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.

arXiv comment29 pages, 2 figures

References in corpus (92)

• Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2018
• B -> M1 M2: Factorization, Charming Penguins, Strong Phases, and Polarization
• 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
• Probing partonic structure in gamma* gamma -> pi pi near threshold
• Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons
• Hard exclusive electroproduction of two pions and their resonances
• Polarization in B->VV Decays
• Exclusive production of pion pairs in gamma^* gamma collisions at large Q^2
• B_l4 decays and the extraction of |V_ub|
• QCD Factorization for Charmless Hadronic B_s Decays Revisited
• Triple-Product Correlations in B -> V1 V2$ Decays and New Physics
• Charmless Three-body Decays of B Mesons
• CP violation and kaon-pion interactions in B --> K pi+ pi- decays
• Three-Body Non-Leptonic B Decays and QCD Factorization
• Revisiting Charmless Hadronic B_{u,d} Decays in QCD Factorization
• Branching Fractions and Direct CP Violation in Charmless Three-body Decays of B Mesons
• Three-body nonleptonic B decays in perturbative QCD
• $B_s\to f_0(980)$ form factors and $B_s$ decays into $f_0(980)$
• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• Generalized Heavy-to-Light Form Factors in Light-Cone Sum Rules
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• $S$-wave resonance contributions to the $B_{(s)}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ and $B_s\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• Use of B->J/ψf0 decays to discern the q anti-q or tetraquark nature of scalar mesons
• Triple product asymmetries in K, D_(s) and B_(s) decays
• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• Loop corrections to sub-leading heavy quark currents in SCET
• Resolution to the $B\to \varphi K^{\ast }$ polarization puzzle
• Anatomy of $B_{s,d}^0\to J/\psi f_0(980)$
• Long-distance effects and final state interactions in B to pion pion K and B to K anti-K K decays
• CP violation and CPT invariance in B+- decays with final state interactions
• Effective Lifetimes of $B_s$ Decays and their Constraints on the $B_s^0$-${\bar{B}}_s^0$ Mixing Parameters
• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Symmetry relations in charmless B->PPP decays
• Revisiting charmless hadronic B decays to scalar mesons
• Charmless B decays to a scalar meson and a vector meson
• Nonfactorizable contributions to $B$ meson decays into charmonia
• Improved Estimates of The $B_{(s)}\to VV$ Decays in Perturbative QCD Approach
• Pomeron-Odderon interference effects in electroproduction of two pions
• Comment on ``B->M_1 M_2: Factorization, charming penguins, strong phases, and polarization''
• Probing CP violation systematically in differential distributions
• Nonleptonic $B_s$ to charmonium decays: analyses in pursuit of determining the weak phase ${\beta }_s$
• U-spin breaking in CP asymmetries in B decays
• Re-analysis of data on a0(1450) and a0(980)
• 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
• The mass of the sigma pole
• S-, P- and D-wave final state interactions and CP violation in B+- --> pi+- pi-+ pi+- decays
• SU(3) Relations and the CP Asymmetry in $B\to K_S{K}_S{K}_S$
• U-spin analysis of CP violation in $B^{-}$ decays into three charged light pseudoscalar mesons
• SU(3) Breaking in Charmless B Decays
• Comprehensive Study of ${\overline{B}}^0\to K^0({\overline{K}}^0)K^{\mp }{\pi }^{\pm }$ Decays in the Factorization Approach
• Scalar mesons in weak semileptonic decays of $B_{(s)}$
• CP Violation in Multibody $B$ Decays from QCD Factorization
• Charmless $B_{(s)}\to VV$ Decays in Factorization-Assisted Topological-Amplitude Approach
• Study of $B\to K^{\ast }\rho ,K^{\ast }\omega$ Decays with Polarization in Perturbative QCD Approach
• Quasi-two-body decays $B_{(s)}\to K^{\ast }(892)h\to K\pi h$ in perturbative QCD approach
• Resonant Contributions to Three-body $B\to KKK$ Decays in Perturbative QCD Approach
• Anatomy of $B_s\to VV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• Branching Ratio and Polarization of $B\to \rho (\omega )\rho (\omega )$ Decays in Perturbative QCD Approach
• The $S$-wave resonance contributions to the three-body decays $B_{(s)}^0\to {\eta }_c{f}_0(X)\to {\eta }_c{\pi }^{+}{\pi }^{-}$ in perturbative QCD approach
• Final-state interaction and s-quark helicity conservation in B -> J/psi K*
• ${\bar{B}}_s\to f_0(980)$ form factors and the width effect from light-cone sum rules
• On Differences Between SCET and QCDF for B->pi pi Decays
• 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
• Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the three-body decays $B\to K\pi h$
• 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
• Study of Decay Modes B -->K_0^*(1430) phi
• Quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ in the perturbative QCD approach
• Polarization, CP Asymmetry and Branching ratios in B \to K^* K^* with Perturbative QCD approach
• $P$-wave contributions to $B\to \psi \pi \pi$ decays in perturbative QCD approach
• Four-body decays $B_{(s)}\to (K\pi {)}_{S/P}(K\pi {)}_{S/P}$ in the perturbative QCD approach
• Searching for New Physics with bbar -> sbar Bs -> V_1 V_2 Penguin Decays
• S-wave contributions in ${\bar{B}}_s^0\to (D^0,{\bar{D}}^0){\pi }^{+}{\pi }^{-}$ within perturbative QCD approach
• Study of $CP$ Violation in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}\sigma (600)$ decays in the QCD factorization approach
• Heavy Quark and Chiral Symmetry Predictions for Semileptonic Decays B->D(D*),pi,l,nu
• Study of scalar meson f_0(980) and K_0^*(1430) from B \to f_0(980)ρ(ω, ϕ) and B \to K^*_0(1430)ρ(ω) Decays
• B_s \to ρ(ω) K^* with Perturbative QCD approach
• New Physics in b -> s Transitions and the B_{d,s}^0 -> V_1 V_2 Angular Analysis
• $S$, $P$ and $D$-wave resonance contributions to $B_{(s)}\to {\eta }_c(1S,2S)K\pi$ decays in the perturbative QCD approach
• Four-body baryonic decays of $B\to p\bar{p}{\pi }^{+}{\pi }^{-}({\pi }^{+}{K}^{-})$ and $\Lambda \bar{p}{\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$
• The semileptonic baryonic decay $D_s^{+}\to p\bar{p}{e}^{+}{\nu }_e$
• Branching Ratios and CP Violations of B \to K_0^*(1430) K^* Decays in the pQCD Approach
• $P$-wave contributions to $B_{(s)}\to \psi K\pi$ decays in perturbative QCD approach
• Study of the $B_s$ $\to$ $\varphi f_0(980)$ $\to$ $\varphi {\pi }^{+}{\pi }^{-}$ decay with perturbative QCD approach
• CPT violation and triple-product correlations in B decays
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach
• Studying the localized $CP$ violation and the branching fraction of the ${\bar{B}}^0\to K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay

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• First observation of $CP$ violation and measurement of polarization in $B^{+}\to \rho (770{)}^0{K}^{\ast }(892{)}^{+}$ decays
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