Searching for possible evidences of new physics in $B\to V_1{V}_2$

Abstract

We explore the decays of $B\to V_1{V}_2$ ($V_{1,2}=(\rho ,\omega ,K^{\ast },\varphi )$ and $B=(B^0,B^{+},B_s)$) with transverse polarizations. We explicitly evaluate the eigenstates of T-odd scalar operators involving spins for the first time, which offer physical insight among the T violating observables. Based on the helicity suppression of tree operators for transverse polarizations in the standard model (SM), we deduce that $\Delta {\varphi }_p=\Delta {\varphi }_{\parallel }-\Delta {\varphi }_{\perp }=0$ with $\Delta {\varphi }_{\perp ,\parallel }$ the weak phases of the transverse amplitudes. In contrast, the experiments show that $\Delta {\varphi }_p(B^0\to K^{\ast 0}\omega )=-0.84\pm 0.54$, which could be a signal of new physics. There is also a discrepancy between our result in the SM and the experimental data for the transverse polarized branching ratio in $B^0\to K^{\ast 0}\omega$. In addition, by counting the helicity flips, we argue that $\sin ({\varphi }_{\parallel }-{\varphi }_{\perp })\approx 0$, which meets well with most of the experiments except for the ones with $B^0\to K^{\ast 0}\omega$, where ${\varphi }_{\parallel ,\perp }$ are the strong phases in the transverse amplitudes.

Comments: 20 pages, 1 figure, revised version accepted by PLB