The spin-orbit potential and Poincar\'e invariance in finite temperature pNRQCD

TL;DR

This paper investigates how finite temperature affects the spin-orbit potential in pNRQCD, revealing that thermal effects break Poincaré invariance, which is preserved at zero temperature, through leading-order thermal corrections.

Contribution

It provides the first calculation of thermal corrections to the spin-orbit potential in pNRQCD_HTL, demonstrating the violation of Poincaré invariance at finite temperature.

Findings

Thermal corrections to spin-orbit potential are computed at leading order.

Poincaré invariance is broken by thermal effects in the effective field theory.

Results highlight the impact of temperature on heavy quarkonium properties.

Abstract

Heavy quarkonium at finite temperature has been the subject of intense theoretical studies, for it provides a potentially clean probe of the quark-gluon plasma. Recent studies have made use of effective field theories to exploit in a systematic manner the hierarchy of energy scales that characterize the system. In the case of a quarkonium in a medium whose temperature is smaller than the typical momentum transfer in the bound state but larger than its energy, the suitable effective field theory is pNRQCD_HTL, where degrees of freedom with energy or momentum larger than the binding energy have been integrated out. Thermal effects are expected to break Poincar\'e invariance, which, at zero temperature, manifests itself in a set of exact relations between the matching coefficients of the effective field theory. In the paper, we evaluate the leading-order thermal corrections to the spin-orbit potentials of pNRQCD_HTL and show that Poincar\'e invariance is indeed violated.