Electromagnetic Production Of Heavy Quarkonium And Its Dissociation In The Thermal Matter

The inelastic electromagnetic production of heavy quarkonium in p-p ultra-relativistic collisions and the heavy quarkonium dissociation in thermal medium through the thermal width mechanism are discussed in this paper.A complete treatment for the inelastic electromagnetic process that the vir-tual photons emitted from the incoming nucleon interact with the partons in the target nucleon is developed. Comparing with the traditional treatment which is called the equivalent photon approximation approach, the complete treatment has a higher accuracy and wider range of application, and recovers the equivalent pho-ton approximation approach in the limit that the photon virtuality Q2â†'0. In order to avoid the double counting problem, the coherent and incoherent contribu-tions are considered simultaneously by using the weight factor method of Martin and Ryskin. The numerical results show that, the equivalent photon approxima-tion approach is only effective in the small Q2 region where Qmax2<1GeV2. It can be seen that, a improper choice of Qmax2, widely used in the previous works where Qmax2 is set to be the order of s (the centre-of-mass frame energy square of the photo-absorption process) or even infinity, will cause obvious errors in the equivalent photon approximation approach (especially the incoherent cross section are more than 2 times larger than the exact one, and more than 6 times larger than the exact one while the weight factor method is not considered), and the ex-act treatment needs to be adopted to dealing with the widely kinematics region of Q2. Although the complete treatment is used to deal with the p-p ultra-peripheral collisions (where the electromagnetic reaction is one of the main processes) in this paper, it also can be used to study the corresponding processes in p-p central collisions where the electromagnetic reaction should be considered as the high or-der corrections for the leading order strong interactions. On the other hand, the framework also can be used to deal with the inelastic electromagnetic production of any other particles in p-p collisions.The thermal width, provided by the imaginary part of the potential, gives the most important contribution to the quarkonium dissociation at high temper-ature. In this paper, the transverse gluon contributions for the thermal width of quarkonium is studied. The single transverse gluon exchange potential is obtained by using the Fourier transforms from the hard-thermal-loop resumed transverse gluon propagator in the static limit. The damping rates resummation method, developed by Hou De-Fu and Li Jia-Rong is used to deal with the infrared prob-lem in the calculation. The thermal width from the transverse gluon is obtained. The results show that the dissociation scales of quarkonia in thermal medium are decreased by the transverse gluon contributions. On the other hand, the assump-tion of hard-thermal-loop approximation, which requires the coupling constant g<<1, conflicts with the fact that the hot matter, generated with the present ex-periment condition, is not a weak-coupling medium. In this paper, the complete forms of the single longitudinal gluon exchange potential are studied. The self energies in covariant and physical gauges are used to obtain the resumed single gluon propagator, and calculate the corresponding effective potential. The com-parisons between the complete results and the corresponding ones with the hard thermal loop approximation are illustrated. The numerical results show that the hard thermal loop thermal single-gluon exchange potential which used in many researches make some errors in the practical calculations at the temperature range accessible in the present experiment, and the problem of gauge dependent can not be avoided when the complete self energy is used.