A new B-flavour anomaly in B d,s → K ∗ 0 K ¯ ∗ 0 $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ : anatomy and interpretation

Abstract

Abstract In the context of the recently measured non-leptonic decays B d → K ∗ 0 K ¯ ∗ 0 $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ and B s → K ∗ 0 K ¯ ∗ 0 $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ we analyse the anatomy of the L VV observable that compares the longitudinal components of B s → VV and B d → 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 → K ∗ 0 K ¯ ∗ 0 $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ and B s → K ∗ 0 K ¯ ∗ 0 $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ , we discuss the main sources of hadronic uncertainty in the SM. We find for the SM prediction L K ∗ K ¯ ∗ = 19.5 − 6.8 + 9.3 $$ {L}_{K^{\ast }{\overline{K}}^{\ast }}={19.5}_{-6.8}^{+9.3} $$ , which implies a 2.6σ tension with respect to the most recent data, pointing to a deficit in the b → s transition of the non-leptonic decay versus the corresponding b → 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 C 4 $$ {\mathcal{C}}_4 $$ and C 8 g $$ {\mathcal{C}}_{8g} $$ 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 C 4 $$ {\mathcal{C}}_4 $$ (Kaluza-Klein gluon) or in C 8 g $$ {\mathcal{C}}_{8g} $$ , with a significant amount of fine tuning, but possible connections to the b → sℓℓ anomalies.

Keywords

• Effective Field Theories
• Heavy Quark Physics