1. 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

2. 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)

3. Deep Inelastic Kinematics and Data Selection
ZEUS 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 trijet events
y  p•q / p•k: fraction of electron energy
transferred (in proton rest frame)
s = (p+k)2 : center of mass energy

4. 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

5. 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/ Good agreement within 1~2% with fixed EM=1/137

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

7. 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 =
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

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

9. Cross Section Ratio: CTEQ6
R3/2=trijet/dijet
CTEQ6 s =
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

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

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

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

13. 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