Impact of a_(0)^(0)(980)-f_(0)(980) mixing on the localized CP violations of the B^(-)→K^(-)π^(+)(π)^(-) decay

In the framework of the QCD factorization approach,we study the localized CP violations of the B^(-)→K^(-)π^(+)(π)^(-)decay with and without the a_(0)^(0)(980)-f_(0)(980) mixing mechanism and observe that the localized CP violation can be enhanced by this mixing effect when the mass of the π^(+)(π)^(-)pair is in the vicinity of the f_(0)(980) resonance.The corresponding theoretical prediction results are A_(CP)(B^(-)→Kf_(0)→K^(-)π^(+)(π)^(-))=[0.126,0.338](0.232±0.106 with the central value form) and A_(CP)(B^(-)→K^(-)f_(0)(a_0)→K^(-)π^(+)(π)^(-))=[0.230,0.615](0.423±0.193 with the central value form),respectively.Meanwhile,we also calculate the branching fraction of the B^(-)→K^(-)f_(0)(980)→K^(-)π^(+)(π)^(-)decay,which is consistent with the experimental results.We suggest that the a_(0)^(0)(980)-f_(0)(980) mixing mechanism should be considered when theoretically and experimentally studying the CP violation of the B or D meson decays.

Phenomenological studies on B^(0)→[K^(-)π^(+)]s/v[π^(+)π^(-)]v/s→K^(-)π^(+)π^(+)π^(-)decay

Within the quasi-two-body decay model,we study the localized CP violation and branching fraction of the four-body decay B^(0)→[K^(-)π^(+)]s/v[π^(+)π^(-)]v/s→K^(-)π^(+)π^(+)π^(-)whenthe K^(-)π^(+)andπ^(-)π^(+)pair invariant masses are 0.35<mK^(-)π^(+)<2.04GeV and 0<mπ^(-)π^(+)<1.06 GeV,with the pairs being dominated by the K*0(700)0,K*(892)0,K*(1410)0,K*0(1430)and K*(1680)0,and fo(500),ρ0(770),ω(782)and f0(980)resonances,respectively.When dealing with the dynamical functions of these resonances,f0(500),ρ0(770),f0(980)and K*0(1430)are modeled with the Bugg model,Gounaris-Sakurai function,Flatte formalism and LASS lineshape,respectively,while the others are described by the relativistic Breit-W igner function.Adopting the end point divergence parametersρA∈[0,0.5]andφA∈[0,2π],our predicted results are ACρ(B0→K-π^(+)π^(+)π^(-))∈[-0.365.0.447]and B(B0→K-π^(+)π^(+)π^(-))∈[6.11,185.32]×10^(-8),based on the hypothetical qq structures for the scalar mesons in the QCD factorization ap-proach.Meanwhile,we calculate the CP violating asymmetries and branching fractions of the two-body decaysB0→SV(VS)and all the individual four-body decays B0→SV(VS)→K^(-)π^(+)π^(-)π^(+),respectively.Our theoretical results for the two-body decays B0→K<(892)0 f0(980),B0→K*0(1430)0ω(782),B0→K*(892)0f0(980),B0→K*0(1430)0ρ,and B0→K*0(1430)0ωare consistent with the available experimental data,with the remaining predic-tions await testing in future high precision experiments.

Studying the localized CP violation and the branching fraction of the B^0→K^-π^+π^+π^-decay

In this work,we study the localized CP violation and the branching fraction of the four-body decay^ˉB 0→K^−π^+π^−π^+by employing a quasi-two-body QCD factorization approach.Considering the interference of^ˉB 0→ˉK^∗0(700)ρ0(770)→K^−π^+π^−π^+and^ˉB 0→ˉK∗(892)f0(500)→K^−π^+π^−π^+channels,we predict ACP(^ˉB 0→K^−π^+π^−π^+)∈[0.15,0.28]and B(^ˉB 0→K^−π^+π^−π^+)∈[1.73,5.10]×10^−7,respectively,which shows that the interference mechanism of these two channels can induce the localized CP violation to this four-body decay.Meanwhile,within the two quark model framework for the scalar mesons f0(500)andˉK^∗0(700),we calculate the direct CP violations and branching fractions of the^ˉB 0→ˉK^∗0(700)ρ0(770)and^ˉB 0→ˉK∗(892)f0(500)decays,respectively.The corresponding results are ACP(^ˉB 0→ˉK^∗0(700)ρ0(770))∈[0.20,0.36],ACP(^ˉB 0→ˉK∗(892)f0(500))∈[0.08,0.12],B(^ˉB 0→ˉK^∗0(700)ρ0(770)∈[6.76,18.93]×10^−8 and B(^ˉB 0→ˉK∗(892)f0(500))∈[2.66,4.80]×10^−6,indicating that the CP violations of these two-body decays are both positive and the branching fractions quite different.These studies provide a new way to investigate the aforementioned four-body decay and can be helpful in clarifying the configuration of the structure of the light scalar meson.