${\rm \overline{B}}_{d,s}\to \rm K^{*0}\overline{K}^{*0}$ decays, a serious problem for the Standard Model

We underline the theoretical and experimental interest of the vector-vector penguin decays ${\rm \overline{B}}_{d,s} \to {\rm K^{*0} \overline{K}^{*0}}$ for which the data show a strong U-spin violation. Indeed, with the latest LHCb data one has for these two modes very different longitudinal polarization fractions, $f_L^{exp}({\rm \overline{B}}_s \to {\rm K^{*0} \overline{K}^{*0}} ) = 0.24 \pm 0.04$ and $f_L^{exp}({\rm \overline{B}}_d \to {\rm K^{*0} \overline{K}^{*0}} ) = 0.74 \pm 0.05$. This feature is very striking because both modes are related by the exchange $s \leftrightarrow d$, i.e. they are related by U-spin symmetry as pointed out in earlier work by other authors. We illustrate this phenomenon by computing different observables for these modes within the QCD Factorization scheme, and we find, as expected, rather close values for the longitudinal fractions, with central values $f_L^{th}({\rm \overline{B}}_s \to {\rm K^{*0} \overline{K}^{*0}} ) \simeq 0.42$ and $f_L^{th}({\rm \overline{B}}_d \to {\rm K^{*0} \overline{K}^{*0}} ) \simeq 0.49$ and rather small errors. Furthermore, due to the $V-A$ nature of the weak currents and the heavy quark limit, one expects $(f_\parallel/f_\perp)_{th}\simeq 1$, which in the $\rm B_s$ case is in contradiction with the data $(f_\parallel/f_\perp)_{\rm exp}\simeq 0.44\pm 0.06$.}