Description
The analysis of $B \to PP$ decays where $B = \{B^0, B^+, B_s^0\}$ and $P = \{ \pi, K \}$ under the flavor SU(3) symmetry (SU(3)$_F$) exhibits disagreement with the SU(3)$_F$ limit of the standard model at the level of 3.6 $\sigma$. The individual fits to $\Delta S$ = 0 and $\Delta S$ = 1 decay modes are good, whereas the combined fit assuming same diagrams for $\Delta S$ = 0 and $\Delta S$ = 1 modes is poor. This suggests that SU(3)$_F$ symmetry is broken in the $B \to PP$ decays. An obvious extension is to test the SU(3)$_F$ breaking in the $B \to VV$ ($V$ = {$\rho,K^*$}) decays. Also, there has been a long standing hadronic anomaly in the $B \to K \pi$ sector known as the $B \to K \pi$ puzzle where the measurements of the observables in these decays show inconsistency with one another at $\sim$ 2 $\sigma$. In this talk, I will discuss about the theoretical formalism for studying the $B \to VV$ modes under SU(3) $\times$ spin, with a particular focus on the $B \to \rho K^*$ sector for any similar puzzle.
