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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