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Year: 2010

Precision measurements with jets and particles at HERA

Müller, K

http://dx.doi.org/10.1016/j.nuclphysbps.2010.10.004.Postprint available at:http://www.zora.uzh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.http://www.zora.uzh.ch

Originally published at:Müller, K (2010). Precision measurements with jets and particles at HERA. Nuclear Physics B -Proceedings Supplements, 207-8:17-20.

http://dx.doi.org/10.1016/j.nuclphysbps.2010.10.004.Postprint available at:http://www.zora.uzh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.http://www.zora.uzh.ch

Originally published at:Müller, K (2010). Precision measurements with jets and particles at HERA. Nuclear Physics B -Proceedings Supplements, 207-8:17-20.

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Precision measurements with jets and particles at HERA

Katharina Mulleron behalf of the H1 and ZEUS Collaborationsa,∗

aPhysikinstitut der Universitat Zurich, Winterthurerstrasse 190, CH - 8057 Zurich, Switzerland.

Abstract

Inclusive jet and multijet cross sections measured inepcollisions in different kinematic regions by the H1 and ZEUSexperiments are shown. The measurements are used to extractthe strong couplingαs as a function of the scale and atthe mass of theZ-boson. Results from prompt photon production in comparison with pQCD calculations are shownin photoproduction and deep-inelastic scattering. Other topics address scaled momentum distributions of chargedparticles, a measurement of the transverse momenta of charged particles and the first measurement of the chargeasymmetry at HERA.

Keywords: Jets,αs, fragmentation, prompt photons, parton dynamics, charge asymmetry

1. Introduction

The HERA ep-collider operated with electrons orpositrons of energy 27.6 GeV and protons of 920 GeV.Each of the two experiments H1 and ZEUS collectedroughly 0.5 fb−1 in fifteen years of running. At HERA,two kinematic regimes are distinguished, deep-inelasticscattering (DIS) with high photon virtualities,Q2

≥

5 GeV2, and photoproduction (γp) with a quasi realphoton,Q2

≃0 GeV2, which is the dominating process.The large statistics of the HERA data allows detailedtests of perturbative QCD (pQCD) based on cross sec-tion measurements with jets or prompt photons. In DISthere are two relevant hard scales,Q and the transversemomentumPT of the jet or the photon, while inγp thereis only PT . Jet measurements in DIS are carried outin the Breit frame. ThekT cluster algorithm, which iscollinear and infrared safe, is used to reconstruct jets.

2. Jet production

Jet production inepscattering provides stringent testsof QCD and an independent assessment of the gluoncontribution to the parton density functions (PDFs). Itfurther allows the extraction of the strong couplingαs asa function of the scale and at the mass of theZ-boson.

∗SpeakerEmail address:kmueller@physik.uzh.ch (Katharina Muller

on behalf of the H1 and ZEUS Collaborations )

In five recent analyses jet production was measuredat HERA in various kinematic regions. ZEUS measuredthe inclusive jet cross section inγp [1] (Q2 < 1 GeV2,PT, jet>17 GeV ) and highQ2 DIS [2] (Q2>125 GeV2,PT, jet> 8 GeV). Both analyses provide a determinationof αs, furthermore the 2-jet cross section is measuredfor the highQ2 [3] region (125< Q2 < 20000 GeV2,PT, jet> 8 GeV). Here the invariant mass of the two jetsis required to beM j, j >20 GeV. The 2-jet cross sectionhas a high sensitivity to the gluon contribution of thePDFs in kinematic regions where its uncertainty is con-tributing significantly to the theoretical error. H1 mea-sured inclusive, 2-jet and 3-jet cross sections as well asthe ratio of the 2-jet to 3-jet cross sections for low [4](5 < Q2 < 100 GeV2, 5 < PT, jet < 80 GeV, M j, j >

18 GeV) and highQ2 [5] (150 < Q2 < 15000 GeV2,7< PT, jet < 50 GeV,M j, j > 16 GeV). For the latter thejet cross sections are normalised to the inclusive DIScross section, which significantly reduces the experi-mental and theoretical errors.

