$B$-meson Ioffe-time distribution amplitude at short distances

Abstract

We propose the approach for a lattice investigation of light-cone distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$-meson, using the formalism of parton pseudo-distributions. A basic ingredient of the approach is the study of short-distance behavior of the $B$-meson Ioffe-time distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA in coordinate space. We construct a reduced ITDA for the $B$-meson, and derive the matching relation between the reduced ITDA and the LCDA. The reduced ITDA is ultraviolet finite, which guarantees that the continuum limit exists on the lattice.