Systematic Parametrization of the Leading $B$-meson Light-Cone Distribution Amplitude

TL;DR

This paper introduces a systematic parametrization of the leading B-meson LCDA in HQET, enabling controlled truncation, analytical expressions, and flexible incorporation of phenomenological constraints for improved theoretical and experimental analyses.

Contribution

It presents a novel conformal transformation-based parametrization of the B-meson LCDA with analytical expressions and RG evolution, facilitating phenomenological applications and error control.

Findings

Provides a Taylor expansion with integral bounds for error control

Derives analytical expressions involving hypergeometric functions

Demonstrates versatility through phenomenological pseudo-fits

Abstract

We propose a parametrization of the leading $B$-meson light-cone distribution amplitude (LCDA) in heavy-quark effective theory (HQET). In position space, it uses a conformal transformation that yields a systematic Taylor expansion and an integral bound, which enables control of the truncation error. Our parametrization further produces compact analytical expressions for a variety of derived quantities. At a given reference scale, our momentum-space parametrization corresponds to an expansion in associated Laguerre polynomials, which turn into confluent hypergeometric functions ${}_1F_1$ under renormalization-group evolution at one-loop accuracy. Our approach thus allows a straightforward and transparent implementation of a variety of phenomenological constraints, regardless of their origin. Moreover, we can include theoretical information on the Taylor coefficients by using the local operator production expansion. We showcase the versatility of the parametrization in a series of phenomenological pseudo-fits.