Within the quasi-two-body decay model, we study the localized $CP$ violation and branching fraction of the four-body decay $\bar{B}^0\rightarrow [K^-π^+]_{S/V}[π^+π^-]_{V/S} \rightarrow K^-π^+π^-π^+$ when $K^-π^+$ and $π^-π^+$ pair invariant masses are $0.35<m_{K^-π^+}<2.04 \, \mathrm{GeV}$ and $0<m_{π^-π^+}<1.06\, \mathrm{GeV}$, with the pairs being dominated by the $\bar{K}^*_0(700)^0$, $\bar{K}^*(892)^0$, $\bar{K}^*(1410)^0$, $\bar{K}^*_0(1430)$ and $\bar{K}^*(1680)^0$, and $f_0(500)$, $ρ^0(770)$ , $ω(782)$ and $f_0(980)$ resonances, respectively. When dealing with the dynamical functions of these resonances, $f_0(500)$, $ρ^0(770)$, $f_0(980)$ and $\bar{K}^*_0(1430)$ are modeled with the Bugg model, Gounaris-Sakurai function, Flatt$\acute{\mathrm{e}}$ formalism and LASS lineshape, respectively, while others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters $ρ_A\in[0,0.5]$ and $ϕ_A\in[0,2π]$, our predicted results are $\mathcal{A_{CP}}(\bar{B}^0\rightarrow K^-π^+π^+π^-)\in[-0.383,0.421]$ and $\mathcal{B}(\bar{B}^0\rightarrow K^-π^+π^+π^-)\in[7.36,199.69]\times10^{-8}$ based on the hypothetical $q\bar{q}$ structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the $CP$ violating asymmetries and branching fractions of the two-body decays $\bar{B}^0\rightarrow SV(VS)$ and all the individual four-body decays $\bar{B}^0\rightarrow SV(VS) \rightarrow K^-π^+π^-π^+$, respectively. Our theoretical results for the two-body decays $\bar{B}^0\rightarrow \bar{K}^*(892)^0$$f_0(980)$, $\bar{B}^0\rightarrow \bar{K}^*_0(1430)^0$$ω(782)$, $\bar{B}^0\rightarrow \bar{K}^*(892)^0f_0(980)$, $\bar{B}^0\rightarrow\bar{K}^*_0(1430)^0ρ$,
Theoretical Uncertainties and Phenomenological Aspects of $B \rightarrow X_s γ$ Decay
我们分析的不确定性的理论预测的包容性分支比$BR[B \rightarrow X_s γ]$。我们发现，主导的不确定性，在领导秩序的表达来自其$μ$依赖。我们讨论了一个下一个领先的顺序计算$B \rightarrow X_s γ$一般条款和检查到何种程度的$μ$的依赖性可以减少在这样的计算。我们提出了对标准模型和双希格斯模型参数的限制，这些参数来自于对$b \rightarrow s γ$衰变的测量。目前的理论不确定性不允许明确限制标准模型参数远远超出其他实验的限制。双希格斯双重模型的边界仍然非常强，尽管比最近文献中的边界弱得多。在双Higgs模型中，$b \rightarrow s γ$、$Z \rightarrow b \bar{b}$和$b \rightarrow c τ\barν_τ$过程足以给出$M_{H^{\pm}}-tan β$平面上最严格的边界。
Phenomenological Study of $Ω_c\rightarrow Ω^-π^+$ at Polarized Electron-Positron Collider
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University（核物理与离子束应用教育部重点实验室和现代物理研究所，复旦大学）；College of Physics, Jilin University（吉林大学物理学院）；Institute of High Energy Physics（高能物理研究所）
The decay widths of $Υ(nS)$ $\rightarrow$ $\bar{d}^{\ast}(2380)+X$ with $n=1,2,3$ are studied in a phenomenological way. With the help of crossing symmetry, the decay widths are obtained by investigating the imaginary part of the forward scattering amplitudes between $d^\ast$ and $Υ(nS)$. The wave functions of $d^\ast$ and deuteron obtained in previous studies are used for calculating the amplitude. The interaction between $d^{\ast}$ ($d$) and $Υ$ is governed by the quark-meson interaction where the coupling constant is determined by fitting the observed widths of $Υ(nS)$ $\rightarrow$ $\bar{d…
Babar, Belle and recently LHCb has reported an excess in the measurements of $R(D^{*})$, $R(D)$ and $\mathcal{B}r(B \rightarrow τν_τ )$ than expected from SM, a possible signature of lepton flavor universality violating NP. In this work we analyze the phenomenological implications for these decay modes in a Flipped/Lepton-Specific 2HDM with anomalously enhanced Yukawa coupling of $H^{\pm}$ to $τ$/b. When experimental and theoretical errors are added in quadrature, we conclude that this phenomenological extension of SM can give results in agreement within 1$σ$ deviation for the combination of $…
