Large SU(3) breaking effects and CP violation in $B^+ $ decays into three charged SU(3) octet pseudoscalar mesons

TL;DR

This paper investigates CP violation in $B^+$ decays into three charged SU(3) octet pseudoscalar mesons, finding that large SU(3) breaking effects are necessary to reconcile theoretical predictions with experimental observations.

Contribution

It introduces a detailed analysis of momentum-dependent and SU(3) breaking effects in $B^+$ decays, highlighting the need for significant SU(3) breaking to match experimental data.

Findings

Large SU(3) breaking effects are required to explain decay patterns.

Momentum dependence alone cannot account for observed CP asymmetries.

Standard SU(3) symmetry assumptions are insufficient for these decays.

Abstract

TThe LHCb collaboration has recently reported evidence for non-zero CP asymmetries in $B^+$ decays into $\pi^+ K^+ K^-,\; \pi^+\pi^+\pi^-,\; K^+ K^+ K^- $ and $K^+\pi^+\pi^-$. The branching ratios for these decays have also been measured with different values ranging from $5\times 10^{-6}$ to $51\times 10^{-6}$. If flavor $SU(3)$ symmetry is a good symmetry for $B$ decays, in the case that the dominant amplitude is momentum independent it is expected that branching ratios $Br$ and CP violating rate differences $\Delta_{CP} = \Gamma - \overline{\Gamma}$ satisfy, $Br(\pi^+\pi^+\pi^-) = 2Br(\pi^+ K^+ K^-)$, $Br(K^+K^+K^-) = 2 Br(K^+\pi^+\pi^-)$, and $\Delta_{CP}(\pi^+\pi^+\pi^-) = 2\Delta_{CP}(\pi^+ K^+K^-) = - \Delta_{CP}(K^+K^+K^-) = -2\Delta_{CP}(K^+\pi^+\pi^-)$. The experimental data do not exhibit the expected pattern for the branching ratios. The rate differences for $B^+\to \pi^+\pi^+\pi^-$ and $B^+\to K^+ K^+ K^-$ satisfy the relation between $\Delta S =0$ and $\Delta S=1$ well, but the other two do not, with the CP asymmetries having different signs than expected. In this work we study how to including momentum dependent and also $SU(3)$ breaking effects on these decays to explain experimental data. We find that only including lowest order derivative terms, in the $SU(3)$ limit, the decay patterns cannot be explained. Large $SU(3)$ breaking effects are needed to explain the data.