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

TL;DR

This paper introduces a lattice-based method to study the short-distance behavior of the $B$-meson Ioffe-time distribution amplitude, facilitating the extraction of the meson's light-cone distribution amplitude.

Contribution

It develops a formalism using parton pseudo-distributions for lattice investigation of heavy-light meson LCDAs, including a finite, continuum-limit-guaranteed reduced ITDA.

Findings

Constructed a reduced ITDA for the $B$-meson.

Derived the matching relation between reduced ITDA and LCDA.

Reduced ITDA is ultraviolet finite, enabling continuum limit on lattice.

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.