Study of J/ Polarization in pp Collisions at = 200 GeV with the PHENIX Experiment

at RHIC

Gobinda C MishraGeorgia State UniversityAtlanta, GA 30303, USA

(For the PHENIX Collaboration)

Quark Matter 2004Oakland, CA

January, 2004

NNS

In this poster we present the status of our first attempt to extract the J/ polarization for p+p collisions at GeV at RHIC using PHENIX muon arm data. The limited statistics we have collected so far, does not allow to precisely extract the polarization parameter . So here we will describe the procedure to extract and estimate how much minimum J/statistics needed to obtain statistically significant result.

Introduction

Why do we need to study polarization This study is a crucial test for various quarkonium

production mechanism as different model predicts different polarization.

Various theoretical models for quarkonium production: color singlet model: Only pair in color singlet state

can bind to form physical quarkonium. color octet model: at color octet state can bind to

make physical quarkonium by emitting a soft gluon. color evaporation model: This model assumes any

produced with small relative momentum can form a physical quarkonium by emission of soft gluons, irrespective of its color or angular momentum configuration

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Motivation

• NRQCD factorization approach including the color octet mechanism predicts that the directly produced J/will be increasingly transversely polarized at higher pt. This is because at high pt region production of J/is dominated by gluon fragmentation and gluon transverse polarization is preserved as the pair turns to a bound state J/ meson. The analysis of J/ and ’ polarization at large pt is one of the most decisive test of NRQCD factorization approach.

hep-ph/0106120

• Color evaporation model predicts that J/ is unpolarized, because it assumes unsuppressed gluon emission from pair during hadronization, which randomizes spin and color.

• CDF result doesn’t agree with the NRQCD prediction at higher pt >12 GeV/c neither for J/ nor ’ ( pp at 1.8TeV )

PRL 85 (2000) 2888

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• One of the Fermilab experiments with + N at 252 GeV observed that J/is unpolarized in most of the kinematics regions, but tends to be longitudinally polarized as xF1

PRL 58 (1987)2523

• It is claimed that the change of spin alignment of J/ at large xF involves higher twist effect (gluon exchange interactions between annihilating quarks and spectator quarks is responsible for this), assuming annihilation mechanism dominate near xF = 1 where as gluon-gluon fusion dominate at low and moderate xF.

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NRQCD formalism with color octet model appears to explain differential cross-section result reasonably well.

NRQCD Prediction for Cross-Section

hep-ph/0106120

NRQCD Prediction for Polarization

There is large discrepancy in polarizationbetween the data and model prediction. Data are from CDF. hep-ph/0106120

• Experimentally one studies the polarization through angular distribution of decay muons.

• Most general form of angular distribution is given as

• The dependence of cross-section gives only and is comparatively easier to measure than dependence.

• is the polar angle between one of the muons (+) in J/ rest frame. There are various ways one can choose axes for the J/ rest frame. We have chosen the Collins-Soper (CS) frame where the z-axix is along the bisector direction of colliding hadrons.

2cossin

2

1cos2sincos1~

cos22

2

dd

d

2cos1~cos

d

d

Angular Distributions

J/Rest Frame (Collins-Sopper Frame)

EE

pp

mM

Ep

zzpairz

pairz

pairzzCS

,

222,

,

where

4/1cosFormula to calculate

cos in Collins-Soper frame from measured kinematics in lab frame

= -1

= 1

= 0

= 1 (Transverse Polarization)= -1 (Longitudinal Polarization)= 0 (No polarization)

= 0.5 = -0.5

cos Distribution for Different Cases

PHENIX Muon Arm

South Muon Arm

Acceptance: -2.2 <<-1.2

North Muon Arm

Acceptance: 1.2 <<2.4

We have used ~4 M triggered events in north arm and ~1.1 M triggered events in south arm for this analysis. These correspond to 184 nb-1 and 208 nb-1 integrated luminosity for north and south arm respectively. The number of J/ obtained from these data sample are 248 and 104 after background subtraction and with pT > 0.5 GeV/c in north and south arm respectively. The data were divided into two pT bins to study the pT dependence of J/ polarization.

Data Selection

Mass Distribution in two pt bins

North Arm

South Arm

These mass

distributions are

after a pT cut

of 0.5 GeV/c

To get the true angular distribution (cos distribution) we have to do acceptance correction. The cos acceptance heavily depends other kinematics variables, viz. pT and xF. Monte Carlo (MC) events with same pT, xF as in data were used to correct for the acceptance for cos distribution from data.

We employ two step acceptance correction technique to get correct cos acceptance. In first step, we generate a set of Monte Carlo events with flat pT, xF, and cos. Use these events to correct pT and xF distribution obtained from real data. The resultant pT and xF distributions were then used in second set of Monte Carlo events to get true cos acceptance.

),,(

),,,(cos)(cos

FT

FT

xpMC

xpDATAF

Analysis Procedure

The data have been divided into 2 pt bins: 0.5-2 GeV/c and 2-4 GeV/c to study the pT dependence. The pT<0.5 GeV/c was excluded from analysis because of pT resolution. The number of J/ at two pT bins from north arm are 197 and 71 respectively, and from south arm 77 and 27 respectively after 0.5 GeV/c pT threshold. The cos acceptance for each pT bin and each arms are shown in following figures. Because of very low statistics, we have not taken the ratio for now. Rather, we have estimated the statistical accuracy of extracted polarization parameter by using a pure J/ events in a perfect detector.

Analysis Procedure (Contd.)

Uncorrected cos Dist.

North Arm

South Arm

NNNN J /

Uncorrected background subtracted cos Distribution

Bin by bin Background Subtraction

North Arm

South Arm

cos Acceptance Distribution.

North Arm

South Arm

Statistical Error Estimation

Here different number of simulated

J/ data events were generated in

PHENIX muon arm acceptance,

and were corrected for acceptance

using very high statistics Monte

Carlo events. The acceptance

corrected cos distributions were

fitted by 1+cos2. The resulting s

with errors are plotted vs number of

simulated data events. The two red

points were obtained using the

procedure described above, but

the blue points were obtained for the

cases where the simulated data and

Monte Carlo events have exactly

same input pT and xF distribution.

• The current J/ polarization study from 200 GeV p+p collisions with PHENIX muon arm data suffers from low J/ statistics.

• A pure statistical study indicates that to

get reliable polarization measurement we should have ~5000 or more J/, which we hope to get in future RHIC runs.

Conclusions and outlook

See the poster on J/ polarization study for d+AuCollisions at RHIc by X. R. Wang (Flavor 8)