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

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.