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Register a new userStudy of localized $CP$ violation in $B^-rightarrow pi^- pi^+pi^-$ and the branching ratio of $B^-rightarrow sigma(600)pi^-$ in the QCD factorization approach
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In this work, within the QCD factorization approach, we study the localized integrated $CP$ violation in the $B^-rightarrow pi^-pi^+pi^-$ decay and the branching fraction of the $B^-rightarrowsigmapi^-$ decay. Both the resonance and nonresonance contributions are included when we study the localized $CP$ asymmetry in the $B^-rightarrow pi^-pi^+pi^-$ decay. The resonance contributions from the scalar $sigma(600)$ and vector $rho^0(770)$ mesons are included. For the $sigma(600)$ meson, we apply both the Breit-Wigner and Bugg models to deal with its propagator, and obtain $mathcal{B}(B^-rightarrow sigma(600)pi^-)<1.67times10^{-6}$ and $mathcal{B}(B^-rightarrow sigma(600) pi^-)<1.946times10^{-5}$ in these two models, respectively. We find that there is no allowed divergence parameters $rho_S$ and $phi_S$ to satisfy the experimental data $mathcal{A_{CP}}(pi^-pi^+pi^-)=0.584pm0.082pm0.027pm0.007$ in the region $m_{pi^+pi^- mathrm{high}}^2>15$ $mathrm{GeV}^2$ and $m_{pi^+pi^-mathrm{low}}^2<0.4$ $mathrm{GeV}^2$ and the upper limit of $mathcal{B}(B^-rightarrow sigma(600)pi^-)$ in the Breit-Wigner model, however, there exists the region $rho_Sin[1.70,3.34]$ and $phi_S in [0.50,4.50]$ satisfying the data for $mathcal{A_{CP}}(pi^-pi^+pi^-)$ and the upper limit of $mathcal{B}(B^-rightarrow sigma(600)pi^-)$ in the Bugg model. This reveals that the Bugg model is more plausible than the Breit-Wigner model to describe the propagator of the $sigma(600)$ meson even though the finite width effects are considered in both models. The large values of $rho_S$ indicate that the contributions from weak annihilation and hard spectator scattering processes are both large, especially, the weak annihilation contribution should not be negleted for $B$ decays to final states including a scalar meson.
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In this work, we study the localized $CP$ violation in $B^-rightarrow K^-pi^+pi^-$ and $B^-rightarrow K^- sigma(600)$ decays by employing the quasi two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the $B^-rightarrow K^-pi^+pi^-$ decay. The resonance contributions include those not only from $[pipi]$ channels including $sigma(600)$, $rho^0(770)$ and $omega(782)$ but also from $[Kpi]$ channels including $K^*(892)$, $K_0^*(1430)$, $K^*(1410)$, $K^*(1680)$ and $K_2^*(1430)$. By fitting the experimental data $mathcal{A_{CP}}(K^-pi^+pi^-)=0.678pm0.078pm0.0323pm0.007$ for $m_{K^-pi^+}^2<15$ $mathrm{GeV}^2$ and $0.08<m_{pi^+pi^-}^2<0.66$ $mathrm{GeV}^2$, we get the end-point divergence parameters in our model, $phi_S in [4.75, 5.95]$ and $rho_Sin[4.2, 8]$. Using these results for $rho_S$ and $phi_S$, we predict that the $CP$ asymmetry parameter $mathcal{A_{CP}} in [-0.094, -0.034]$ and the branching fraction $mathcal{B} in [1.82, 20.0]times10^{-5}$ for the $B^-rightarrow K^-sigma(600)$ decay. In addition, we also analyse contributions to the localized $CP$ asymmetry $mathcal{A_{CP}}(B^-rightarrow K^-pi^+pi^-)$ from $[pipi]$, $[Kpi]$ channel resonances and nonresonance individually, which are found to be $mathcal{A_{CP}}(B^-rightarrow K^-[pi^+pi^-] rightarrow K^-pi^+pi^-)=0.585pm0.045$, $mathcal{A_{CP}}(B^-rightarrow [K^-pi^+] pi rightarrow K^-pi^+pi^-)=0.086pm0.021$ and $mathcal{A_{CP}}^{NR}(B^-rightarrow K^-pi^+pi^-)=0.061pm0.0042$, respectively. Comparing these results, we can see that the localized $CP$ asymmetry in the $B^-rightarrow K^-pi^+pi^-$ decay is mainly induced by the $[pipi]$ channel resonances while contributions from the $[Kpi]$ channel resonances and nonresonance are both very small.
