Investigating non-local contributions in $B_s\to \varphi \bar{\ell }\ell$ including higher-twist effects

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 $B_s\to \varphi \bar{\ell }\ell$ 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 $\varphi ,J/\Psi$ and $\psi (2S)$ mesons. Here, the LCSR predictions serve as inputs, supplemented by experimental data from two-body decays $B_s\to \varphi +$ 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.

Comments: 35 Pages, 4 Figures and 12 Tables. Text improvement, new tables and references added. Version accepted for publication in JHEP