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Di-hadron correlations and parton intrinsic transverse momentum ٭

Di-hadron correlations and parton intrinsic transverse momentum ٭. RHIC has moved beyond initial phase. George Fai, Gábor Papp, Péter Lévai ELTE / Kent State University / CRIP. ٭ Supported in part by U.S. DOE DE-FG02-86ER-40251, NSF INT-0435701, Szent-Györgyi scholarship 34/2004.

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Di-hadron correlations and parton intrinsic transverse momentum ٭

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  1. Di-hadron correlations and parton intrinsic transverse momentum٭ RHIC has moved beyond initial phase George Fai, Gábor Papp, Péter Lévai ELTE / Kent State University / CRIP ٭ Supported in part by U.S. DOE DE-FG02-86ER-40251, NSF INT-0435701, Szent-Györgyi scholarship 34/2004

  2. Outline Di-hadron correlations and back-to-back jets Di-jet correlations in proton-proton collisions 3. Jet-jet correlation scenarios 2 2 kinematics 2 3 kinematics partial correlation by randomization 4. Degree of randomization 5. Comparison to data 6. Application to single-particle spectra 7. Conclusion transverse structure of the proton alternative: kT factorization formalism QM2005, Budapest

  3. Pedestal&flow subtracted Why di-hadron (and photon-hadron) correlations? Statistical tool to study jets (probably the only way in 200 GeV Au + Au collisions) test of pQCD modified by the medium, i.e. info on the medium (single and di) jet tomography Examples: gluon density (Baier, Dokshitzer, Gyulassy, Lévai, Wang, Vitev, …) collective dynamics (Armesto, Salgado, Wiedemann, …) sound speed (Casalderrey, Shuryak, Stöcker, Teaney, …) J. Adams et al. (STAR), Phys. Rev. Lett. 91 (2003) 072304 QM2005, Budapest

  4. Jet basics Rcone=0.7 rad Transverse energy deposition in two variables: fragmentation parton hard process pQCD parton hadrons Focus on azimuthal angle correlations QM2005, Budapest

  5. High pT particle High pT particle e+ + e- jet + jet p + p  jet + jet Au + Au  stuff + jet + jet measure these… here?! Jets in various collisions F. Wang, RBRC Workshop, March 10, 2005 “We can do it but with some care…” QM2005, Budapest

  6. High pT particle High pT particle e+ + e- jet + jet p + p  jet + jet Au + Au  stuff + jet + jet Jets in various collisions Au + Au collisions substantially more complicated: new results; focus on p + p (pbar) collisions for this talk (but see following 4 presentations and tomorrow’s plenary session) QM2005, Budapest

  7. Di-hadron correlations in pp at 200 GeV STAR: p-p jet event Analyze jets by measuring Df between high-pT hadrons dN/dDf 0º 180º Df B. Cole, RHIC & AGS Users Meeting, June 20, 2005 Rich content already in p + p collisions: widths of the near and away side peaks QM2005, Budapest

  8. Leading Jet Charged particle density at the Tevatron Df dependence of the charged particle density, dNchg/dhdf, for pT > 0.5 GeV/c and |h| < 1 relative to jet#1 (rotated to 270o) for “leading jet” events 30 < ET(jet#1) < 70 GeV. p+pbar 2 TeV R. Field, ISMD’04 dNchg/dhdf, for charged particles in the range pT > 0.5 GeV/c and |h| < 1 for “min-bias” collisions. QM2005, Budapest

  9. What can we learn from di-hadron correlations in pp collisions? Experimental difficulty: extract parton-level information Goals: 1. separate initial and final-state effects 2. understand fragmentation process 3. connect initial state information to intrinsic transverse momentum of partons in the proton History: summarized in M.J. Tannenbaum, nucl-ex/0507020 R.P. Feynman, R.D. Field, and G.C. Fox, Nucl. Phys. B 128 (1977) 1 A.L.S. Angelis et al. (CCOR), Phys. Lett. B 97 (1980) 163 QM2005, Budapest

  10. What can we learn from di-hadron correlations in pp collisions? Near side fragmentation process (e.g. di-hadron fragmentation functions) identified hadrons Unidentified (e.g. baseline for baryon-meson puzzle) Away side transverse structure of the proton (e.g. transverse momentum distribution) [in addition to fragmentation] QM2005, Budapest

