A new $B$-flavour anomaly in $B_{d,s}\to K^{*0}\bar{K}^{*0}$: anatomy and interpretation

In the context of the recently measured non-leptonic decays B$_{d}$→$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $ and B$_{s}$→$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $ we analyse the anatomy of the L$_{VV}$ observable that compares the longitudinal components of B$_{s}$→VV and B$_{d}$→VV decays. This observable is cleaner than the longitudinal polarisation fraction as it is afflicted only at subleading order in a 1/m$_{b}$ expansion by the theoretical uncertainties arising in the transverse components entering the polarisation fraction. Focusing on the particular case of B$_{d}$→$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $ and B$_{s}$→$ {K}^{\ast 0}{\overline{K}}^{\ast 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} $, 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 $ and $ {\mathcal{C}}_{8g} $ 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 $ (Kaluza-Klein gluon) or in $ {\mathcal{C}}_{8g} $, with a significant amount of fine tuning, but possible connections to the b→sℓℓ anomalies.