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

Abstract

In the context of the recently measured non-leptonic decays $B_d\to K^{\ast 0}{\bar{K}}^{\ast 0}$ and $B_s\to K^{\ast 0}{\bar{K}}^{\ast 0}$ we analyse the anatomy of the $L_{VV}$ observable that compares the longitudinal components of $B_s\to VV$ and $B_d\to VV$ 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 $B_d\to K^{\ast 0}{\bar{K}}^{\ast 0}$ and $B_s\to K^{\ast 0}{\bar{K}}^{\ast 0}$, we discuss the main sources of hadronic uncertainty in the SM. We find for the SM prediction $L_{K^{\ast }{\bar{K}}^{\ast }}=19.5_{-6.8}^{+9.3}$, which implies a $2.6\sigma$ tension with respect 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 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 $b\to s\ell \ell$ anomalies.

Comments: Final version to appear in JHEP. 25 pages, 5 figures