An analysis of the decays of $B^mp rightarrow D K^mp$ and $B^mp rightarrow D pi^mp $ is presented in which the $D$ meson is reconstructed in the three-body final states $K^mp pi^pm pi^0$, $pi^+ pi^- pi^0$ and $K^+ K^- pi^0$. Using data from LHCb corresponding to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collisions, measurements of several $CP$ observables are performed. First observations are obtained of the suppressed ADS decay $B^mp rightarrow [pi^mp K^pm pi^0]_D pi^mp$ and the quasi-GLW decay $B^mp rightarrow [K^+ K^- pi^0]_D pi^mp$. The results are interpreted in the context of the unitarity triangle angle $gamma$ and related parameters.
The three-body charmless hadronic decay $B^0_s rightarrow K^{0}_{rm S} pi^{+}pi^{-}$ provides a number of novel possibilities to search for CP violation effects and test the Standard Model of particle physics. These include fits to the Dalitz-plot distributions of the decay-time-integrated final state, decay-time-dependent (but without initial state flavour tagging) fits to the Dalitz-plot distribution, as well as full decay-time-dependent and flavour tagged fits. The relative sensitivities of these different approaches are investigated.
In this work, we study the localized $CP$ violation and the branching fraction of the four-body decay $bar{B}^0rightarrow K^-pi^+pi^-pi^+$ by employing a quasi-two-body QCD factorization approach. Considering the interference of $bar{B}^0rightarrow bar{K}_0^*(700)rho^0(770)rightarrow K^-pi^+pi^-pi^+$ and $bar{B}^0rightarrow bar{K}^*(892)f_0(500)rightarrow K^-pi^+pi^-pi^+$ channels, we predict $mathcal{A_{CP}}(bar{B}^0rightarrow K^-pi^+pi^-pi^+)in[0.15,0.28]$ and $mathcal{B}(bar{B}^0rightarrow K^-pi^+pi^-pi^+)in[1.73,5.10]times10^{-7}$, respectively, which shows that this two channels interference mechanism can induce the localized $CP$ violation to this four-body decay. Meanwhile, within the two quark model framework for the scalar mesons $f_0(500)$ and $bar{K}_0^*(700)$, we calculate the direct CP violations and branching fractions of the $bar{B}^0rightarrow bar{K}_0^*(700)rho^0(770)$ and $bar{B}^0rightarrow bar{K}^*(892)f_0(500)$ decays, respectively. The corresponding results are $mathcal{A_{CP}}(bar{B}^0rightarrow bar{K}_0^*(700)rho^0(770)) in [0.20, 0.36]$, $mathcal{A_{CP}}(bar{B}^0rightarrow bar{K}^*(892)f_0(500))in [0.08, 0.12]$, $mathcal{B} (bar{B}^0rightarrow bar{K}_0^*(700)rho^0(770)in [6.76, 18.93]times10^{-8}$ and $mathcal{B} (bar{B}^0rightarrow bar{K}^*(892)f_0(500))in [2.66, 4.80]times10^{-6}$, respectively, indicating the $CP$ violations of these two two-body decays are both positive and the branching fractions are quite different. These studies provide a new way to investigate the aforementioned four-body decay and could be helpful in clarifying the configuration of the structure of light scalar meson.
The results of an amplitude analysis of the charmless three-body decay $B^+ rightarrow pi^+pi^+pi^-$, in which $C!P$-violation effects are taken into account, are reported. The analysis is based on a data sample corresponding to an integrated luminosity of $3 text{fb}^{-1}$ of $pp$ collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behaviour of the $pi^+ pi^-$ S-wave contribution, which is achieved by using three complementary approaches based on the isobar model, the K-matrix formalism, and a quasi-model-independent procedure. Additional resonant contributions for all three methods are described using a common isobar model, and include the $rho(770)^0$, $omega(782)$ and $rho(1450)^0$ resonances in the $pi^+pi^-$ P-wave, the $f_2(1270)$ resonance in the $pi^+pi^-$ D-wave, and the $rho_3(1690)^0$ resonance in the $pi^+pi^-$ F-wave. Significant $C!P$-violation effects are observed in both S- and D-waves, as well as in the interference between the S- and P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of $C!P$-violation effects in $B^+ rightarrow pi^+pi^+pi^-$ decays.
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