In-medium heavy quark-antiquark $T$-matrix without partial wave expansion

TL;DR

This paper introduces a method to compute the heavy quark-antiquark T-matrix in quark-gluon plasma without partial wave expansion, revealing the necessity of many partial waves for accurate results and enabling the study of bound states.

Contribution

The paper presents a novel approach to calculate the T-matrix directly without partial wave expansion, improving efficiency and accuracy in analyzing quark-antiquark interactions in QGP.

Findings

Many partial waves (10-20) are needed for accurate scattering amplitude matching.

The new method efficiently computes the full scattering amplitude.

Bound states with different quantum numbers are identified below the mass threshold.

Abstract

The T-matrix of the heavy quark-antiquark ($Q\bar{Q}$) pair interacting through a screened Cornell potential in the quark-gluon plasma (QGP) is computed without employing the partial wave expansion. This is compared with the results obtained using the conventional method of partial wave expansion. Through a comprehensive survey over a range of screening mass and center-of-mass energy, which, when combined, determine the orbital angular momentum involved in the scattering through the associated force range and incident momentum, it is demonstrated that a substantial number of partial wave terms are necessary to precisely match the full scattering amplitude directly obtained from the method without partial wave expansion. For moderate screening masses (corresponding to one to two times the crossover transition temperature) and center-of-mass energy, the number of partial waves required for satisfactory matching turns out as large as 10-20, substantially larger than what one would expect based on simply measuring the magnitudes of the first few partial wave amplitudes. This highlights the efficiency of the new method in directly obtaining the full scattering amplitude needed for further computation of phenomenological observables. We also employ the new method to calculate the T-matrix at center-of-mass energies below the $Q\bar{Q}$ mass threshold, and demonstrate the presence of bound states of different orbital quantum numbers simultaneously in a single energy scan.