Temperature-dependent cross sections
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Temperature-dependent cross sections for charmonium dissociation in collisions with pions and rhos in hadronic matter. Xiao-Ming Xu Collaborator: Jie Zhou. phenomena: (a) J/ suppression in a heavy ion collision; (b) J/  enhancement in some momentum region.

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Xiao-Ming Xu Collaborator: Jie Zhou

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Temperature-dependent cross sectionsfor charmonium dissociation in collisions with pions and rhos in hadronic matter

Xiao-Ming Xu

Collaborator: Jie Zhou


phenomena:(a) J/ suppression in a heavy ion collision;(b) J/  enhancement in some momentum region.

Dissociation mechanisms (color screening, charmonium dissociation in collisions with gluons, charmonium dissociation in collisions with hadrons), recombination mechanism and nuclear parton shadowing build various models to explain the phenomena.


J/ suppression reasons:

Color screening (T. Matsui, H. Satz, Phys. Lett. B178 (1986) 416)

Dissociated by a gluon (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)

Dissociated by a 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)

J/ + hadron  charmed mesons (charmed baryons)

Nuclear shadowing


J/ enhancement reason

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) 054905


Evidence of nuclear shadowing at LHCX.-M. Xu, Nucl. Phys. A697 (2002) 825; CMS-HIN-10-006


evidence of the recombination mechanism at LHCCMS-HIN-10-006


quark model calculations:

K. Martins et al., Phys. Rev. C51 (1995) 2723

C.-Y. Wong et al., Phys. Rev. C65 (2001) 014903

T. Barnes et al., Phys. Rev. C68 (2003) 014903

X.-M. Xu et al., Nucl. Phys. A713 (2003) 470

············

meson exchange model calculations:

S.G. Matinyan, B. Muller, Phys. Rev. C58 (1998) 2994

K .Haglin, Phys. Rev. C61 (2000) 031902

Z. Lin, C.M. Ko, Phys. Rev. C62 (2000) 034903

············

For J/ + hadron  charmed mesons (charmed baryons),early works assumed that hadron-charmonium dissociation cross sections are constants; quark model calculations or meson exchange model calculations have obtained the dissociation cross sections that depend on the center-of-mass energy of J/ and hadron.


problem

What is the temperature dependence of hadron-charmonium dissociation cross sections?


Prior form: gluon propagation before quark interchange


Post form: gluon propagation after quark interchange


phase shift

Experimental data of S-wave I=2 elastic phase shifts for  scattering in vacuum for

are reproduced.


unpolarized cross section


transition amplitude in the prior form

transition amplitude in the post form


Buchmuller-Tye potential in vacuum

Linear confinement and the potential arising from one gluon exchange plus perturbative one- and two-loop corrections

W. Buchmuller, S.-H.H. Tye, Phys. Rev. D24 (1981) 132


T=0.58Tc

T=0.66Tc

T=0.74Tc

T=0.84Tc

T=0.9Tc

T=0.94Tc

T=0.97Tc

T=1.06Tc

T=1.15Tc

F. Karsch, et al., Nucl. Phys. B605, 579 (2001)


Medium Effect

Lattice QCD calculations give temperature-dependent quark-quark potential.

Medium screening leads to weak binding of quarks.

When temperature increases, the confinement potential gets weak and the bound state gets loose.


central spin-independent andtemperature-dependent potential in medium

critical temperature Tc=0.175 GeV.

Y.-P. Zhang, X.-M. Xu, H.-J. Ge, Nucl. Phys. A 832 (2010) 112


the parametrization fit to the lattice data


spin-spin interaction

arising from one gluon exchange plus perturbative one- and two-loop corrections by means of Foldy-Wouthuysen canonical transformation.


meson masses at T=0

mass splittings experimental values

m-m=0.6294 GeV 0.6304 GeV

mK*-mK=0.39865 GeV 0.3963 GeV

masses

mJ/=3.13509 GeV 3.096916 GeV

m´=3.69248 GeV 3.68609 GeV

mc=3.50578 GeV 3.5253 GeV

mD=1.90578 GeV 1.86722 GeV

mD*=2.05274 GeV 2.00861 GeV


meson masses from the Schrodinger equation with Vsi+Vss


meson masses from the Schrodinger equation with Vsi+Vss


charmonium dissociation

Calculate the transition amplitudes, and ,

with the Fourier transform of thepotential Vsi+Vss to obtain unpolarized cross sections for 15 reactions


parametrizations

For endothermic reactions

For exothermic reactions


SUMMARY

We have offered

(1) a temperature-dependent quark potential;

(2) temperature-dependent meson masses;

(3) temperature-dependent cross sections for -charmonium and -charmonium dissociation reactions.


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