0211012]

ZEUS: Dijet cross sections in DIS [Phys. Lett. B 507 (2001) 70]

ZEUS: Inclusive jet cross sections in DIS [Phys. Lett. B 547 (2002) 164]

H1: Inclusive jet cross sections in DIS [Eur. Phys. J. C 19 (2001) 289]

ZEUS: NLO QCD fit [Phys. Rev. D 67 (2003) 012007]

H1: NLO QCD fit [Eur. Phys. J. C 21 (2001) 33]

ZEUS: Jet shapes in DIS [Contributed paper to ICHEP 01]

ZEUS: Subjet multiplicity in DIS [Phys. Lett. B 588 (2003) 41]

ZEUS: Inclusive jet cross sections in γp [hep-ex/0212064]

0.1 0.12 0.14

αs(MZ)0.16 0.18

0.2

0.4

0.6

10 102

103

Q2 (GeV2)

R3/2 = σ3jet / σ2jet

H1 data

QCD: LO (1+δhadr)

QCD: NLO (1+δhadr)αs(MZ) = 0.118 ±0.006

gluon: CTEQ5M1 ±15% 0.5 < (∝r /

ET) < 2

Mn-jet > 25 GeV

3-Jet/2-Jet Ratio in DIS

Small scale uncertaintySmall influence of gluon PDF

Promises precision measurement of αs

Jet PhysicsTesting perturbative QCD ...

... at large Q2

no photon structureproton PDF precisely known

Dijet and Trijet DIS Cross Section

10-3

10-2

10-1

1

10

10 2d

σ /

dQ

2 (p

b/G

eV2 )

ZEUS (prel.) 98-00 Dijets

ZEUS (prel.) 98-00 Trijets

Mn-jet > 25 GeV

NLO (1 + δhadr) : O(αs2)

NLO (1 + δhadr) : O(αs3)

Energy Scale Uncertainty

0.75

1

1.25

1.5 Dijets / NLO : O(αs2) NLO : 0.5 < (µr / E

–T) < 2

dat

a / t

heo

ry

0.8

1

1.2

1.4

1.6

102

103

dat

a / t

heo

ry

Q2 (GeV2)

Trijets / NLO : O(αs3) NLO : 0.5 < (µr / E

–T) < 2

EtBreit > 5 GeV

MJets > 25 GeV

Cross sectionwell describedby NLO

Azimuthal Asymmetry of Jets[A clean test of perturbative QCD]

0.2

0.3

0.4

50 100 1500.2

0.3

0.4 125 < Q2 < 250 GeV 2

(1/σ

) d

σ/d

|φ

B

jet |

0.2

0.3

0.4

50 100 150

250 < Q2 < 500 GeV 2

0.2

0.3

0.4

50 100 1500.2

0.3

0.4 500 < Q2 < 1000 GeV 2

0.2

0.3

0.4

50 100 150

Q2 > 1000 GeV 2

0 /2π π

|φ B jet | (rad)

0.2

0.3

0.4

50 100 1500.2

0.3

0.4 All Q2

0 /2π π

|φ B jet | (rad)

NLO QCD DISENT (µR=EB T,jet )

LO QCD DISENT (µR=EB T,jet )

ZEUS 96-97

dσdφjet

B---------- A C cos 2φjet

B( )⋅+=

Inclusive jets:

extra cosφ term only if q/g-jets are distinguished

Asymmetry predictedto decrease with rising Q2

Q2 Dependenceof azimuthal asymmetry of jets

-0.1

0.0

0.1

Asymmetry from the cos φ B jet term

LO QCD prediction (µR=EB T,jet )

NLO QCD prediction (EB T,jet /2 < µR < 2EB

T,jet )

a)ZEUS 96-97

All Q2

0.0

0.1

0.2

102

103

Asymmetry from the cos 2φ B jet term

All Q2

b)

1σ----

dσd φjet

B------------⋅ 1

π--- 1 f1 φjetB( )cos f2 2φjet

B( )cos+ +[ ]=

f1

f2

Q2 [GeV2]

NLO pQCD calculationin agreement with measurement

f1 = –0.0273 + 0.0188 – 0.0175 [Data]

f1 = –0.0003 + 0.0025 – 0.0044 [NLO]

f2 = +0.0947 + 0.0158 – 0.0195 [Data]

f2 = +0.0984 + 0.0074 – 0.0131 [NLO]

x,kt

Hard Process

Parton

Q2

Cascade

DGLAP evolution:

kt-ordering: kt,1 << ... << kt,n << Q2

Gluon density: g(x,Q2)

BFKL, CCFM evolution:

non-kt-orderingGluon density: g(x,Q2,kt)

kt ≈ 0Correct?

kt > 0possible.

