$CP$ violation for $B^{0}\rightarrow \rho^{0}(\omega)\rho^{0}(\omega) \rightarrow \pi^+\pi^-\pi^+\pi^-$ in QCD factorization

TL;DR

This paper investigates direct CP violation in B0 decays to four pions via rho-omega mixing using QCD factorization, revealing potential CP violation up to 28% near the omega resonance.

Contribution

It introduces a detailed analysis of CP violation in B0 decays considering rho-omega mixing within the QCD factorization framework, highlighting the enhancement near the omega resonance.

Findings

CP violation can reach 28% near the omega resonance.

Double rho-omega mixing enhances CP violation.

QCD factorization results differ from naive factorization.

Abstract

In the QCD factorization (QCDF) approach we study the direct $CP$ violation in $\bar{B}^{0}\rightarrow\rho^0(\omega)\rho^0(\omega)\rightarrow\pi^+\pi^-\pi^+\pi^-$ via the $\rho-\omega$ mixing mechanism. We find that the $CP$ violation can be enhanced by double $\rho-\omega$ mixing when the masses of the $\pi^+\pi^-$ pairs are in the vicinity of the $\omega$ resonance, and the maximum $CP$ violation can reach 28{\%}. We also compare the results from the naive factorization and the QCD factorization.