Effective field theory approach to processes involving both light and heavy fields

Abstract

The matrix elements of operators containing both heavy quark (Q) fields and light particle fields can contain logarithms of the type In( m Q μ ) if (in some frame) the heavy quark is approximately static (i.e., | p Q |⪡m Q ) and the light particles' typical momentum is of order μ⪡ m Q. By performing the functional integral over the heavy quark fields first and treating their mass as very large (so that the heavy quarks are essentially static color sources), the logarithms of ( m Q μ ) are determined by the “infinite” parts of Feynman diagrams involving only the light fields. We show how to sum these logarithms using a renormalization group equation derived from a mass-independent subtraction scheme.