Study of $B_{(s)}\to (\pi \pi )(K\pi )$ decays in the perturbative QCD approach

Abstract

In this work, we provide estimates of the branching ratios, direct $CP$ asymmetries and triple product asymmetries in $B_{(s)}\to (\pi \pi )(K\pi )$ decays in the perturbative QCD approach, where the $\pi \pi$ and $K\pi$ invariant mass spectra are dominated by the vector resonances $\rho (770)$ and $K^{\ast }(892)$, respectively. Some scalar backgrounds, such as $f_0(500,980)\to \pi \pi$ and $K_0^{\ast }(1430)\to K\pi$ are also accounted for. The $\rho (700)$ is parametrized by the Gounaris-Sakurai function. The relativistic Breit-Wigner formula for the $f_0(500)$ and Flatté model for the $f_0(980)$ are adopted to parameterize the time-like scalar form factors $F_S({\omega }^2)$. We also use the D.V. Bugg model to parameterize the $f_0(500)$ and compare the relevant theoretical predictions from different models. While in the region of $K\pi$ invariant mass, the $K_0^{\ast }(1430)$ is described with the LASS lineshape and the $K^{\ast }(892)$ is modeled by the Breit-Wigner function. We find that the decay rates for the considered decay modes agree with currently available data within errors. As a by-product, we extract the branching ratios of two-body decays $B_{(s)}\to \rho (770)K^{\ast }(892)$ from the corresponding four-body decay modes and calculate the relevant polarization fractions. Our prediction of longitudinal polarization fraction for $B^0\to \rho (770{)}^0{K}^{\ast }(892{)}^0$ decay deviates a lot from the recent LHCb measurement, which should be resolved. It is shown that the direct $CP$ asymmetries are large due to the sizable interference between the tree and penguin contributions, but they are small for the tree-dominant or penguin-dominant processes. The PQCD predictions for the triple product asymmetries are small which are expected in the standard model, and consistent with the current data reported by the LHCb Collaboration.Our results can be tested by the future precise data from the LHCb and Belle II experiments.

29 pages, 2 figures

References in corpus (22)

• Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach
• Branching fractions, polarisation and asymmetries of B -> VV decays
• Charmless Three-body Decays of B Mesons
• $B_s\to f_0(980)$ form factors and $B_s$ decays into $f_0(980)$
• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• $S$-wave resonance contributions to the $B_{(s)}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ and $B_s\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• Charmless B decays to a scalar meson and a vector meson
• Improved Estimates of The $B_{(s)}\to VV$ Decays in Perturbative QCD Approach
• Nonleptonic $B_s$ to charmonium decays: analyses in pursuit of determining the weak phase ${\beta }_s$
• Study of scalar mesons f_0(980) and f_0(1500) from $B\to f_0(980)K$ and $B\to f_0(1500)K$ Decays
• Re-analysis of data on a0(1450) and a0(980)
• The mass of the sigma pole
• Scalar mesons in weak semileptonic decays of $B_{(s)}$
• CP Violation in Multibody $B$ Decays from QCD Factorization
• Quasi-two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))\to D\pi \pi$ in the perturbative QCD factorization approach
• Global Analysis of Charmless $B$ Decays into Two Vector Mesons in Soft-Collinear Effective Theory
• Searching for New Physics with B-Decay Fake Triple Products
• Branching Fractions and CP Asymmetries of the Quasi-Two-Body Decays in $B_s\to K^0({\overline{K}}^0)K^{\pm }{\pi }^{\mp }$ within PQCD Approach
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach

Cited by in corpus (1)

• Study of the four-body decays $B_S^0\to \pi \pi \pi \pi$ in the perturbative QCD approach