Long-distance weak annihilation contribution to the $B^{\pm}\to (\pi^{\pm},K^{\pm}) \ell^+\ell^-$ decays

TL;DR

This paper evaluates the long-distance weak annihilation contribution to rare B meson decays into pions and kaons, highlighting its significance for decay rates and CP asymmetry, and emphasizing its importance in new physics searches.

Contribution

It introduces an alternative hadronic approach to estimate long-distance weak annihilation effects in B decays, bridging low and intermediate energy descriptions.

Findings

Weak annihilation significantly affects branching ratios and CP asymmetry in B to pion decays.

Interference with short-distance amplitudes induces sizable CP asymmetry.

The contribution is negligible for lepton-universality tests but crucial for accurate decay analysis.

Abstract

We propose an alternative evaluation of the long-distance weak annihilation (WA, also called one-photon exchange in this paper) contribution to the rare semileptonic $B^{\pm}\to (\pi^{\pm},K^{\pm})\ell^+\ell^-$ ($\ell=e,\,\mu$) decays. This hadronic description at low energies is matched at intermediate energies to its short-distance counterpart in terms of quark and gluon degrees of freedom. Although the WA contribution does not contribute to solve the possible breaking of lepton-universality observed by LHCb in the $B^{\pm}\to K^{\pm}(\mu^+\mu^-/e^+e^-)$ ratio, nor provides an important hadronic contamination to their decay rates, its contribution to the branching ratios (and direct CP asymmetry) of the $B^{\pm}\to \pi^{\pm}\ell^+\ell^-$ transitions turns out to be significant. This hadronic pollution should be taken into account when looking for new physics effects in decays into pions, which suggests to restrict these searches to squared lepton-pair invariant mass in the $(1,8)$ GeV$^2$ range. The interference of the one-photon exchange contribution with the dominant short-distance one-loop amplitude induces a sizable CP asymmetry in these rare decays, which calls for dedicated measurements.