Fig. 1 shows the inclusive jet cross section as a func-tion of the transverse energy of the jet for the ZEUSmeasurement inγp and highQ2 DIS. For both kine-matic regions the cross section falls steeply. The dataare very precise, the dominant experimental error beingthe uncertainty of the energy scale of the jets, which is1(3)% for jet energies above (below) 10 GeV. The mea-surement is compared to NLO QCD predictions whichdescribe the measurement very well. The theoreticaland experimental errors are of comparable size. The

Preprint submitted to Nuc. Phys. (Proc. Suppl.) September 7, 2010

theoretical errors are dominated by the renormalisationscale uncertainty.

ZEUS

10-3

10-2

10-1

1

10

10 2ZEUS (prel.) 189 pb-1

NLO (GRV-HO)

-1 < η jet < 2.5

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jet energy scale uncertainty

theoretical uncertainty

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dEje

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GeV

)

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NLO hadr Z0⊗ ⊗

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|cos γh| < 0.65

jet energy scale uncertainty

theoretical uncertainty

dσ/

dEje

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,B (

pb/G

eV)

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-0.2

0

0.2

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5 10 15 20 25 30 35 40 45 50 55 Ejet

T,B (GeV)

rel.

diff

. to

NL

O

Figure 1:Differential cross section for inclusive jet production in photoproduc-tion (left) with Q2<1 GeV2 and NC DIS (right) with (125<Q2<20000 GeV2).Jets are found with the longitudinally inclusivekT -algorithm in the Breit frame.

Similar results are obtained for multijet cross sec-tions. Overall the description by the NLO calculationsis very good in all kinematic regions, though the lowQ2

analysis suffers from large theoretical uncertainties ofup to 30%.

2.1. Extraction of runningαs andαs(MZ)

The jet cross sections discussed above are used toextract the strong couplingαs at different values ofthe renormalisation scaleµr and at theZ-boson mass.Statistical, systematic and correlated uncertainties aretaken into account. The dominant theory uncertainty isestimated by varying the renormalisation and factorisa-tion scales by a factor 0.5 and 2. The running ofαs as afunction of the renormalisation scale is shown in Fig. 2.The values are extracted from the H1 data at low andhigh Q2, similar results exist from ZEUS. In the lowQ2 region the values and experimental uncertainties arefound to be in good agreement with the QCD expecta-tion which is based on the extracted value ofαs(MZ) ofthe highQ2 measurement.

Fig. 3 shows a summary of recentαs measurementsusing jets at HERA together with the most precise deter-mination ofαs from LEP [6] and from TEVATRON [7].All measurements are in good agreement with eachother in different kinematic regions (γp, low and highQ2) and with the world average. Further measurementsusing different jet algorithms (anti-kT and SISCone [8])lead to similar results. For many of the precise HERAresults the theoretical uncertainties dominate the error.Higher order calculations are expected to improve theresults.

from Jet Cross Sections in DISsα

/ GeV r

µ10 210

0.10

0.15

0.20

0.25

/ GeV r

µ10 210

αs

0.10

0.15

0.20

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2 < 100 GeV2H1 data for 5 < Q2 > 150 GeV2H1 data for Q

Central value and exp. unc.

PDF unc.⊕Theory

(th.) ± 0.0016 (PDF)−0.0030+0.0046± 0.0007 (exp.) = 0.1168 sα

[arXiv:0904.3870]2 > 150 GeV2Fit from Q

Figure 2: αs as a function of the scaleµr =

√

(Q2 + P2T, jet)/2 from jet cross

sections at low and highQ2.

)Z

(Msα0.11 0.12 0.13

exp. uncert.

th. uncert.

World averageS. Bethke, Eur. Phys. J. C 64, 689 (2009)

D0 incl. midpoint cone jetsPhys. Rev. D 80, 111107 (2009)

G. Dissertori et al., Aleph 3-jet ratePhys. Rev. Lett. 104, 072002 (2010)

jetsT

p incl. kγZEUS ZEUS-prel-10-003

jetsTZEUS incl. kZEUS-prel-10-002

ZEUS incl. SISCone jetsDESY-10-034 (2010)

jetsTZEUS incl. anti-kDESY-10-034 (2010)

jetsTZEUS incl. kPhys. Lett. B 649, 12 (2007)

multijetsT k2H1 low QEur. Phys. J. C 67, 1 (2010)

multijetsT norm. k2H1 high QEur. Phys. J. C 65, 363 (2010)

Figure 3:Recent values ofαs from HERA, LEP and TEVATRON.

