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

We analyze the impact of higher-twist three-particle Bs-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 Bs→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 C9, which is higher than, but still consistent with the Standard Model prediction within uncertainties. Additionally, we update the local form factors to include contributions from higher-twist three-particle Bs−meson LCDAs. The phenomenological implications, particularly for the differential branching fraction and angular observables, are also discussed.