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

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.

28 pages, 1 table. Numerical factors in formulas (23), (25), (26) and (28), as well as a few misprints elswhere corrected. Supersedes journal version

References in corpus (14)

• Effective field theories for heavy quarkonium
• Real-time static potential in hot QCD
• Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
• The HQET/NRQCD Lagrangian to order alpha/m^3
• Potential NRQED: The Positronium Case
• Rigourous QCD Evaluation of Spectrum and Ground State Properties of Heavy Quarkonium Systems; with a Precision Determination of the bottom quark mass and of the eta-b mass
• Heavy quarkonium in any channel in resummed hot QCD
• Positronium S state spectrum: analytic results at O(m alpha^6)
• A resummed perturbative estimate for the quarkonium spectral function in hot QCD
• The Lamb Shift in Dimensional Regularization
• Logarithms of alpha in QED bound states from the renormalization group
• Radiative decays and the nature of heavy quarkonia
• Renormalization group improvement of the spectrum of Hydrogen-like atoms with massless fermions
• Open questions in quarkonium and electromagnetic probes

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