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Jets in PHENIX

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

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Jets in PHENIX

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

  2. Hard-scattering and Jet fragmentation • Partons scatters with large Q2 – 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 Dqh(z) Leading hadron Q2 Jiangyong Jia

  3. jT and kT jet • jT = Momentum perpendicular to jet axis: jT= pT sinDf • <jT> is related to the non-perturbative QCD. • Typical value is 500 MeV/c, very weakly depends on pT and s. • Jets are not exactly back-to-back in transverse direction • kT = Intrinsic + radiative transverse momentum of the initial partons. Jiangyong Jia

  4. Same jet correlation • Assuming ftq and faq are statistical independent Cross terms = 0 • Simple relations derived for trigger and associated particles Projected to azimuth plane ftq trigger-parton faq associated-parton fta trigger-associated Jiangyong Jia

  5. Far side jet correlation • Assuming ftq , faq and fqq are statistical independent Cross terms = 0 At small angle, fqq is So we have • ,fqq is the angle between the jets. Projected to azimuth plane Jiangyong Jia

  6. jT, kT RMS values • Pout is directly related to the angular width: • 1D RMS value: (for Gauss statistics) • Comparing with Jan’s formula (QM2004) Jiangyong Jia

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

  8. kT Broadening in dAu 1(GeV/c)2 0.9(GeV/c)2 7(GeV/c)2 Au W.Volgelsang, hep-ph/0312320 For STAR pp d • This was thought to be the origin of Cronin enhancement Small additional kT: C~ 0.2-0.4 Typical additional broadening is 0.8-1.6 (GeV/c)2 in central collisions p+p p+A • Presence of cold medium can broaden the jet kT Jiangyong Jia

  9. Is kT in dAu sensitive to broadening? • Radiation contribution is even stronger at higher pT Pythia p-h correlation • Seems radiation contribution dominate over the broadening I.Vitev hep-ph/0310274 10% difference between dAu and pp for 4.5 GeV trigger the sensitivity on broadening decreases as pT increases. Jiangyong Jia sfar not very sensitive to additional broadening

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

  11. Two particle azimuth correlation method • Real distribution is modulated by pair acceptance function Acc(Df, Dh). • Pair acceptance function can be determined from event mixing technique • Real/mix gives the acceptance corrected CY (modulo constant background l). • In ideal acceptance, real pair distribution is Jiangyong Jia

  12. Pair acceptance function ACC in PHENIX Single particle acceptance Pair acceptance in Dh Pair acceptance in Df Shape from overlapping four triangles: west1-west2, east1-east2, west1-east2, east1-west2 Triangle results from convoluting two flat distribution effi is 100% at Df=0, Dh=0 Average is 25% Jiangyong Jia

  13. Normalization for 2D and 1D CY Detected triggers Underling triggers Mix normalized to pair phase space Acceptance+ efficiency • 1D CY can be obtained by integrating out Dh . Single particle efficiency in full azimuth and 1 unit h Pair cuts and two track resolution Fraction of jet yield falls in h acceptance Can be calculated analytically assuming Gauss shape • 2D CY Jiangyong Jia

  14. 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 |h|<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 Dh— the integral of the gauss. • Cut | Dh|<0.7 on associated particle  full yield in |Dh|<0.7(away side) • Far side jet has a very broad shape in Dh. • PHENIX acceptance cut  measured yield in near and away side. Jiangyong Jia

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

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

  17. Conditional yield in PHENIX acceptance • Trigger pt > 5 GeV/c, 1<pTasso <1.5 GeV/c • Trigger |h|<0.35, and associated |h|<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). Raw conditional yield FG MIX Jiangyong Jia

  18. Corrected CY compared with true CY Far side Near side Jiangyong Jia

  19. The ratio between true and corrected • The agreement is good. • This implies that our correction and extrapolation is valid. Jiangyong Jia

  20. 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 Jiangyong Jia

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