3. Prompt Photon Production

Events with an isolated photon emerging from the hardsubprocessep→ eγX - so called prompt photons - offeran alternative method to study hard interactions. Recentresults have been published on prompt photon produc-tion in γp [9] for transverse energies of the photon 6<EγT <15 GeV by H1 and in DIS [10] (4<EγT <15 GeV)by ZEUS. Both experiments use the shower shapes ofthe electromagnetic cluster to discriminate the signal ofsingle photons from multiple photons of decays of neu-tral hadrons. As already observed in previous publica-tions, the new results show that the available calcula-tions are not able to describe all the measured distribu-tions well. In photoproduction it is found that the NLOcalculations underestimate the inclusive prompt photoncross section, while there is reasonable agreement forevents with a prompt photon and a jet. However, theirtransverse correlation, which is sensitive to higher orderprocesses, is not well described. In DIS the cross sec-tion receives contributions from radiation off the elec-

2

tron (LL) and also off the quark (QQ). The differentialcross section as a function ofQ2 is shown in Fig. 4.The orderα3 QCD prediction (GGP) significantly un-derestimates the data at lowQ2. Also included in thefigure is the prediction of MRST for the LL part of thecross section. This calculation is based on QED con-tributions to the PDFs which increases the LL contri-bution. MRST together with the QQ contribution fromGGP shows similar deficits at lowQ2.

Figure 4:Isolated photon differential cross sectiondσ/dQ2. The data is com-pared to a orderα3 calculation (GGP) as well as to a calculation with an in-creased contribution of the LL part (MRST).

4. Charged Particle Production

4.1. Rapidity spectra of charged particlesHERA experiments are able to access very smallBjorken x, a kinematic region where it is expected thatthe parton dynamics differs from the description by theDGLAP evolution equations. The latter imply a strongordering of the transverse momentakT in the parton cas-cade from the proton to the virtual photon. Measure-ments of the hadronic final state are sensitive to the dy-namics of the parton cascade. Fig. 5 shows theη∗ spec-tra of charged particles with a transverse momentum inthe hadronic centre of mass systemp∗T > 1 GeV in dif-ferent bins ofx andQ2 as measured by H1 in lowQ2

DIS events [11]. The data are compared to two MC pre-dictions. RAPGAP is based on the DGLAP evolutionequations for the parton dynamics, whereas DJANGOHfollows the Color Dipole Model, in which parton radi-ation is not ordered inpT . At small x and Q2 and inthe forward (proton) direction the RAPGAP predictionsare significantly below the data, whereas the data aredescribed reasonably well over the full kinematic rangeby the approach based on the Color Dipole Model.

4.2. Scaled momentum distributionsQuark fragmentation may be studied at HERA by us-ing the scaled momentumxp in the current region of

*ηd

dn

N1

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2 < 50 GeV2 20 < Q

* η 0 2 4

0

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2 < 50 GeV2 20 < Q

0 2 40

0.2

0.4

0.6

H1 data (prelim.)

RAPGAP

DJANGOH

H1 Preliminary

* > 1 GeV T

p

* η

Figure 5: Rapidity spectra of charged particle withp⋆T > 1 GeV for differentbins ofQ2 andx.

the Breit frame as observable. Here,xp = 2PBreit/Qwith PBreit the momentum of a hadron. Scaled mo-mentum distributions were measured by ZEUS for 10<Q2 < 41000 GeV2 for tracks with a transverse momen-tum larger than 0.15 GeV. Fig. 6 shows the density ofcharged particles per unit ofxp as a function ofQ in binsof xp. As the energy scaleQ increases, the phase spacefor soft gluon emission increases, leading to a rise ofthe number of particles with smallxp, which is clearlyseen in Fig. 6. In this figure the data from HERA areshown together with data frome+e− which were scaledto half of the centre-of-mass energy. The overall agree-ment between the different data sets supports the con-cept of fragmentation universality. NLO calculationspredict too weak scaling violation and also Monte Carlopredictions are not able to describe the data in the fullkinematic range.