QCD Dynamics

2

2

2

at low x

Azimuthal Correlationsin inclusive dijet production

InclusiveDijet selection

∆φ∗ =

Study:

NLO: max. 3 jetsi.e. ∆φ∗ > 120o → S = 0.

50∆φ∗ [Degrees]100 1500

Arb

itra

ry U

nits

S dijet events with ∆φ* 120°<all dijet events

------------------------------------------------------------------------------= NLOPrediction

More partonswith non-zero kt

jet 1jet 2∆φ∗

azimuthal angle between two most energetic jets

RAPGAP direct

[50<Q2<100 GeV2][30<Q2<50 GeV2]

[20<Q2<30 GeV2][15<Q2<20 GeV2]

[10<Q2<15 GeV2][5<Q2<10 GeV2]

RAPGAP direct+resolved

H1 Data (Preliminary)

x [× 103]10.5 2

x [× 103]10.5 2

x [× 103]0.50.2 1

x [× 103]0.50.2 1

x [× 103]1 2

x [× 103]1 23 40.5 5

0

0.1

S

S

S

0

0.1

0

0.1

0

0.1

S

S

S

0

0.1

0

0.1NLOµ2

r= E—

T*2, µ2

f=70 GeV2

(Corr. for Hadronization)

• NLO fails to describe the S-distribution[as expected due to ∆φ > 120o]

• LO Monte Carlo [RAPGAP][with kt-ordered parton emission]

- direct only: fails- dir. + res.: fails at small x

• Substantial contributionfrom partons/gluons with non-zero kt

S-Distribution[Comparison with NLO and RAPGAP]

[50<Q2<100 GeV2][30<Q2<50 GeV2]

[20<Q2<30 GeV2][15<Q2<20 GeV2]

[10<Q2<15 GeV2][5<Q2<10 GeV2]

x [× 103]10.5 2

x [× 103]10.5 2

x [× 103]0.50.2 1

x [× 103]0.50.2 1

x [× 103]1 2

x [× 103]1 23 40.5 5

CASCADE - KMR

ARIADNECASCADE - JS2001

H1 Data (Preliminary)

0

0.3S

0.2

0.1

0

0.3S

0.2

0.1

0

0.3S

0.2

0.1

0

0.3S

0.2

0.1

0

0.3S

0.2

0.1

0

0.3S

0.2

0.1

• Best description ofS-distribution by ARIADNE[non-kt-order parton emission (CDM)]

• CASCADE Monte Carlo [incorporates CCFM evolution equations]

Fails for both avail. sets ofunintegr. gluon distributions[difference: hardness of kt-spectrum]

Measurement provides

• Constraints on unintegrated gluon density

S-Distribution[Comparison with ARIADNE and CCFM]

?

Searches

Searches at HERA

Contact Interactions

Large Extra Dimensions

Compositeness

Excited Fermions

Rp-violating SUSY

Magnetic Monopoles

Odderons

Instantons

Leptoquarks

Lepton Flavour Violation

Isolated High Pt Leptons

Multi-Lepton Events

Single Top Production

Flavour Changing NC

Many limits — Excess seen in two areas

High Pt Leptonswith missing Transverse Momentum

Pt,miss = 43.5 GeV

MT(µν) = 22.6 GeV

Pt,µ = 27.7 GeV

Clear Signature!

