Inverse moment of the $B$-meson quasi distribution amplitude

TL;DR

This paper investigates the inverse moment of the $B$-meson quasi distribution amplitude, deriving evolution equations and exploring factorization in the large velocity limit to aid lattice calculations and perturbative matching.

Contribution

It provides the first derivation of the renormalization group and velocity evolution equations for the inverse moment of $B$-meson quasi-DA, revealing factorization properties at large velocities.

Findings

Derived evolution equations for the inverse moment of quasi-DA.

Showed factorization into LCDA moments in the large velocity limit.

Facilitated understanding of perturbative matching and lattice evaluations.

Abstract

We perform a study on the structure of inverse moment (IM) of quasi distributions, by taking $B$-meson quasi distribution amplitude (quasi-DA) as an example. Based on a one-loop calculation, we derive the renormalization group equation and velocity evolution equation for the first IM of quasi-DA. We find that, in the large velocity limit, the first IM of $B$-meson quasi-DA can be factorized into IM as well as logarithmic moments of light-cone distribution amplitude (LCDA), accompanied by short distance coefficients. Our results can be useful either in understanding the patterns of perturbative matching in Large Momentum Effective Theory or evaluating inverse moment of $B$-meson LCDA on the lattice.