Laboratory-frame $T$-matrix and heavy quark drag in the quark-gluon plasma

Abstract

Non-perturbative scattering $T$-matrix is a core input for the evaluation of transport phenomena in a strongly-coupled medium. Existing in-medium $T$-matrix calculations are typically formulated in the two-particle center-of-mass frame, where the scattering equation can be reduced to a lower-dimensional problem. However, a medium explicitly breaks Lorentz invariance and defines a preferred reference frame, entailing that physical observables be constructed from scattering amplitudes evaluated in the medium rest (laboratory) frame. In this work, by exploiting the rotational symmetry about the scattering-pair-momentum axis, we develop a practical framework for solving the in-medium two-body $T$-matrix directly in the laboratory frame while retaining the full dependence on the total pair-momentum and scattering geometry. We demonstrate that the resulting amplitudes differ significantly from conventional center-of-mass-frame results and, when applied to heavy-light quark scattering in the quark-gluon plasma (QGP), lead to 25-40% corrections to heavy-quark drag coefficients at low momenta, thereby removing a significant source of theoretical uncertainty in extracting the QGP transport properties with heavy-quark probes.