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In the context of the recently measured non-leptonic decays $B_{d}\toK^{*0}\bar{K}^{*0}$ and $B_{s}\to K^{*0}\bar{K}^{*0}$ we analyse the anatomy ofthe $L_{VV}$ observable that compares the longitudinal components of $B_s \toVV$ and $B_d \to VV$ decays. This observable is cleaner than the longitudinalpolarisation fraction as it is afflicted only at subleading order in a $1/m_b$expansion by the theoretical uncertainties arising in the transverse componentsentering the polarisation fraction. Focusing on the particular case of$B_{d}\to K^{*0}\bar{K}^{*0}$ and $B_{s}\to K^{*0}\bar{K}^{*0}$, we discuss themain sources of hadronic uncertainty in the SM. We find for the SM prediction$L_{K^*\bar{K}^*}=19.5^{+9.3}_{-6.8}$, which implies a $2.6\sigma$ tension withrespect to the most recent data, pointing to a deficit in the $b \to s$transition of the non-leptonic decay versus the corresponding $b \to d$transition. We discuss possible New Physics explanations for this deviation,first at the level of the Weak Effective Theory and we identify that the twoWilson coefficients ${\cal C}_{4}$ and ${\cal C}_{8g}$ can play a central rolein explaining this anomaly. Finally, we briefly explore two differentsimplified New Physics models which can explain the anomaly through acontribution either in ${\cal C}_4$ (Kaluza-Klein gluon) or in ${\cal C}_{8g}$,with a significant amount of fine tuning, but possible connections to the $b\to s \ell \ell$ anomalies.

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

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