  11. What can we learn from di-hadron correlations in pp collisions? Near side fragmentation process (e.g. di-hadron fragmentation functions) identified hadrons Unidentified (e.g. baseline for baryon-meson puzzle) Away side transverse structure of the proton (e.g. transverse momentum distribution) QM2005, Budapest

  12. Starting point: transverse momentum conservation for a 2 2 partonic process Gaussian for magnitude of kT Calculate QM2005, Budapest

  13. Jet-jet correlation scenarios Strongly correlated Partially correlated 2 2 due to scattering, gluon radiation, or any combination of collisions and 2 n processes QM2005, Budapest

  14. Degree of randomization α = 4[< (pT2 sinΔΦ)² > - 2σk²] / pT1² β = 4[< (pT2 cosΔΦ)² > - 2σk²] / pT1² uniform in [Φ2 – δΦ, Φ2 + δΦ] Randomization prescriptions: Gauss: QM2005, Budapest

  15. Partially correlated case QM2005, Budapest

  16. Partially correlated case Fit parameters: Use to describe single-particle spectra at RHIC ! QM2005, Budapest

  17. To extract width from hadron correlations Need to take fragmentation into account Near side Away side QM2005, Budapest

  18. To extract width from hadron correlations Approximations More elaborate approximations available in e.g. • J. Rak et al. (PHENIX) J. Phys. G 30 (2004) S1309 • J. Jia, J. Phys. G 31 (2005) S521 • J. Qiu and I. Vitev, Phys. Lett. B 570 (2003) 161 An example: QM2005, Budapest

  19. To extract width from hadron correlations Need to take fragmentation into account Procedure: 1. Fix trigger transverse momentum 2. Measure near and away-side widths at given pT 3. Estimate average fragmentation momentum fraction QM2005, Budapest

  20. Application to single-particle spectra 2 QM2005, Budapest

  21. Nuclear effects • Shadowing • Isospin • Broadening Shadowing function <kT2>pA = <kT2>pp + C hpA (b) QM2005, Budapest

  22. Reproduces Cronin effect at midrapidity At ISR and FNAL energies At RHIC energies nucl-th/0306019 Phys. Rev. C65 (2002) 034903 G.G. Barnaföldi, Monday afternoon QM2005, Budapest

  23. Conclusions • Di-hadron correlations in proton-proton collisions can be described in • terms of partial randomization • Degree of randomization extract width of intrinsic transverse mom. • distribution of partons in the proton • Width can be used as a basis to reproduce single-particle spectra • in proton-proton, proton-nucleus, and nucleus-nucleus collisions • background for jet-quenching studies • Variation with trigger momentum between pp and dAu can provide an • alternative way to separate initial and final-state effects • Jet quenching observed directly in disappearance of away-side peak • in central Au+Au • FOLLOWING TALKS pTtrig  0 QM2005, Budapest

  24. Backups QM2005, Budapest

  25. kTat RHIC from p+p data Statistical Errors Only di-hadron B. Jacak, Hard Probes 2004 J. Rak, Wed. J. Rak, DNP03 PHENIX preliminary Df near-side away-side QM2005, Budapest

  26. Mass number dependence EVIDENCE FOR MULTIPLE SCATTERING OF HIGH-ENERGY PARTONS IN NUCLEI. By E609 collaboration (M.D. Corcoran et al.) Phys.Lett.B259:209-215,1991 QM2005, Budapest

  27. CCOR ztrig measurement Angelis et al (CCOR): Nucl.Phys. B209 (1982) QM2005, Budapest

  28. In Practice parton momenta are not known  Simple relation Fragmentation Function (distribution of parton momentum among fragments) J. Rak, Hot Quarks 2004 jet In Principle Fragmentation function QM2005, Budapest

  29. CCOR (ISR) s = 63 GeV see A.L.S. Angelis, Nucl Phys B209 (1982) Correct +- 1/xE  -5.3 xE in pp collisions J. Rak, Hot Quarks 2004 PHENIX preliminary 1/xE  -4 to –5 QM2005, Budapest

  30. FFn D(z) Slope of the fragmentation function in p+p collisions at s=200 GeV ztrigg PHENIX preliminary z extracted from pp data xTtrigg=2.pTtrigg/s We measured xE and parton distribution J. Rak, Hot Quarks 2004 QM2005, Budapest

  31. Monte carlo Monte carlo Di-jet fragmentation J. Rak, Hot Quarks 2004 Q2 > Q2 z>z z<z pTassoc pTq pTq pTtrig QM2005, Budapest

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