The cross sections of $e^+e^- \rightarrow πZ_c(3900) \rightarrow ππJ/ψ$ and $e^+e^- \rightarrow πZ_c(3900) \rightarrow πD\bar{D}^{*}$ have been measured by BESIII experiment. We try to perform a combined fit to the cross sections with one Breit-Wigner function, the fit results show the structure's mass and width are $M=(4232\pm5)$ MeV/$c^2$, $Γ=(65\pm21)$ MeV. The ratio $\frac{\mathcal{B}(Z_c(3900)\rightarrow D\bar{D}^{*})}{\mathcal{B}(Z_c(3900)\rightarrowπJ/ψ)}$ is determined to be $(16\pm6)$. We also try to fit the cross sections with two Breit-Wigner functions, while we can't come to any de…
In this work, we study the localized $CP$ violation and the branching fraction of the four-body decay $\bar{B}^0\rightarrow K^-π^+π^-π^+$ by employing a quasi-two-body QCD factorization approach. Considering the interference of $\bar{B}^0\rightarrow \bar{K}_0^*(700)ρ^0(770)\rightarrow K^-π^+π^-π^+$ and $\bar{B}^0\rightarrow \bar{K}^*(892)f_0(500)\rightarrow K^-π^+π^-π^+$ channels, we predict $\mathcal{A_{CP}}(\bar{B}^0\rightarrow K^-π^+π^-π^+)\in[0.15,0.28]$ and $\mathcal{B}(\bar{B}^0\rightarrow K^-π^+π^-π^+)\in[1.73,5.10]\times10^{-7}$, respectively, which shows that this two channels' interf…
Adding a scalar singlet provides one of the simplest extensions of the Standard Model. In this work we briefly review the latest constraints on the mass and mixing of the new Higgs boson and study its production and decay at the LHC. We mainly focus on double Higgs production in the $hh \rightarrow b \bar{b} WW \rightarrow b \bar{b} \ell^+ ν\ell^- \barν$ decay channel. This decay is found to be efficient in a region of masses of the heavy Higgs boson of 260 - 500 GeV, so it is complementary to the 4$b$ channel, more efficient for Higgs bosons having masses greater than 500 GeV. We analyse this…
We investigate roads for evaluating model-independent cross-section distributions for the sequential hyperon decay $Σ^0\rightarrowΛγ;Λ\rightarrow pπ^- $ and its corresponding antihyperon decay. The hyperons are produced in the reaction $e^+e^-\rightarrow J/ψ\rightarrow Σ^0\barΣ^0$. Cross-section distributions are calculated using the folding technique.
We study the three-body baryonic B decay $\bar{B}^{0}_{s}\rightarrow p\barΛ K^{-}$ within the framework of the pole model via the baryonic $Λ_{b}$ pole. In our calculation, we require the strong coupling constant $g_{Λ_{b}B_{s}Λ}$ and investigate if $g_{Λ_{b}B_{s}Λ}=10.49\pm1.57$ is adopted, the branching ratio agrees with the experimental result, reported by the LHCb collaboration.
The semileptonic $Ω_c^0 \rightarrow Ω^- l ν$ and non-leptonic $Ω_c^0 \to Ω^- π^+$, $Ω_c^0 \to Ω^- ρ^+$ decays of charmed $Ω_c$ baryon are studied within the light cone sum rules. The form factors responsible for $Ω_c \to Ω$ transitions are calculated using the distribution amplitudes of $Ω_c$ baryon. With the obtained form factors, the branching ratios of $Ω_c^0 \to Ω^- l^+ ν_l$, $Ω_c^0 \rightarrow Ω^- π^+$, and $Ω_c^0 \rightarrow Ω^- ρ^+$ decays are estimated. The results are compared with Belle data as well as the findings of the other approaches.
