Bc mesons in the deconfined phase

We investigate the early production of heavy quarkonia and their survival while crossing the deconfined medium in relativistic heavy ion collisions. The Bc formation could be favored in a nucleusnucleus collision where many partonic (hard) scatterings can occur simultaneously and then the Bc production might be significantly enhanced. We examine the modification of binding energy of Bc meson due to the increasing temperature of the plasma. In order to study the temperature evolution of the mass and energy eigenvalues of the Bc mesons, we employ a non-relativistic potential model.


Introduction
We investigate the early production of heavy quarkonia and their survival while crossing the deconfined medium in relativistic heavy ion collisions.The B c formation could be favored in a nucleusnucleus collision where many partonic (hard) scatterings can occur simultaneously and then the B c production might be significantly enhanced.We examine the modification of binding energy of B c meson due to the increasing temperature of the plasma.
In order to study the temperature evolution of the mass and energy eigenvalues of the B c mesons, we employ a non-relativistic potential model.

Model and Results
Free energy of a heavy quark-antiquark pair placed at a distance r in a thermal bath of gluons and light dynamical fermions is extracted in lattice calculations from the Polyakov loop correlation function and is fited to: where the coupling α is fixed by the customary RGE, but employing a temperature dependent scale, with coefficients determined, at each temperature (see figure 1).Next, the singlet internal energy  is calculated U = −T 2 ∂(F/T )/∂T, since heavy quarks are acting as static sources of the color field, the internal energy coincides with the potential.V(r, T ) = U(r, T ) − U(r → ∞, T ) and V(r, T ) is then inserted into the Schrödinger equation, from which the binding energy of the different stable states and their evolution with the temperature are obtained, figure 2.
The radial wave function R(0) (or of its first derivative R (0) for the P wave state), figure 3, evaluated in the origin for the B c and χ B c states respectively are used to build the spectral functions at different temperatures.
The spectral function for a generic meson channel σ M (ω, T ) can be written as where F 2 PS = N c 2π |R(0)| 2 for the pseudo-scalar state, figure 4 and for the P-wave scalar state, figure 5.
Finaly, in table 1, we show the dissociation temperatures (defined as the value where the binding energy vanishes) obtained for the various states, in units of the critical temperature T c = 202 MeV.From the table 1 and figure 4, which shows the evolution of the S wave spectral function with the   temperature, one can see that the fundamental bound state peak survives above critical temperature (up to ∼ 2 T c ), while the excited state dissociates around T c .In figure 5 we have the shape of the P-wave spectral function and we see that the fundamental P-wave state dissociates at T ∼ T c .

Conclusions
We have investigated the survival above the critical temperature of a few special quarkonium states, the ones of the B c family, with the main purpose of drawing the attention of the on-going experiments at LHC on these intriguing heavy quarkonia.B c mesons can survive above the temperature for deconfinement of the medium and give important information on the properties of the hot medium itself.

Figure 1 .
Figure 1.The colour singlet free energy F 1 (r, T )/ √ σ at different values of T/T c as a function of the separation r √ σ of the Q Q sources resulting from our fitting procedure compared to the lattice data at different temperatures, with √ σ = 420 MeV [4].

Figure 2 .
Figure 2. Mass as a function of temperature of the lowest S -wave, first S -wave excited and lowest P-wave bc(c b) states as a function of temperature.

Figure 3 .Figure 4 .
Figure 3. Squared value in the origin, for the bc system of the S -wave radial wave function and of the first derivative of the P-wave radial wave function, as a function of temperature.

c b bc m c = 1 . 4
GeV m c = 1.4 GeV m c = 1.6 GeV m c = 1.6 GeV m b = 4.3 GeV m b = 4.7 GeV m b = 4.3 GeV m b = 4.7 GeV B c

Table 1 .
The dissociation temperatures obtained for the various states, in units of T c = 202 MeV.
Figure 5.The bc P-wave channel spectral function divided by ω 2 as a function of ω at different temperatures.