ELSEVIER Nuclear Physics B (Proc. Suppl.) 79 (1999) 494-496

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PROCEEDINGS SUPPLEMENTS

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Subjet Multiplicity in Quark and Gluon Jets at DO R. Snihur (for the DO Collaboration) Northwestern University, Evanston IL 60208, USA

We measure the subjet multiplicity M in jets reconstructed with a successive combination type of jet algorithm (kT). We select jets with 55 < ET < 100 GeV and Iql < 0.5. We compare similar samples of jets at v ~ = 1800 and 630 GeV. The HERWIG Monte Carlo simulation predicts that 59% of the jets are gluon jets at ~ -- 1800, and 33% at ~ --- 630. Using this information, we extract the subjet multiplicity in quark (Mq) and gluon (Mg)

jets. We also measure the ratio R ---- IMql-1 ----- 1.91 4- 0.04(stat)+°~(sys). ( ~ , , ) - 1 -

1. I N T R O D U C T I O N

The Tevatron proton-antiproton collider is a rich environment for studying high energy physics. The dominant process is jet production, described in Quantum Chromodynamics (QCD) by scattering of the elementary quark and gluon constituents of the incoming hadron beams. In leading order (LO) QCD, there are two partons in the initial and final states of the elementary process. A jet is associated with the energy and momentum of each final state parton. Experi- mentally, however, a jet is a cluster of energy in the calorimeter. Understanding jet s tructure is the motivation for the present analysis. QCD predicts tha t gluons radiate more than quarks. Asymptotically, the ratio of objects within gluon jets to quark jets is expected to be in the ratio of their color charges C A / C F ---- 9/4 [1].

2. T H E kT J E T A L G O R I T H M

We define jets in the DO detector [2] with the kT algorithm [3]. The jet algorithm starts with a list of energy preclusters, formed from calorimeter cells or from particles in a Monte Carlo event gen- erator. The preclusters are separated by AT~ ---- v/Ar]2 + A¢2 > 0.2, where 77 and ¢ are the pseu- dorapidity and azimuthal angle of the preclusters. The steps of the jet algorithm are:

1. For each object i in the list, define dii = E2,i, where ET is the energy transverse to the beam. For each pair (i, j ) of objects, also define

dq = m i n ( E ~ i , ~ 2 ~ where D is a param- , L~T, j ) D 2 ,

0 9 2 0 - 5 5 3 2 / 9 9 / $ - see front m a t t e r © 1999 Elsev ie r Sc ience B . ~

PII S 0 9 2 0 - 5 6 3 2 ( 9 9 ) 0 0 7 6 4 - l

eter of the jet algorithm. 2. If the minimum of all possible dii and dij is a

dij, then replace objects i and j by their 4-vector sum and go to step 1. Else, the minimum is a dii so remove object i from the list and define it to be a jet.

3. If any objects are left in the list, go to step 1. The algorithm produces a list of jets, each sep-

arated by AM > D. For this analysis, D = 0.5. The subjet multiplicity is a natural observable

of a kT jet [4,5]. Subjets are defined by rerunning the kT algorithm starting with a list of preclus- ters in a jet. Pairs of objects with the small- est dij are merged successively until all remain- ing dij > YcutE2(jet). The resolved objects are called sub jets, and the number of sub jets within the jet is the sub jet multiplicity M. The analysis in this article uses a single resolution parameter Ycut -- 10-3.

3. J E T S E L E C T I O N

In LO QCD, the fraction of final state jets which are gluons decreases with x ,-, ET/vfs , the momentum fraction of initial state partons within the proton. For fixed ET, the gluon jet frac- tion decreases when x/~ is decreased from 1800 GeV to 630 GeV. We define gluon and quark en- riched jet samples with identical cuts in events at v ~ = 1800 and 630 GeV to reduce experi- mental biases and systematic effects. Of the two highest ET jets in the event, we select jets with 55 < ET < 100 GeV and I~?1 < 0.5.

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R. Snihur/Nuclear Physics B (Proc. Suppl.) 79 (1999) 494-496 495

4. Q U A R K A N D G L U O N SUB J E T M U L - T I P L I C I T Y

There is a simple method to extract a mea- surement of quark and gluon jets on a statistical basis, using the tools described in the previous sections. M is the sub jet multiplicity in a mixed sample of quark and gluon jets. It may be written as a linear combination of subjet multiplicity in gluon and quark jets:

M = f i g + (1 - f ) i q (1)

The coefficients are the fractions of gluon and quark jets in the sample, f and (1 - f ) , respec- tively. Consider Eq. (1) for two similar samples of jets at x/~-- 1800 and 630 GeV, assuming Mg and Mq are independent of x/~. The solutions are

ffSOOM63O _ f63OM18OO

Mq ---- flsoo __ f630 (2)

(1 - f630) MlSOO _ (1 - f1800) M630 Mg = flsoo __ f630 (3)

w h e r e M is00 and M 630 a r e the experimental mea- surements in the mixed jet samples at x/~ -- 1800 and 630 GeV, and fls0o and f63o are the gluon jet fractions in the two samples. The method relies on knowledge of the two gluon jet fractions.

