Impact of Helicity-Isospin Convention Matching on the Extraction of $\alpha$ from $B^0\to (\rho \pi {)}^0$

Abstract

We show that the $\rho \to \pi \pi$ helicity convention used in the time-dependent Dalitz-plot measurements of $B^0\to (\rho \pi {)}^0$ decays does not match the convention assumed in the subsequent isospin analysis. Once corrected, the tension between the direct determination of the unitarity-triangle angle $\alpha$ from these decays and its indirect determination from global fits decreases from $2.9\sigma$ to $2.1\sigma$. Combined with the $B\to \pi \pi$ and $B\to \rho \rho$ modes, the direct determination becomes $\alpha =(87.0_{-4.7}^{+11.8}{)}^{\circ }$, compared with the original world average $(84.1_{-3.0}^{+3.7}{)}^{\circ }$.