In the context of the recently measured non-leptonic decays Bd→$$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ K ∗ 0 K ¯ ∗ 0 and Bs→$$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ K ∗ 0 K ¯ ∗ 0 we analyse the anatomy of the LVV observable that compares the longitudinal components of Bs→VV and Bd→VV decays. This observable is cleaner than the longitudinal polarisation fraction as it is afflicted only at subleading order in a 1/mb expansion by the theoretical uncertainties arising in the transverse

more »

... entering the polarisation fraction. Focusing on the particular case of Bd→$$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ K ∗ 0 K ¯ ∗ 0 and Bs→$$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ K ∗ 0 K ¯ ∗ 0 , we discuss the main sources of hadronic uncertainty in the SM. We find for the SM prediction $$ {L}_{K^{\ast }{\overline{K}}^{\ast }}={19.5}_{-6.8}^{+9.3} $$ L K ∗ K ¯ ∗ = 19.5 − 6.8 + 9.3 , which implies a 2.6σ tension with respect to the most recent data, pointing to a deficit in the b→s transition of the non-leptonic decay versus the corresponding b→d transition. We discuss possible New Physics explanations for this deviation, first at the level of the Weak Effective Theory and we identify that the two Wilson coefficients $$ {\mathcal{C}}_4 $$ C 4 and $$ {\mathcal{C}}_{8g} $$ C 8 g can play a central role in explaining this anomaly. Finally, we briefly explore two different simplified New Physics models which can explain the anomaly through a contribution either in $$ {\mathcal{C}}_4 $$ C 4 (Kaluza-Klein gluon) or in $$ {\mathcal{C}}_{8g} $$ C 8 g , with a significant amount of fine tuning, but possible connections to the b→sℓℓ anomalies.