Higher-order Wilson coefficients for c → u transitions in the standard model

Abstract

The standard theoretical framework to deal with weak decays of heavy mesons is the so-called weak effective Hamiltonian. It involves the short-distance Wilson coefficients, which depend on the renormalisation scale μ. For specific calculations one has to evolve the Wilson coefficients down from the electroweak scale μ = MW to the typical mass scale of the decay under consideration. This is done by solving a renormalisation group equation for the effective operator basis. In this paper the results of a consistent two-step running of the c → u ℓ+ℓ− Wilson coefficients for dimension-6 operators are presented. This running involves the intermediate scale μ = mb (with MW> mb> mc) where the bottom quark is integrated out. The matching coefficients and anomalous dimensions are taken to the required order by generalizing and extending results from b → s or s → d transitions available in the literature.