Non-relativistic bound states at finite temperature (I): the hydrogen atom

Understand

We illustrate how to apply modern effective field theory techniques and dimensional regularization to factorize the various scales which appear in non-relativistic 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 non-relativistic 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.