Non-local matrix elements in $B_{(s)}\to \{K^{(*)},\phi\}\ell^+\ell^-$

TL;DR

This paper refines the theoretical calculation of non-local matrix elements in rare B-meson decays using improved sum rules and introduces a dispersive bound to better control extrapolation errors, with applications to form factor predictions.

Contribution

It provides the first dispersive bound on non-local matrix elements and improves the calculation of these elements using updated light-cone sum rules.

Findings

Recalculated hadronic matrix elements at subleading power.

Derived the first dispersive bound on non-local matrix elements.

Provided numerical results for B_s to phi form factors.

Abstract

We revisit the theoretical predictions and the parametrization of non-local matrix elements in rare $\bar{B}_{(s)}\to \lbrace \bar{K}^{(*)},\phi\rbrace\ell^+\ell^-$ and $\bar{B}_{(s)}\to \lbrace \bar{K}^{*}, \phi\rbrace \gamma$ decays. We improve upon the current state of these matrix elements in two ways. First, we recalculate the hadronic matrix elements needed at subleading power in the light-cone OPE using $B$-meson light-cone sum rules. Our analytical results supersede those in the literature. We discuss the origin of our improvements and provide numerical results for the processes under consideration. Second, we derive the first dispersive bound on the non-local matrix elements. It provides a parametric handle on the truncation error in extrapolations of the matrix elements to large timelike momentum transfer using the $z$ expansion. We illustrate the power of the dispersive bound at the hand of a simple phenomenological application. As a side result of our work, we also provide numerical results for the $B_s \to \phi$ form factors from $B$-meson light-cone sum rules.