10-2

10-1

1

10

10 2

0 20 40 60 80

PT / GeV

Eve

nts

PX / GeV

Ndata = 18NSM = 12.4±1.7

Electron

Electron

γ,Z

Quark `

Quark

Lepton

Neutrino

W

Xof high Pt Lepton

PtX Distributions

DominantSM contribution

W-Production

H1: Excess in e/µ–channelZEUS: Excess in τ–channel

H1ZEUS

Electrons & Muons Taus

High Pt Leptons at High PtX

Data/Expectation comparison

H194-00 e+p (104.7 pb-1)

Electronsobs/exp. (W)

Muonsobs/exp. (W)

Tausobs/exp. (W)

25 < PTX < 40 GeV 1 / 0.94 ± 0.14 (0.82) 3 / 0.89 ± 0.14 (0.77) —

PTX > 40 GeV 3 / 0.54 ± 0.11 (0.45) 3 / 0.55 ± 0.12 (0.51) —

ZEUS94-00 e±p (130.1 pb-1)

Electronsobs/exp. (W)

Muonsobs/exp. (W)

Tausobs/exp. (W)

PTX > 25 GeV 2 / 2.90 + 0.59

– 0.32 (45%) 5 / 2.75 + 0.21 – 0.21 (50%) 2 / 0.12 + 0.02

– 0.02 (83%)

PTX > 40 GeV 0 / 0.94 + 0.11

– 0.10 (61%) 0 / 0.95 + 0.14 – 0.10 (61%) 1 / 0.06 + 0.01

– 0.01 (83%)

Anomalous Top Production in FCNC

ZEUS

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

(hep-ex/0302010)MTOP = 170 GeVMTOP = 175 GeVMTOP = 180 GeV

Excluded by CDF(Phys Rev Lett 80 (1998) 2525)

Excluded by H1 (prel.)(Contributed paper to ICHEP02)

Excluded by L3(Phys Lett B 549 (2002) 290)

κtuγ – vtuZ exclusion region

κtcγ = vtcZ =0

κtuγ

v tuZ

• HERA e+p → etX[very sensitive to κtuγ]

• LEP e+e– → tu

• TEVATRON top decay → γq,Zq

Selection:

• 2 electrons withPt > 10 GeV (5 GeV)[with 20o < θ < 150o]

• 3rd electron (if any) with E3 > 5 GeV (10 GeV)[with 5o < θ < 175o]

Multi-Electron

Pt=63GeV

Pt=62GeV

Production

M12 = 130 GeV

Multi-Electron Event

Observation of 6 events with M12 > 100 GeV

1(2)

Multi-Electron AnalysisH1 Preliminary

0

20

40

60

0 50

2eH1 Data 115 pb-1

GRAPE

NC-DIS+Compton

E-Pz (GeV)

Eve

nts

10-2

10-1

1

10

102

0 20

2e

PT

miss (GeV)

Eve

nts

10-1

1

10

102

0 20 40

2e

PT

hadrons (GeV)

Eve

nts

0

10

20

0 50

3e

E-Pz (GeV)

Eve

nts

10-2

10-1

1

10

0 20

3e

PT

miss (GeV)

Eve

nts

10-1

1

10

0 20 40

3e

PT

hadrons (GeV)E

vent

s

Good overall description of data by MC prediction

Multi-Electron Analysis

H1 Preliminary

10-2

10-1

1

10

102

0 50 100 150

2e

H1 Data 115 pb-1

GRAPENC-DIS

+Compton

M12 (GeV)

Eve

nts

0

50

100

150

0 50 100 150 M12 (GeV)

PT

e1+P

Te2

(G

eV)

2eLMC(GRAPE)≅ 500×�LDATA

10-2

10-1

1

10

0 50 100 150

3e

M12 (GeV)

Eve

nts

0

50

100

150

0 50 100 150 M12 (GeV)

PT

e1+P

Te2

(G

eV)

3e LMC(GRAPE)≅ 500×�LDATA

Excess @ high Mee>100 GeV

M12 > 100 GeV H1 Prel.Data SM

2e 3 0.25±0.05

3e 3 0.23±0.04

M12 > 100 GeV ZEUS Prel.Data SM

2e 2 0.77±0.08

3e 0 0.37±0.04

Needs confirmationwith HERA II data

Summary

Proton StructureImproved precision — F2 error ~2-3% (bulk)

PDF extraction — extraction of xF3 FL measurements provide important QCD test.

QCD Tests and αs-Measurementsαs results competative — NNLO DIS promises world beating αs

pQCD tests using azimuthal jet asymmetries

QCD DynamicsStudy of azimuthal jet separation

provides constraint on unintegrated gluon distributions

Searches at HERAExcess seen for: Isolated leptons, multi-leptons