We report on a study of the sequential hyperon decay $Σ^0\rightarrowΛγ;Λ\rightarrow pπ^- $ and its corresponding anti-hyperon decay. We derive a multi-dimentional and model-independent formalism for the case when the hyperons are produced in the reaction $e^+e^-\rightarrowΣ^0\barΣ^0$. Cross-section distributions are calculated using the folding technique. We also study sequential decays of single-tagged hyperons.
The spin of the $τ$ lepton in the semiletonic process ${\bar{B}}^0\rightarrow D^{+} τ^- {\barν}$ can be polarized in the direction which is normal to the reaction plane, if the charged Higgs boson exists and its coupling to quarks has a complex phase. We calculate this transverse polarization of the $τ$ lepton by using the experimentally measured $B$ to $D$ transition form factors.
The associated production of a Higgs boson and a top-quark pair, $t{\bar t} H$, in proton-proton collisions is addressed in this paper for a center of mass energy of 13TeV at the LHC. Dileptonic final states of $t{\bar t}H$ events with two oppositely charged leptons and four jets from the decays $t\rightarrow bW^+ \rightarrow b \ell^+ν_\ell$, $\bar{t}\rightarrow \bar{b}W^- \rightarrow \bar{b} \ell^-\barν_\ell$ and $h\rightarrow b\bar{b}$, are used. Signal events, generated with MadGraph5_aMC@NLO, are fully reconstructed by applying a kinematic fit. New angular distributions of the decay produc…
Motivated by an anomaly in $R(D^{(*)})={\rm BR}(\bar{B}\rightarrow D^{(*)} τ^-\barν)/{\rm BR}(\bar{B}\rightarrow D^{(*)} l^-\barν)$ reported by BaBar, Belle and LHCb, we study $R(D^{(*)})$ in a general two Higgs doublet model (2HDM). Although it has been suggested that it is difficult for the 2HDM to explain the current world average for $R(D^{(*)})$, it would be important to clarify how large deviations from the standard model predictions for $R(D^{(*)})$ are possible in the 2HDM. We investigate possible corrections to $R(D^{(*)})$ in the 2HDM by taking into account various flavor physics con…
The rare decays $\bar B\rightarrow X_sγ$ and $B_s^0\rightarrow μ^+μ^-$ are important to research new physics beyond standard model. In this work, we investigate two loop electroweak corrections to $\bar B\rightarrow X_sγ$ and $B_s^0\rightarrow μ^+μ^-$ in the minimal supersymmetric extension of the SM with local $B-L$ gauge symmetry (B-LSSM), under a minimal flavor violating assumption for the soft breaking terms. In this framework, new particles and new definition of squarks can affect the theoretical predictions of these two processes, with respect to the MSSM. Considering the constraints fro…
Cross-section distributions are calculated for the reaction $e^+ e^- \rightarrow J/ψ\rightarrow \barΛ(\rightarrow \bar{p}π^+) Λ(\rightarrow pπ^-)$, and related annihilation reactions mediated by vector mesons. The hyperon-decay distributions depend on a number of structure functions that are bilinear in the, possibly complex, psionic form factors $G_M^ψ$ and $G_E^ψ$ of the Lambda hyperon. The relative size and relative phase of these form factors can be uniquely determined from the unpolarized joint-decay distributions of the Lambda and anti-Lambda hyperons. Also the decay-asymmetry parameters…
We present the two-loop master integrals relevant to the ${\mathcal O}(αα_s)$-corrections to the decay $H \rightarrow b \bar{b}$ through a $H t \bar{t}$-coupling. We keep the full dependence on the heavy particle masses, but neglect the $b$-quark mass. The occurring square roots can be rationalised and the result is expressed in terms of multiple polylogarithms.
