Nonrelativistic Bound States in Quantum Field Theory

TL;DR

This paper develops an effective field theory approach to nonrelativistic bound states, enabling precise calculations of energy levels and cross-sections in QED and QCD with reduced uncertainties.

Contribution

It introduces the use of the velocity renormalization group to sum large logarithms, improving the accuracy of bound state predictions in quantum field theory.

Findings

Computed energy corrections up to order alpha^8 ln^3 alpha in QED.

Determined quark potentials in QCD using the velocity renormalization group.

Achieved a tenfold reduction in scale uncertainties for t-tbar production cross-section.

Abstract

Nonrelativistic bound states are studied using an effective field theory. Large logarithms in the effective theory can be summed using the velocity renormalization group. For QED, one can determine the structure of the leading and next-to-leading order series for the energy, and compute corrections up to order alpha^8 ln^3 alpha, which are relevant for the present comparison between theory and experiment. For QCD, one can compute the velocity renormalization group improved quark potentials. Using these to compute the renormalization group improved t-tbar production cross-section near threshold gives a result with scale uncertainties of 2%, a factor of 10 smaller than existing fixed order calculations.