Leading logarithms of heavy quark masses in processes with light and heavy quarks

Abstract

The matrix elements of operators containing both heavy quark (Q) and light quark (q) fields can contain large logarithms of the type ln( m Q 2/ μ 2), where μ is a typical QCD mass scale and m Q is the heavy quark mass. We outline a method for summing leading logarithms of this type. We apply it to the decay constant f M of a low lying pseudoscalar meson M with Q̄q flavor quantum numbers and predict the ratios of decay constants for mesons with different heavy flavors. We also apply it to a matrix element of a four-quark operator which is relevant for B 0−B̄ 0 mixing.