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.

arXiv comment34 pages, 8 figures, 1 table

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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