J/  momentum distribution in heavy ion collisions at LHC Xiao-Ming Xu

outline a brief review of J/  mechanisms dissociation cross sections from a quark- interchange model prediction on J/  produced in central Au- Au collisions at LHC summary

fundamental processes verified at SPS

dissociation in QGP T. Matsui, H. Satz, Phys. Lett. B178 (1986) 416 color screening M.E. Peskin, Nucl. Phys. B156 (1979) 365 G. Bhanot, M.E. Peskin, Nucl. Phys. B156 (1979) 391 D. Kharzeev, H. Satz, Phys. Lett. B334 (1994) 155 LO T. Song, S.H. Lee, Phys. Rev. D72 (2005) NLO

dissociation in hadronic matter (1) constant cross sections J/  + hadron  charmed mesons Dissociation cross sections of J/  in collisions with hadrons are assumed to be independent of the center- of-mass energy of J/  and hadron. J. Ftacnik et al., Phys. Lett. B207 (1988) 194 S. Gavin et al., Phys. Lett. B207 (1988) 257 R. Vogt et al., Phys. Lett. B207 (1988) 263 C. Gerschel et al., Phys. Lett. B207 (1988) 253

dissociation in hadronic matter (2) quark model calculations J/  + hadron  charmed mesons Barnes-Swanson quark-interchange model The dissociation cross sections depend on the center- of-mass energy of J/  and hadron. K. Martins et al., Phys. Rev. C51 (1995) 2723 C.-Y. Wong et al., Phys. Rev. C65 (2001) T. Barnes et al., Phys. Rev. C68 (2003) X.-M. Xu et al., Nucl. Phys. A713 (2003) 470

dissociation in hadronic matter (3) meson exchange model calculations J/  + hadron  charmed mesons hadronic effective Lagrangians The dissociation cross sections depend on the center-of- mass energy of J/  and hadron. S.G. Matinyan, B. Muller, Phys. Rev. C58 (1998) 2994 K.Haglin, Phys. Rev. C61 (2000) Z. Lin, C.M. Ko, Phys. Rev. C62 (2000) ············

fundamental processes verified at RHIC

recombination mechanism X.-M. Xu, Nucl. Phys. A658 (1999) 165 P. Braun-Munzinger, J. Stachel, Phys. Lett. B490 (2000) 196 R.L. Thews, M. Schroedter, J. Rafelski, Phys. Rev. C63 (2001) L. Grandchamp, R. Rapp, Phys. Lett. B523 (2001) 60. M.I. Gorenstein, A.P. Kostyuk, H. Stöcker, W. Greiner, Phys. Lett. B509 (2001) 277 ············

Azimuthal Asymmetry of J/  production X.-N. Wang, F. Yuan, Phys. Lett. B540 (2002) 62 J/  is affected only by v 2 ( p T =3 GeV, N P =130 )  at RHIC Z.W. Lin, D. Molnar, Phys. Rev. C68 (2003) V. Greco, C.M. Ko, R. Rapp, Phys. Lett. B595 (2004) 202 L. Yan, P. Zhuang, N. Xu, Phys. Rev. Lett. 97 (2006) J/  is affected by dissociation and recombination But the recombination dominates the elliptic flow v 2 at LHC.

Challenge: Can we discover a new mechanism for J/  at LHC?

Results of quark interchange processes

Prior form: gluon propagation before quark interchange

Post form: gluon propagation after quark interchange

T. Barnes, E.S. Swanson, C.-Y. Wong, X.-M. Xu, Phys. Rev. C 68, (2003) interaction: T-matrix element: unpolarized cross section:

Few model predictions on J/  for LHC nucleus-nucleus collisions X.-M. Xu, D. Kharzeev, H. Satz, X.-N. Wang, Phys. Rev. C53 (1996) 3051 X.-M. Xu, Nucl. Phys. A658 (1999) 165  X.-M. Xu, Nucl. Phys. A697 (2002) 825  ············

history of Au-Au nuclear collisions initial nucleon-nucleon collisions; thermalization of quark-gluon matter; evolution of quark-gluon plasma; hadronization at a critical temperature; evolution of hadronic matter until freeze-out.

production of is a pointlike color singlet or a color octet pair from is produced in the initial nuclear collisions, during the thermalization of quark-gluon matter, in the evolution of quark-gluon plasma.

recombination Probability for to form a bound state is proportional to the NRQCD nonperturbative matrix elements  Ο 8 H ( 3 S 1 )  = constant  Ο 8 H ( 1 S 0 )  = constant  Ο 8 H ( 3 P 0 )  = constant Ο 8 H ( 3 S 1 )=χ + σT a ψ · (a + H a H )ψ + σT a χ Ο 8 H ( 1 S 0 )=χ + T a ψ (a + H a H ) ψ + T a χ ψ the field that annihilates a heavy quark. χ the field that creates a heavy antiquark.

dissociation penetrates through deconfined matter and hadronic matter, interacts with partons in deconfined matter interacts with hadrons in hadronic matter

two definitions Charmonium is prompt if the point at which the charmonium state is produced and the collision point of the colliding beams cannot be resolved using a vertex detector. A charmonium coming from the decay of b-hadrons is not prompt. Charmonium is direct if the charmonium is prompt but does not come from the decay of a higher charmonium state. The prompt J/  includes direct J/  as well as the radiative feeddown from direct  cJ and direct .

= short-distance production  recombination  dissociation charmonium from initial nuclear collisions charmonium from prethermal stage charmonium from thermal stage

p T - and y- spectra Momentum distribution of J/  : produced during the thermalization of quark-gluon matter and in the evolution of quark-gluon plasma cause enhancement of J/  in some momentum region.

Nucl. Phys. A658(1999)165  direct J/  at y=0

Nucl. Phys. A658(1999)165  direct J/  at p T =4 GeV

Nucl. Phys. A697(2002)825  prompt J/  at p T =4 GeV in the left panel and at y=0 in the right panel

Summary (1) Has the study of J/  at both SPS and RHIC accomplished the discovery of mechanisms for J/  in nucleus-nucleus collisions? (2) Quark interchange model offers a way to calculate cross sections for charmonia dissociated by hadrons, which depend on the center-of-mass energy of hadron-charmonium. (3) Competition between charmonium dissociation and charmonium formed from charm quarks and antiquarks in deconfined matter. (4) J/  Enhancement in some momentum region.

S-wave dominates the reaction

P-wave dominates the reaction

Discrepancy of prior form and post form results

Post-prior discrepancy

F. Karsch et al., Nucl. Phys. B 605, 579 (2001) central inter-quark potential of lattice gauge results C.-Y. Wong, Phys. Rev. C 65, (2002) temperature-dependent central potential for spin-spin term  =0.28 GeV and T c =0.175 GeV X.-M. Xu, C.-Y. Wong, T. Barnes, Phys. Rev. C 67, (2003)