Investigating non-local contributions in Bs→ϕℓ¯ℓ including higher-twist effects

We analyze the impact of higher-twist three-particle B<inf>s</inf>-meson light-cone distribution amplitudes (LCDAs) on the non-local form factors for the Bs→ϕℓ¯ℓ 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 ϕ, J/Ψ and ψ(2S) mesons. Here, the LCSR predictions serve as inputs, supplemented by experimental data from two-body decays B<inf>s</inf> → ϕ + 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 (q²)-dependent correction to the Wilson coefficient C<inf>9</inf>, 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<inf>s</inf>-meson LCDAs. The phenomenological implications, particularly for the differential branching fraction and angular observables, are also discussed.