5 . R E S U L T S

The HERWIG 5.9 [6] Monte Carlo event genera- tor provides an estimate of the gluon jet fractions. The method is tested using the detector simula- tion and CTEQ4M PDF. We tag every selected jet in the detector as either quark or gluon by the identity of the nearer (in ~? × ¢ space) final state patton in the QCD 2-to-2 hard scatter. Fig. 1 shows that gluon jets in the detector simulation have more sub jets than quark jets. The tagged sub jet multiplicity distributions are similar at the two center of mass energies, verifying the assump- tions in § 4.

We count tagged gluon jets and find fas00 = 0.59 ± 0.02 and f63o __ 0.33 5= 0.03, where the uncertainties are estimated from different gluon PDF's. The nominal gluon jet fractions and the Monte Carlo measurements at x/~ -- 1800 and 630

io.4 z

" 5

i 0.2 z

HERWIG 5.9 Full Detector Simulotion

,+o Q u a r k J e t s

ao Extrocted Togcled, ~/s = 1800 GeV b~ j Tog~ed, v's = 630 GeV

z~3

Cluon Jets

~b a¢

Sub je t Mul t ip l i c i ty M

Figure 1. Raw subjet multiplicity in fully sim- ulated Monte Carlo quark and gluon jets. For visibility, we shift the open symbols horizontally.

GeV are used in Eqs. (2-3). The extracted quark and gluon jet distributions in Fig. 1 agree with the tagged distributions and demonstrate closure of the method.

Fig. 2 shows the raw subjet multiplicity in DO data at x/~ -- 1800 GeV is higher than at x/~ -- 630 GeV. This is consistent with the predic- tion that there are more gluon jets at v ~ = 1800 GeV compared to x/~ -- 630 GeV, and gluons ra- diate more than quarks. The combination of the distributions in Fig. 2 and the gluon jet fractions gives the raw sub jet multiplicity distributions in quark and gluon jets, according to Eqs. (2-3).

The quark and gluon raw sub jet multiplicity distributions need separate corrections for vari- ous detector-dependent effects. These are derived from Monte Carlo, which describes the raw DO data well. Each Monte Carlo jet in the detector simulation is matched (within A~R < 0.5) to a jet reconstructed from particles without the detector simulation. We tag detector jets as either quark or gluon, and study the subjet multiplicity in par- ticle jets M ptct vs. that in detector jets M def. The correction u n s m e a r s M det to give M ptcl, in bins of M det. Fig. 3 shows the corrected subjet mul- tiplicity is clearly larger for gluon jets compared

496 R. Snihur /Nuclear Physics B (Proc. Suppl.) 79 (1999) 494-496

l 0.4 Z "0

"0

Z~0.3

0.25

0.2

0,15

D~ Prel iminary D = 0.5. y=, = 10 -~ 55< E ~ < IOOGeV Ifi~l < 0.5

(M is°°) = 2.74 4- 0.01

(M 63°) = 2.54 4- 0.04

• Vs = 1 8 0 0 GeV O

[] V s = 6 3 0 G e V

1 J ; ' ; Subjet Multiplicity M

l 0,6

Z -o

~ 0.5

l Z

0,4

0.3

t D~ Prel iminory D = 0.5, y=~ = 10 -~ 55 < Et ~ < IOOGeV 17/~1 < 0.5

• Quork Je ts

[~ Gluon Jets

÷ ¢

i

Subjet Multiplicity M

Figure 2. Raw sub jet multiplicity in jets from DO data at v~ = 1800 and 630 GeV.

Figure 3. Corrected subjet multiplicity in quark and gluon jets, extracted from DO data.

to quark jets. The gluon jet fractions are the largest source

of systematic error. We vary the gluon jet frac- tions by the uncertainties in an anti-correlated fashion at the two values of v~ to measure the effect on R. The systematic errors listed in Ta- ble 1 are added in quadrature to obtain the total uncertainty in the corrected ratio R -- /M'q}--l(Mq)--I ----

0 04 ~,.,~+0.23 1.91-t- . (~a~]_o.19(sys).

Table 1 Systematic Errors Source JR Gluon Jet Fraction +u.is - - 0 . 1 2

Jet ET cut +0.12 Detector Simulation -t-0.08 Unsmearing 4-0.04

6. C O N C L U S I O N

We extract the Ycut -- 10-3 subjet multiplic- ity in quark and gluon jets from measurements of mixed jet samples at v~ -- 1800 and 630

GeV. On a statistical level, gluon jets have more subjets than quark jets. We measure the ratio of additional sub jets in gluon jets to quark jets R ~ 1.9 :t: 0.2. The ratio is well described by the HERWIG patton shower Monte Carlo, and is only slightly smaller than the naive QCD prediction 9/4.

R E F E R E N C E S

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