Rapidity resummation for $B$-meson wave functions

TL;DR

This paper reviews recent advances in rapidity resummation techniques for $B$-meson wave functions, highlighting their impact on TMD factorization and phenomenological predictions in $B$-decays.

Contribution

It summarizes the progress on rapidity resummation for $B$-meson wave functions and discusses its effects on TMD factorization and decay form factors.

Findings

Rapidity resummation suppresses $B$-meson wave functions at small light-quark momentum.

Resummation enhances the applicability of TMD factorization in exclusive $B$-decays.

Improved wave functions influence predictions of $B o \pi$ transition form factors.

Abstract

Transverse-momentum dependent (TMD) hadronic wave functions develop light-cone divergences under QCD corrections, which are commonly regularized by the rapidity $\zeta$ of gauge vector defining the non-light-like Wilson lines. The yielding rapidity logarithms from infrared enhancement need to be resummed for both hadronic wave functions and short-distance functions, to achieve scheme-independent calculations of physical quantities. We briefly review the recent progress on the rapidity resummation for $B$-meson wave functions which are the key ingredients of TMD factorization formulae for radiative-leptonic, semi-leptonic and non-leptonic $B$-meson decays. The crucial observation is that rapidity resummation induces a strong suppression of $B$-meson wave functions at small light-quark momentum, strengthening the applicability of TMD factorization in exclusive $B$-meson decays. The phenomenological consequence of rapidity-resummation improved $B$-meson wave functions is further discussed in the context of $B \to \pi$ transition form factors at large hadronic recoil.