Anatomy of a new anomaly in non-leptonic B decays

Abstract

We discuss the anatomy of the $L_{VV}$ observable designed as a ratio of the longitudinal components of $B_s \to VV$ versus $B_d \to VV$ decays. We focus on the particular case of $B_{d,s} \to K^{*0} {\bar K^{*0}}$ where we find for the SM prediction $L_{K^* \bar{K}^*}=19.5^{+9.3}_{-6.8}$ implying a 2.6$\sigma$ tension with respect to data. The interpretation of this tension in a model independent way identifies two Wilson coefficients ${\cal C}_{4}$ and ${\cal C}_{8g}$ as possible sources. The example of one simplified model including a Kaluza-Klein (KK) gluon is discussed. This KK gluon embedded inside a composite/extra dimensional model combined with a $Z^\prime$ can explain also the $b\to s\ell\ell$ anomalies albeit with a significant amount of fine-tuning.