We have performed the calculations for the nonleptonic $Ξ_b^- \rightarrow π^- \ Ξ_c^0 (2790) \left(J=\frac{1}{2}\right)$ and $Ξ_b^- \rightarrow π^- \ Ξ_c^0 (2815) \left(J=\frac{3}{2}\right)$ and the same reactions replacing the $π^-$ by a $D_s^-$. At the same time we evaluate the semileptonic rates for $Ξ_b^- \rightarrow \barν_l l \ Ξ_c^0 (2790)$ and $Ξ_b^- \rightarrow \barν_l l \ Ξ_c^0 (2815)$. We look at the reactions from the perspective that the $Ξ_c^0 (2790)$ and $Ξ_c^0 (2815)$ resonances are dynamically generated from the pseudoscalar-baryon and vector-baryon interactions. We evaluate ra…
We consider a scenario where, along with the usual Higgs doublet, two scalar triplets are present. The extension of the triplet sector is required for the Type~II mechanism for the generation of neutrino masses, if this mechanism has to generate a neutrino mass matrix with two-zero texture. One CP-violating phase has been retained in the scalar potential of the model, and all parameters have been chosen consistently with the observed neutrino mass and mixing patterns. We find that a large phase ($\gtrsim 60^{\circ}$) splits the two doubly-charged scalar mass eigenstates wider apart, so that th…
We investigate the prospects for detecting axion-like particles (ALPs, dubbed as "a") via the decay $Z\rightarrow a f\bar{f}$ at future $Z$ factories. Considering the decay channels $a\rightarrow μ^+ μ^-$ and $a\rightarrow b \bar{b}$ , four types of signals $μ^+ μ^- /E$, $b b /E$, $e^+ e^- μ^+ μ^-$ and $e^+ e^- b b$ are explored. We demonstrate that these channels are promising for detecting ALPs at $Z$ factories and obtain the sensitivity bounds on the couplings $g_{aZZ}$ and $g_{aγZ}$.
Using the Bethe-Salpeter equation (BSE) we investigate the forward-backward asymmetries $( A_{FB}) $ in $Λ_b \rightarrow Λl^+ l^-(l=e,μ,τ)$ in the quark-diquark model. This approach provides precise form factors that are different from those of QCD sum rules. We calculate the rare decay form factors for $Λ_b \rightarrow Λl^+ l^-$ and investigate the (integrated) forward-backward asymmetries in these decay channels. We find that the integrated $A^l_{FB}$, $\bar{A}^l_{FB}(Λ_b \rightarrow Λe^+ e^-) \simeq -0.1371 $, $\bar{A}^l_{FB}(Λ_b \rightarrow Λμ^+ μ^- ) \simeq -0.1376 $, $\bar{A}^l_{FB}(Λ_b …
We obtain a lower limit on the compactification scale of extra dimension via comparison of the branching ratio in the baryonic $Λ_b\rightarrow Λμ^+ μ^-$ decay channel recently measured by CDF collaboration and our previous theoretical study. We also use the newly available form factors calculated via light cone QCD sum rules in full theory to analyze the flavour changing neutral current process of the $Σ_b \rightarrow Σ\ell^+ \ell^-$ in universal extra dimension scenario in the presence of a single extra compact dimension. We calculate various physical quantities like branching ratio, forward-…
We report on the status of the ongoing calculation of multiparticle contributions to the inclusive radiative $\bar{B} \rightarrow X_s γ$ decay at next-to leading order. This effort amounts to the evaluation of the four-particle process $b\rightarrow s \bar{q} q γ$ at the one-loop level, supplemented by the corresponding five-particle tree-level cuts $b\rightarrow s \bar{q} q γ+ g$ of the gluon bremsstrahlung. Knowledge of these pieces will formally complete the $\bar{B} \rightarrow X_s γ$ decay at the next-to-leading order. The different steps such as the generation of the amplitude, its renor…
Exclusive $B_c^\ast \rightarrow D_{s}~ν\barν$ decay is studied in the framework of the three--point QCD sum rules approach. The two gluon condensate contributions to the correlation function are calculated and the form factors of this transition are found. The decay width and total branching ratio for this decay is also calculated.
