Resolving the $\phi_2$ ($\alpha$) ambiguity in $B^0 \to a_1^\pm \pi^\mp$

Abstract

I propose an alternative method for measuring the $CP$ violating phase $\phi_2$ ($\alpha$) without ambiguity in an extended SU(3) flavour symmetry analysis, which can ultimately be achieved by exploiting interference effects between $B \to AP$ and $B \to VV$ decay channels, where $A, V, P$ indicates an axial-vector, vector and pseudo-scalar meson, respectively. Under certain assumptions on the relevant decays based on current experimental results and minimal theoretical input, I demonstrate with an idealised amplitude model that a programme to extract a single solution for $\phi_2$ in the range [0,$\pi$], with the added possibility to simultaneously constrain non-factorisable SU(3)-breaking effects, could be executed to similar precision using Run 3 data at LHCb and the final Belle II sample.