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

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