We study the three-body baryonic decay $ \bar{B}^{0}\rightarrowΛ^+_c \bar{p} π^0$ based on the factorization approach. The most important Feynman diagrams for this decay mode are factorizable and non-factorizable contributions, so that the former plays the key role in the decay amplitude and the latter affects the amplitude coefficient $a_2$. We calculate the decay branching ratio for some values of $a_2$ in the range of $0.16-0.40$ and we find that the value of $a_2=0.17$ leads us to the result of $(1.50\pm0.21)\times10^{-4}$ which evidently agrees with the experimental result $(1.55\pm0.17\p…
In the framework of the littlest Higgs model with T-parity(LHT), we investigate the double Higgs production processes $e^{+}e^{-}\rightarrow ZHH$ and $e^{+}e^{-}\rightarrow ν\barνHH$ at high energy $e^{+}e^{-}$ colliders. We calculate the production cross sections and find that the relative correction at the center-of-mass energy $\sqrt{s}=500$ GeV can maximally reach $-30%$ for the process $e^{+}e^{-}\rightarrow ZHH$ and $-16%$ for the process $e^{+}e^{-}\rightarrow ν\barνHH$ in the allowed parameter space, respectively. These large relative corrections can reach the detection range of the fu…
New data analysis with Pauli blocking explains observation of CP violation in $B^o\rightarrow Kπ$ decays, absence in $B^{\pm} \rightarrow Kπ$ decays and gives new predictions agreeing with experiment. Branching ratio data show pure I=1/2 amplitude predicted by pure penguin transitions for separate relations within charged and neutral B decays, but strong violation of penguin I=1/2 isospin relation between charged and neutral decays. $B(B^o \rightarrow K^+ π^-) - 2B(B^o\rightarrow K^o π^o) = %(19.4 \pm 0.6)- 2\cdot (9.4 \pm 0.6) = (0.6 \pm 1.3)\cdot 10^-6 \approx 0$ $2B(B^+ \rightarrow K^+ π^o)…
Radiative $\bar{B}^0(\bar{B}^0_s)\rightarrow J/ψγ$ decays provide an interesting case to test our understanding of (non)perturbative QCD and eventually to probe physics beyond the standard model. Recently, the LHCb Collaboration has reported an upper bound, updating the results of the BABAR Collaboration. Previous theoretical predictions based on QCD factorization or perturbative QCD have shown large variations due to different treatment of nonfactorizable contributions and meson-photon transitions. In this paper, we report on a novel approach to estimate the decay rates, which is based on a r…
We study the quark flavor violating Higgs-boson decay $h \rightarrow \bar b s + b \bar s$ in the Minimal Supersymmetric Standard Model (MSSM). The decay is analyzed first in a model independent, and in a second step in the minimal flavor violationg (MFV) Constrained MSSM. The experimental constraints from $B$-Physics observables (BPO) and electroweak precision observables (EWPO) are also calculated and imposed on the parameter space. It is shown that in some cases the EWPO restrict the flavor violating parameter space stronger than the BPO. In the model independent analysis values of ${\cal O}…
In this paper we present a fully-differential calculation for the contributions to the partial widths $H\rightarrow b\bar{b}$ and $H\rightarrow c\bar{c}$ that are sensitive to the top quark Yukawa coupling $y_t$ to order $α_s^3$. These contributions first enter at order $α_s^2$ through terms proportional to $y_t y_q$ ($q=b,c$). At order $α_s^3$ corrections to the mixed terms are present as well as a new contribution proportional to $y_t^2$. Our results retain the mass of the final-state quarks throughout, while the top quark is integrated out resulting in an effective field theory (EFT). Our r…
We investigate the anomalous $W^+W^-γ$ couplings through the process $e^-e^+\,\rightarrow\,ν_e\barν_eγ$ for unpolarized and polarized electron (positron) beams at the International Linear Collider. We give the 95$\%$ Confidence Level limits on the anomalous couplings with and without the systematic uncertainties for various values of center-of-mass energies and the integrated luminosities. We show that the obtained limits on the anomalous couplings through the process $e^-e^+\,\rightarrow\,ν_e\barν_eγ$ can highly improve the current experimental limits.
