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

TL;DR

This paper applies effective field theory and dimensional regularization to analyze the hydrogen atom at finite temperature, exploring scale interactions and implications for quarkonium states in quark-gluon plasma.

Contribution

It introduces a modern effective field theory approach to non-relativistic bound states at finite temperature, detailing scale factorization and extending insights to heavy quarkonium.

Findings

Effective field theory techniques effectively separate scales in finite temperature bound states.

Finite temperature introduces new scales affecting the bound state dynamics.

Implications for heavy quarkonium behavior in quark-gluon plasma are discussed.

Abstract

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.