Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators

Abstract

When the bilocal heavy-quark effective theory (HQET) operator for the B-meson distribution amplitude has a light-like distance t between the quark and antiquark fields, the scale ∼1/t separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat these notorious UV and IR behaviors simultaneously using the operator product expansion, with the local operators of dimension d⩽5 and radiative corrections at order αs for the corresponding Wilson coefficients. The result is derived in the coordinate space, which manifests the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This result yields the B-meson distribution amplitude for t less than ∼1 GeV−1, in terms of Λ¯=mB−mb and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive B decays, λB, is also discussed.