4.3. Hadronic charge asymmetry

The hadronic charge asymmetry were measured in theBreit frame by H1 [12]. Fig. 7 shows the event nor-malised distribution of the scaled momentum for all,positively and negatively charged particles. There aresignificantly more particles produced at lowxp than athigh xp. At low xp the distribution is very similar fornegative and positive particles. This is expected sincelow xp particles are predominantly produced in frag-mentation. Fig. 7c illustrates that the original asym-metry observed on quark level is not visible anymoreon hadron level at lowxp. At high xp there is anovershoot of positively charged particles reflecting thecharge asymmetry of the proton. The asymmetry is re-produced by various models. The data are expected tofurther constrain the valence quark distributions in the

3

Q (GeV)10 210

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rangepx

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0.02 − 0.05 (x5)

0.05 − 0.1 (x2)

0.1 − 0.2

0.2 − 0.3

0.3 − 0.4

0.4 − 0.5

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0.7 − 1.0

ZEUS

Figure 6: n∗ distribution in the hadronic centre of mass system of chargedparticles withp∗T >1 GeV.

proton and to provide useful information on the frag-mentation functions.

5. Conclusions

Several results of inclusive jets and multijets productionin different kinematic regions have been presented. Theaccurate measurements are well described by NLO cal-culations and allow the extraction of the strong couplingαs as a function of the scale and atMZ with small ex-perimental errors.

Results of prompt photon production in photoproduc-tion and DIS are compared to theoretical predictions.They have problems describing the data in some kine-matic regions both inγp and DIS. In general they under-estimate the data, most significantly at lowQ2 in DIS.

Measurements of the hadronic final states are usedto study the parton dynamics and fragmentation pro-cesses. The charged particle spectra at lowQ2 and lowx are sensitive to the parton dynamics and comparisonsto models hint at dynamics beyond the conventionalDGLAP evolution equations at NLO. The scaled mo-mentum spectra have been measured in DIS. Large scal-ing violations are observed. Comparing the data toe+e−

results supports the concept of quark-fragmentationuni-versality. The hadronic charge asymmetry was mea-sured and found to be largest at large scaled momentaxp. The results are consistent with the expectation thatat highxp the asymmetry is directly related to the quarkcontent of the proton.

) pD

(x

-110

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H1 DataH1 Data pos H1 Data neg

2 < 8,000 GeV2100 < Q

(a)

CDMCDM posCDM neg

)p

A(x

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H1 DataPSCDMHERWIGGAL

px0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)p

A(x

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(c)

CDM hadron

CDM quark

Figure 7:Normalised distribution of the scaled momentumD=1/Ndn/dxp (a)for all, positively charged and negatively charged particles and charge asymme-try A(xp) as a function ofxp. The data is compared to Monte Carlo predictionswith different parton cascade and hadronisation processes and to theparton levelbefore the hadronisation.

Acknowledgements

I like to thank the organisers of this interesting confer-ence and my colleagues from H1 and ZEUS for valuableinputs to the talk and these proceedings.

References[1] ZEUS collaboration, “Inclusive jet cross sections in photopro-

duction”, ZEUS-prel-10-003.[2] ZEUS collaboration, “Inclusive jet production in NC DISwith

HERA II”, ZEUS-prel-10-002.[3] ZEUS collaboration, “ Dijets in NC DIS”, ZEUS-prel-10-005.[4] F. D. Aaronet al.[H1 Collaboration], Eur. Phys. J. C67 (2010)

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[7] V. M. Abazovet al.[D0 Collaboration], Phys. Rev. D80 (2009)111107 [arXiv:0911.2710 [hep-ex]].

[8] H. Abramowicz et al. [The ZEUS Collaboration],arXiv:1003.2923 [hep-ex].

[9] F. D. Aaronet al.[H1 Collaboration], Eur. Phys. J. C66 (2010)17 [arXiv:0910.5631 [hep-ex]].

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[11] H1 Collaboration, “Transverse Momentum of Charged Parti-cles at lowQ2 at HERA ”, H1prelim-10-035

[12] F. D. Aaronet al. [H1 Collaboration], Phys. Lett. B681 (2009)125 [arXiv:0907.2666 [hep-ex]].

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