Resolving the $\phi_2$ ($\alpha$) ambiguity in $B \to \rho \rho$

TL;DR

This paper proposes a novel method to measure the CP-violating phase $\,phi_2$ ($\,alpha$) without ambiguity by exploiting interference effects in B meson decays, potentially achievable with current experimental data.

Contribution

It introduces an alternative approach using interference effects in B decays to resolve the $\,phi_2$ ambiguity, extending the isospin analysis framework.

Findings

Potential deviations in $\,phi_2$ measurement due to penguin contamination are significant.

The method can be implemented with current LHCb Run 3 data and Belle II.

Idealised amplitude models show the feasibility of the approach.

Abstract

I propose an alternative method for measuring the $CP$ violating phase $\phi_2$ ($\alpha$) without ambiguity in an extended SU(2) isospin triangle analysis, which can ultimately be achieved by exploiting interference effects between $B^0 \to \rho^0 \rho^0$ and $B^0 \to a_1^\pm \pi^\mp$ in a time-dependent flavour-tagged amplitude analysis. Under certain assumptions on the effective $\phi_2$ in each channel, I demonstrate with an idealised amplitude model that potential deviations in the measured $\phi_2$ due to penguin contamination in $B^0 \to a_1^\pm \pi^\mp$ are sufficiently large within current experimental uncertainties that this programme could be executed with Run 3 data at LHCb and easily at Belle II.