Nonrelativistic bound states at finite temperature: The hydrogen atom

We illustrate how to apply modern effective field theory techniques and dimensional regularization to factorize the various scales that appear in nonrelativistic bound states at finite temperature. We focus here on the simplest case: the hydrogen atom. We discuss in detail the interplay of the hard, soft, and ultrasoft scales of the nonrelativistic system at zero temperature with the additional scales induced at finite temperature. We also comment on the implications of our results for heavy quarkonium bound states in the quark gluon plasma.