In our previous work, based on the $SU(6)$ spin-flavor wave function, we regard $Λ$ and $p$ as composed of different quark-diquark configurations and established the Bethe-Salpeter (BS) equations of configurations for quark and scalar diquark. In our present work, we apply this model to calculate the form factors of the semileptonic transitions $Λ_b\rightarrowΛl^+l^-$ $(l=μ,e,τ)$ and $Λ_b\rightarrow p l\barν$ within the Standard Model (SM). The decay $Λ_b\rightarrowΛμ^+μ^-$ is especially interesting since it has been measured in CDF and LHCb Collaborations and this rare decay is very sensitive…
It is emphasized that a rare decay $K^+ \rightarrow π^+ ν\barν$ becomes promising in a future search for a new particle, because the theoretical treatment is well established and the value of the branching ratio $Br(K^+ \rightarrow π^+ ν\barν)$ is sensitive to a search for a new particle with a TeV scale mass. As an example, according to a U(3) family gauge boson model which predicts the lowest family gauge boson with a few TeV mass $M_{11}$, the branching ratio $Br(K^+ \rightarrow π^+ ν\barν)$ is discussed. If we can obtain, in future, a slightly lower value $Br^{obs} \sim 0.9 \times 10^{-10}…
At Moriond 2019, Belle collaboration announced their new measurements on $R_D$ and $R_{D^*}$ which are in agreement with their Standard Model (SM) predictions within $1.2σ$. After inclusion of these measurements, the discrepancy between the world averages and the SM predictions of $R_D$-$R_{D^*}$ comes down from $4.1σ$ to $3.1σ$. Here we do a global fit by taking all measurements in $b\rightarrow cτ\barν$ transition. We find that there are seven allowed new physics solutions, each with different Lorentz structure. Further we show that it is possible to distinguish between them by means of the …
We calculate the transition form factors of the semileptonic $B_c\rightarrow χ_{c2} l \barν $ in the framework of QCD sum rules taking into account the two-gluon condensate corrections. Using the obtained results of form factors we estimate the decay widths and branching ratios related to this transition at all lepton channels. A comparison of the obtained results with the predictions of other non-perturbative approaches are also made. The orders of branching ratios for different lepton channels indicate that the $B_c\rightarrow χ_{c2} l \barν $ transition can be studied at LHC using the colle…
We investigate $J/ψ$ decays into octet baryon-antibaryons pairs. The decay amplitudes are computed within the collinear QCD factorisation framework. The subleading amplitude, which describes the decay of longitudinally polarised charmonium, is computed using twist-4 three-quark distribution amplitudes. The obtained results are used for a qualitative analysis of the experimental data. It is found that the polarisation parameter $α_B$ can be described with an accuracy $10-30\%$, which may indicate that the pQCD contribution dominates this observable.
The form factors of the semileptonic $χ_{b2}(1P)\rightarrow B_{c}\bar{l}ν$ decay are calculated using the QCD sum rule approach. The results obtained are then used to estimate the decay widths of this transition in all lepton channels. The orders of decay rates indicate that this transition is accessible at LHC for all lepton channels.
The potentialities of the production of the scalar $K\bar K$ molecules in the $ϕ$ radiative decays are considered beyond the narrow resonance width approximation. It is shown that $BR(ϕ\rightarrowγf_0(a_0)\rightarrowγππ(πη))\approx (1÷2)\times 10^{-5}\ ,\BR(ϕ\rightarrowγ(f_0+a_0)\rightarrowγK^+K^-)\alt 10^{-6}$ and $BR(ϕ\rightarrowγ(f_0+a_0) \to γK^0\bar K^0)\alt 10^{-8}$. The mass spectra in the $ππ ,\ πη ,\ K^+K^-\ ,\ K^0\bar K^0$ channels are calculated. The imaginary part of the amplitude $ϕ\rightarrowγf_0(a_0)$ is calculated analytically. It is obtained the phase of the scalar resonance p…
We study the electromagnetic form factors of $Λ$ hyperon in the timelike region using the recent experimental data in the exclusive production of $\barΛ Λ$ pair in electron-position annihilation. We present a pQCD inspired parametrization of $G_E(s)$ and $G_M(s)$ with only two parameters, and we consider a suppression mechanism of the electric form factor $G_E(s)$ compared to the magnetic form factor $G_M(s)$. The parameters are determined through fitting our parametrization to the effective form factor data in the reaction $e^+e^-\rightarrow \barΛΛ$. Except the threshold region, our parametri…
An investigation about localized CP asymmetries for the processes of $\bar{B}_{s}^{0} \rightarrow π^{+}π^{-}π^{0} (K^{0})$ is presented in this paper. The innovation of this paper is that there is a consideration of three-particle $ρ^0(770)$, $ω(782)$ and $ϕ(1020)$ interferences effect. Generally, $ω(782)$ and $ϕ(1020)$ both can decay into $π^+π^-$ pair where can cause extremely small contribution from isospin symmetry breaking. Nevertheless, our analysis shows that $\bar{B}_{s}^{0} \rightarrow π^+π^-π^{0}(K^{0})$ decay process can bring differential CP asymmetry about $65\%$ ($36\%$) because …
