1 Jets in PHENIX Jiangyong Jia, Columbia Univerisity How to measure jet properties using two particle correlation method (In PHENIX)? Discuss formula for jT, kT Discuss formula for the conditional yield Hot Quark Matter, Taos Valley, NM

07/23/2004Jiangyong Jia2 Hard-scattering and Jet fragmentation Partons scatters with large Q 2 – hard-scattering Outgoing partons fragment into sprays of hadrons –Jets Properties that we want to measure The spread of the hadrons around the jet axis and relative orientation of the two jets – jT, kT. The multiplicity of hadrons – fragmentation function D q  h (z) Leading hadron Q2Q2

07/23/2004Jiangyong Jia3 jT and kT jT = Momentum perpendicular to jet axis: jT= pT sin  is related to the non-perturbative QCD. Typical value is 500 MeV/c, very weakly depends on pT and  s. jet Jets are not exactly back-to-back in transverse direction kT = Intrinsic + radiative transverse momentum of the initial partons.

07/23/2004Jiangyong Jia4 Projected to azimuth plane Same jet correlation Assuming  tq and  aq are statistical independent Cross terms = 0 Simple relations derived for trigger and associated particles  tq trigger-parton  aq associated-parton  ta trigger-associated

07/23/2004Jiangyong Jia5 Far side jet correlation,  qq is the angle between the jets. Assuming  tq,  aq and  qq are statistical independent Cross terms = 0 At small angle,  qq is So we have Projected to azimuth plane

07/23/2004Jiangyong Jia6 jT, kT RMS values 1D RMS value: Pout is directly related to the angular width: (for Gauss statistics) Comparing with Jan’s formula (QM2004)

07/23/2004Jiangyong Jia7 Comparison using Pythia simulation Trigger pt>5 GeV/c, change associated pT Jan’s formula This formula “Seagull” effect at low pT. Some of the pt dependence is due to z Trig bias (mean z ~ 0.7)

07/23/2004Jiangyong Jia8 kT Broadening in dAu Presence of cold medium can broaden the jet kT p+pp+A d Au C~ Small additional kT: Typical additional broadening is (GeV/c) 2 in central collisions This was thought to be the origin of Cronin enhancement 1(GeV/c) 2 0.9(GeV/c) 2 7(GeV/c) 2 W.Volgelsang, hep-ph/ For STAR pp

07/23/2004Jiangyong Jia9 hep-ph/ I.Vitev Is kT in dAu sensitive to broadening? Seems radiation contribution dominate over the broadening 10% difference between dAu and pp for 4.5 GeV trigger  far not very sensitive to additional broadening Radiation contribution is even stronger at higher pT   -h correlation Pythia the sensitivity on broadening decreases as pT increases.

07/23/2004Jiangyong Jia10 Fragmentation function  Conditional yield Direct jet reconstruction. e+e-e+e- => CCOR,  s = 63 GeV Two particle correlation methods are used to extract FF. Jet direction and momentum approximated by the trigger define

07/23/2004Jiangyong Jia11 Two particle azimuth correlation method In ideal acceptance, real pair distribution is Pair acceptance function can be determined from event mixing technique Real/mix gives the acceptance corrected CY (modulo constant background ). Real distribution is modulated by pair acceptance function Acc (  ).

07/23/2004Jiangyong Jia12 Pair acceptance function ACC in PHENIX Single particle acceptance Triangle results from convoluting two flat distribution Pair acceptance in  Pair acceptance in  effi is 100% at ,  Average is 25% Shape from overlapping four triangles: west1-west2, east1-east2, west1-east2, east1-west2

07/23/2004Jiangyong Jia13 Normalization for 2D and 1D CY 2D CY Acceptance+ efficiency Mix normalized to pair phase space Underling triggersDetected triggers 1D CY can be obtained by integrating out . Pair cuts and two track resolution Single particle efficiency in full azimuth and 1 unit  Fraction of jet yield falls in  acceptance Can be calculated analytically assuming Gauss shape

07/23/2004Jiangyong Jia14 Test the correction with Pythia simulation Generate 1 M triggered events and 1 M minimum bias events. Mixed distribution is obtained by mixing trigger with minbias event. Requiring trigger always has |  |<0.35. If we don’t constrain associated particle, we would get full yield. Compare three correlations. No cut on associated particle  full jet yield (near side) Near side jet has a gauss shape in  — the integral of the gauss. Cut |  |<0.7 on associated particle  full yield in |  |<0.7(away side) Far side jet has a very broad shape in  PHENIX acceptance cut  measured yield in near and away side.

07/23/2004Jiangyong Jia15 CY, with no constrain on associated particle Trigger pt > 5 GeV/c, associated 1<pT <1.5 GeV/c Trigger |  |<0.35, associated no eta cut. This gives the true conditional yield for the near side :0.717 FG MIX True conditional yield

07/23/2004Jiangyong Jia16 CY, with associated particle in |  |<0.7 Trigger pt > 5 GeV/c, 1<pTasso <1.5 GeV/c Trigger |  |<0.35, and associated particle: |  |<0.7 This gives the true conditional yield with in |  |<0.7 for the far side: 0.92 FG MIX True conditional yield Because the away side correlation is very wide in . We just want the yield in |  |<0.7, which is the range sampled by PHENIX.

07/23/2004Jiangyong Jia17 Conditional yield in PHENIX acceptance Trigger pt > 5 GeV/c, 1<pTasso <1.5 GeV/c Trigger |  |<0.35, and associated |  |<0.35. Azimuth acceptance cut on both particles.. This gives the Measured conditional yield for same side and way side 0.279(near), 0.233(far). FG MIX Raw conditional yield

07/23/2004Jiangyong Jia18 Corrected CY compared with true CY Near side Far side

07/23/2004Jiangyong Jia19 The ratio between true and corrected The agreement is good. This implies that our correction and extrapolation is valid.

07/23/2004Jiangyong Jia20 Summary Discuss the general formula for and Some difference from previously used formula, especially for kTz and low associated pT region. The sensitivity on kT dies out as the trigger pT increases. Discuss the how to extract the conditional yield using two particle correlation method and event mixing. The correction factor is derived for limited detector acceptance(can be trivially generalized to other detectors). Verified with Pythia simulation