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

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 ${}_1{F}_1$ 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.

34 pages, 8 figures, 1 table

References in corpus (7)

• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• Modelling light-cone distribution amplitudes from non-relativistic bound states
• SCET sum rules for B->P and B->V transition form factors
• B-Meson Light-Cone Distribution Amplitude: Perturbative Constraints and Asymptotic Behaviour in Dual Space
• Two-loop evolution equation for the B-meson distribution amplitude
• Renormalization and Scale Evolution of the Soft-Quark Soft Function
• Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes

Cited by in corpus (4)

• Precision calculations of $B_{d,s}\to \pi ,K$ decay form factors in soft-collinear effective theory
• On the contribution of the electromagnetic dipole operator ${\mathcal{O}}_7$ to the ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay amplitude
• Power corrections to quasi-distribution amplitudes of a heavy meson
• Determination of $B$-meson distribution amplitudes from $B\to \pi ,K,D$ transition form factors