The CKM phase $\alpha$ through $B \to a_0 \pi$

Abstract

We propose the decay modes $B \to a_0 (\to \eta \pi) \pi$ to determine the CKM phase $\alpha$. One can analyze these modes through (i) the $B \to a_0 \pi$ isospin pentagon, (ii) the time dependent Dalitz plot of $B^0(t) \to a_0^{\pm} \pi^{\mp} \to \eta \pi^+ \pi^-$, and (iii) the time dependence of $B^0(t) \to a_0^0 (\to \eta \pi^0) \pi^0$. We show that the $a_0 \pi$ modes have certain advantages as compared to the $\rho \pi$ modes, and strongly recommend the time dependent Dalitz plot analysis in the $a_0 \pi$ channel.