The influence of heavy quark potential on quarkonium production in quark-gluon plasma

Abstract

Remler formalism is the Wigner projection of a two particle state to bound states, which is carried out when the bound state begins to exist or when one of the two particles scatters in medium. This method has been successfully applied to quarkonium production in box simulations and in heavy-ion collisions. In this study this method is extended to strongly bound states with considerable binding energies by taking into account the potential energy between heavy quark pairs in the quark-gluon plasma (QGP). We find that an attractive heavy-quark potential enhances quarkonium production and the results are consistent with those from the statistical model in box simulations, if a proper spatial cutoff is introduced to the potential to mimic quantum effects.

Figures (9)

• Figure 1: The ratio of color singlet to color octet at $T_c$ as a function of charm fugacity in the presence of pQCD heavy quark potential from Eq. (\ref{['V-pQCD']}), assuming $\alpha_s$ and $m_c$ are respectively $\pi/12$ and 1.8 GeV Song:2024rjh.
• Figure 2: (Upper) Wavefunction of $J/\psi$ at the temperature from 1.0 $T_c$ to 1.2 $T_c$ and (lower) the mass, binding energy and radius of $J/\psi$ along with charm quark mass for the free-energy potential Gubler:2020hftSatz:2005hx as a function of temperature.
• Figure 3: Wigner functions at 1.0 $T_c$ (upper) from the definition of the Wigner function in Eq. (\ref{['wigner-general']}) and (lower) from the gaussian form in Eq. (\ref{['wigner']}).
• Figure 4: The ratios of the number density from the Wigner projection to that from the statistical model for (upper) $J/\psi$ and (lower) $\Upsilon (1S)$ with and without the modification of the heavy quark distribution due to the free energy heavy-quark potential Gubler:2020hftSatz:2005hx. The ratio is separated into the two different cases where the Wigner function is calculated directly from the wavefunction as in Eq. (\ref{['wigner-general']}) and calculated from the gaussian form in Eq. (\ref{['wigner']}).
• Figure 5: The probability for the ground state in 1-dimensional simple harmonic oscillator as a function of scaled temperature in quantum statistics and from the Wigner projection