Effective Field Theory and Matching in Non-Relativistic Gauge Theories

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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11 pages LATEX. Version to appear in PRD. Paragraph regarding non-local four quark operators included. Comparison of magnetic

Scientific paper

10.1103/PhysRevD.57.78

The effective Lagrangian and power counting rules for non-relativistic gauge theories are derived via an expansion in $1/c$. It is shown that the $1/c$ expansion leads to an effective field theory which incorporates a multipole expansion. Failure to use this expansion in the low energy theory leads to a loss of predictive power as the matching procedure becomes intractable. It is emphasized that there is not a one-to-one correspondence between operators in the modified low energy theory and those in the heavy quark effective theory.We also discuss the Lamb shift as a pedagogical example of the power counting scheme.

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