BOOST 2024 - 16th International Workshop on Boosted Object Phenomenology, Reconstruction, Measurements, and Searches at Colliders

Nonfactorizable charm loop in rare Bs→γl+l− decay

30 Jul 2024, 15:40

20m

Palazzo Ducale (Genova, Italy)

Talk Heavy Flavours Heavy Flavours

Speaker

Ilia Belov (Istituto Nazionale di Fisica Nucleare)

Description

We present the first theoretical calculation of nonfactorizable charm-quark loop contributions to the $B_s\to \gamma l^{+}{l}^{-}$ amplitude. This contribution involves the $B$-meson three-particle Bethe-Salpeter amplitude, $⟨0|\overline{s}(y)G_{\mu \nu }(x)b(0)|{\overline{B}}_s(p)⟩$, for which we take into account constraints from analyticity and continuity. We calculate the relevant form factors, $H_{A,V}^{\mathrm{N}\mathrm{F}}(k^{\prime 2},k^2)$, and provide convenient parametrizations of our results, applicable in the region below hadron resonances, $k^{\prime 2}<M_{J/\psi }^2$ and $k^2<M_{\varphi }^2$. We report that factorizable and nonfactorizable charm contributions to the $B_s\to \gamma l^{+}{l}^{-}$ amplitude have opposite signs. To compare the charm and the top contributions, the nonfactorizable charming loop contribution is expressed as a non-universal (i.e., dependent on the reaction) $q^2$-dependent correction ${\mathrm{\Delta }}^{\mathrm{N}\mathrm{F}}{C}_7(q^2)$ to the Wilson coefficient $C_7$. For the $B_s\to \gamma l^{+}{l}^{-}$ amplitude the correction is found to be positive, ${\mathrm{\Delta }}^{\mathrm{N}\mathrm{F}}{C}_7(q^2)/C_7>0$. Our numerical results for the form factors $H_i^{\mathrm{N}\mathrm{F}}(k^{\prime 2},k^2)$ depend sizeably on the precise value of the parameter ${\lambda }_{B_s}$, and for a fixed value of ${\lambda }_{B_s}$, $H_i^{\mathrm{N}\mathrm{F}}(k^{\prime 2},k^2)$ may be calculated with about 10% accuracy.

Presentation materials

NF_charm.pdf