DIS 2004 XII International Workshop Test of QCD Using Multijets in Neutral Current DIS at HERA Liang Li University of Wisconsin On behalf of the ZEUS Collaboration

Motivation for Multijets Study Add a gluon radiation to dijet or split a gluon to  direct test of QCD at O(s2) Example An ideal laboratory for studying gluon radiation.  In the ratio trijet/dijet = O(s), cancellation of many correlated experimental and theoretical uncertainties. =xbj(1+Mjjj2/Q2) Mjjj2 is the invariant mass squared of the trijet system The trijet cross section in DIS is already proportional to O(αs2) in leading order in pQCD. Unlike e+e– Annihilation measurements, the ones in ep scattering are not at a fixed value of Q2. Take the ratio of R3/2 = trijet/dijet = O(s), reduce uncertainty fq(x,2 ) and g(x, 2 ) are the densities of the quarks and gluons respectively. fq(x,2) comes from other experiments trijet is the inclusive trijet cross section. q and g are the partonic cross sections for processes initiated by the quarks and gluons respectively (calculated by theory).  Is the momentum fraction of the struck parton NLO (x)->(x,2) NLO calculations reduce dependency on the factorization scale. The principle of “asymptotic freedom” determines that the renormalized QCD coupling is small only at high energies, and it is only in the domain that high-precision tests can be performed using perturbation theory(pQCD). The strong coupling constant is the only parameter relevant to the high-energy regime of QCD that needs to be determined, as, in principle, everything else can be calculated from first principles. The strong coupling is one of the fundamental `constants' of nature, and, as such, there is no limit to the accuracy with which we would like to know its value. Beside setting the overall precision of any fixed-order perturbative QCD (pQCD) calculation, an accurate knowledge of αs is, for example, necessary to extract electroweak parameters from precise e+e– data, as well as to see all forces of nature are unified at some large energy scale. Because the measurement of αs is so important, people would like to use as many ways to measure it as possible. The most frequently used ones are: e+e– Annihilation, High-energy hadron collisons and ep collisions. Multijet NLO Calculations available (Ref: Phys.Rev.Lett.87:082001,2001)

Deep Inelastic Kinematics and Data Selection ZEUS 1998-2000 data 82.2 pb-1 = 318 GeV Ep=920 GeV, Ee=27.5 GeV Kinematic Range 10 GeV2 < Q2 < 5000 GeV2 YEL < 0.6, YJB > 0.04 coshad < 0.7 Jet Reconstruction Invariant KT algorithm in Breit frame (inclusive) ET,jetBRT > 5 GeV -1 <jetLAB < 2.5 Invariant mass M2,3jet >25 GeV Neutral Current: e p e X (  , Z ) + Q2  -q2 : momentum transfer x  Q2 / 2pq: momentum fraction carried by struck quark (QPM) 37089 dijet events and 13665 trijet events y  p•q / p•k: fraction of electron energy transferred (in proton rest frame) s = (p+k)2 : center of mass energy

LO and NLO Calculation LO MC NLO Program LEPTO (6.5.1) used for acceptance corrections and hadronization corrections ARIADNE (4.0.8) used for systematic checks GEANT (3.13) used for detector simulation NLO Program NLOJET by Nagy Trocsanyi (Phys.Rev.Lett.87:082001,2001) Renormalization and factorization scales tested for and Dijet: , trijet: PDF: CTEQ6, MRST2001, CTEQ4 Data and NLO compared at hadron level First NLO program for trijets, cross checked for dijets ET2 (ET2 + Q2)/4 ET= (ET,1 + ET,2)/2 ET= (ET,1 + ET,2+ ET,3)/3

Comparison of NLOJET and DISENT Dijet Dijet LO Dijet NLO EM=1/137 EM=1/137 By default, NLOJET: Running EM, DISENT: fixed EM=1/137 Good agreement within 1~2% with fixed EM=1/137

Compare Data vs. NLOJET : Choice of Scale Scale r= f = ET2 Scale r= f = (ET2 + Q2)/4 CTEQ6 s = 0.1179 Dijet Trijet NLO with fixed EM Choose renormalization and factorization scale = (ET2 + Q2)/4

Compare Data vs. NLOJET : CTEQ6 PDF Scale r= f = (ET2 + Q2)/4 Compare Data vs. NLOJET : CTEQ6 PDF Dijet NLO: O(s) Trijet NLO: O(s2) CTEQ6 s = 0.1179 Measurement down to low Q2 Test of scale dependence High renormalization scale dependence in low Q2 Good description of both dijets and trijets over 3 orders of magnitude in Q2 NLO with fixed EM

Compare Data vs. NLOJET : MRST2001 and CTEQ4 MRST s = 0.1190 CTEQ4M s = 0.116 Good description of both dijets and trijets over 3 orders of magnitude in Q2 for both PDFs

Cross Section Ratio: CTEQ6 R3/2=trijet/dijet CTEQ6 s = 0.1179 Systematic uncertainties substantially reduced Scale dependence reduced Very sensitive test of QCD calculation Good description of data over large range of scales more sensitive test

Cross Section Ratio: MRST2001 and CTEQ4 CTEQ4M s = 0.1160 MRST2001 s = 0.1190 NLO with fixed EM NLO using MRST2001 and CTEQ4 PDF also describes data well over large kinematic range

Cross Section Ratio : CTEQ4 and MRST2001 Some sensitivity to PDF is observed NLO with fixed EM

Cross Section Ratio : CTEQ4 with Different s As expected, predictions within one PDF are sensitive to s NLO with fixed EM

Summary and Outlook NLO with fixed EM describes data well using 3 different PDFs: CTEQ4, CTEQ6 and MRST2001 R3/2 cross section ratio is sensitive to s but some sensitivity to PDF is also observed and under study MRST2001 and CTEQ6 with different s sets are needed