[Paper Review] Survival of Bc mesons in a hot plasma within a potential model

W.M. Alberico, Stefano Carignano+4 more|arXiv (Cornell University)|Nov 22, 2013

High-Energy Particle Collisions Research4 citations

TL;DR

This paper investigates the survival of $B_c$ mesons in a hot quark-gluon plasma using a finite-temperature potential model derived from lattice QCD data. By solving the Schrödinger equation with a temperature-dependent potential, the study finds that the $B_c$ ground state remains bound up to approximately 1.9–2.0$T_c$, while excited states dissociate near $T_c$, indicating robust survival of $B_c$ mesons in high-temperature environments relevant to heavy-ion collisions at the LHC.

ABSTRACT

We extend a previous work on the study of heavy charmonia and bottomonia in a deconfined quark-gluon plasma by considering the Bc family of mesons. With the introduction of this bound state of a charm and a beauty quark, we investigate at finite temperature the behavior of the quarkonium, in an energy region between the ψ and the Υ states.

Motivation & Objective

• To investigate the stability and survival of $B_c$ mesons in a deconfined quark-gluon plasma at finite temperature.
• To extend existing potential models for charmonia and bottomonia to include the $B_c$ meson, a bound state of a charm and a beauty quark.
• To determine the dissociation temperatures of $B_c$ states and assess their potential as probes of the deconfined medium in heavy-ion collisions.
• To compute spectral functions and radial wave functions at finite temperature to connect theoretical predictions with lattice QCD and experimental observables.

Proposed method

• A non-relativistic potential model is employed, based on effective temperature-dependent potentials extracted from lattice QCD calculations of the color singlet free energy.
• The potential is constructed using a fit to lattice data for $F_1(r,T)$, incorporating a temperature-dependent coupling $\alpha(r,T)$ via the renormalization group equation.
• The Schrödinger equation is solved numerically with the effective potential $V(r,T) = U_1(r,T) - U_1(\infty,T)$ to obtain energy eigenvalues and radial wave functions.
• Spectral functions are computed using the radial wave function values at the origin, $|R(0)|^2$ and $|R'(0)|^2$, to model meson correlators and compare with lattice results.
• Finite widths ($\Gamma = 100$ MeV) and asymptotic $\omega^2$ behavior corrections are applied to spectral functions for improved comparison with lattice and perturbative QCD.
• Dissociation temperatures are determined as the point where binding energy vanishes, corresponding to the disappearance of the bound state peak in the spectral function.

Experimental results

Research questions

• RQ1 At what temperature does the $B_c$ meson begin to dissociate in a hot quark-gluon plasma?
• RQ2 How does the binding energy of the $B_c$ meson evolve with increasing temperature above $T_c$?
• RQ3 Can the $B_c$ meson survive above $T_c$ and serve as a probe of the deconfined medium in heavy-ion collisions?
• RQ4 How do the spectral functions of $B_c$ states, including $S$- and $P$-wave states, evolve with temperature?
• RQ5 What is the role of the $B_c$ meson's long lifetime and suppressed decay channels in its detectability in high-energy experiments?

Key findings

• The $B_c$ ground state survives up to approximately 1.9–2.02$T_c$, depending on the choice of quark masses, indicating strong stability in the hot medium.
• The $\chi_{B_c}$ P-wave state dissociates at $T \sim 1.05T_c$, while the $B_c'$ excited state dissociates slightly later, at $T \sim 1.04$–$1.05T_c$.
• The $S$-wave spectral function shows a broadened but still visible peak up to $2T_c$, indicating persistence of the bound state beyond $T_c$.
• The radial wave function at the origin, $|R(0)|^2$, decreases with temperature but remains non-zero up to $\sim 1.9T_c$, supporting continued binding.
• The P-wave spectral function shows a clear dissociation near $T_c$, with the peak vanishing as $T$ increases.
• The model predicts that $B_c$ mesons can be detected in heavy-ion experiments such as ALICE and CMS, especially via the $J/\psi + \pi$ decay channel, due to their long lifetime and robust survival.