Study of the four-body decays $B^{0}_{S} \rightarrow \pi\pi\pi\pi$ in the perturbative QCD approach

TL;DR

This paper analyzes four-body B_s decays into pions using perturbative QCD, calculating branching ratios and CP asymmetries, and compares results with other approaches, finding consistency with experimental data.

Contribution

It introduces a detailed perturbative QCD framework for four-body B_s decays including S-wave and P-wave resonances, providing new predictions for branching ratios and CP asymmetries.

Findings

Branching ratios are around 10^{-7}.

CP asymmetries can be significantly enhanced near  resonance.

Results are consistent with existing experimental data.

Abstract

In this work, we analyse the CP-averaged branching ratios and direct CP-violating asymmetries of the four-body decays B_{S} \rightarrow \pi\pi\pi\pi decay from the S-wave resonances, f_{0}(980) and f_{0}(500) and P-wave resonances, \rho(770) by introducing the S-wave and P-wave \pi\pi distribution amplitudes within the framework of the perturbative QCD approach. We also calculate branching ratios of the two-body decays B^{0}_{S}\rightarrow\rho^{0}\rho^{0}, B^{0}_{S}\rightarrow\rho^{+}\rho^{-} from the corresponding quasi-two-body decays models and compare our results with those obtained in previous perturbative QCD approach, QCD factorization approach and FAT approach, it is found that the predictions are consistent with present data within errors. The branching ratios of our calculations for the four-body decays B_{S}\rightarrow \pi\pi\pi\pi are at the order of the 10^{-7}. For the CP-violating asymmetries, we found that CP-violating asymmetry can be enhanced largely by the \rho-\omega mixing resonances when \pi\pi pairs masses are in the vicinity of \omega resonance.