Investigating non-local contributions in $B_{s} \to \phi \bar{\ell} \ell$ including higher-twist effects

TL;DR

This paper studies how higher-twist effects in B_s meson distribution amplitudes influence non-local form factors in B_s to phi l+l- decays, revealing significant enhancements and implications for Standard Model predictions.

Contribution

It introduces a detailed analysis of higher-twist contributions to non-local form factors using light-cone sum rules and hadronic dispersion relations, improving theoretical understanding of charm-loop effects.

Findings

Higher-twist LCDAs increase non-local form factors by about an order of magnitude.

The correction to the Wilson coefficient C_9 is larger but remains within Standard Model uncertainties.

Updated local form factors include higher-twist contributions, affecting decay observables.

Abstract

We analyze the impact of higher-twist three-particle $B_s$-meson light-cone distribution amplitudes (LCDAs) on the non-local form factors for the $B_s\to \phi \bar{\ell} \ell$ transition focusing on the `charm-loop' contribution within the light-cone sum rule (LCSR) framework. To analytically continue these charm-loop contributions into the kinematically allowed region of the decay, we employ a hadronic dispersion relation that incorporates intermediate resonant states such as the $\phi,\,J/\Psi$ and $\psi(2S)$ mesons. Here, the LCSR predictions serve as inputs, supplemented by experimental data from two-body decays $B_s \to \phi ~+$ resonance states. Our results indicate that the inclusion of twist-5 and twist-6 LCDAs enhances the non-local form factors by approximately an order of magnitude compared to previous estimates, due to partial disruption of cancellation among different twist contributions. This leads to a dilepton invariant mass-squared ($q^2$)-dependent correction to the Wilson coefficient $C_9$, which is higher than, but still consistent with the Standard Model prediction without the non-factorizable charm-loop corrections within uncertainties. Additionally, we update the local form factors to include contributions from higher-twist three-particle $B_s$-meson LCDAs. The phenomenological implications, particularly for the differential branching fraction and angular observables, are also discussed.