Anatomy of a new anomaly in non-leptonic B decays

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 $B_{d,s}\to K^{\ast 0}{\bar{K}}^{\ast 0}$ where we find for the SM prediction $L_{K^{\ast }{\bar{K}}^{\ast }}=19.5_{-6.8}^{+9.3}$ implying a 2.6$\sigma$ tension with respect to data. The interpretation of this tension in a model independent way identifies two Wilson coefficients ${\mathcal{C}}_4$ 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 $Z^{\mathrm{\prime }}$ can explain also the $b\to s\mathrm{\ell }\mathrm{\ell }$ anomalies albeit with a significant amount of fine-tuning.