arXiv subjects

Gang Lü

Publications and source records attributed to Gang Lü.

At least 19 recordsLinked to original sources

arXiv2026

CP violation induced by the real part of the interference term in $ρ^0 - ω$ mixing

To circumvent the severe numerical cancellations in the standard integrated CP asymmetry ($A_{CP}$) near the $ω$ mass $m_ω$, we propose a modified CP-violating observable, $A_{CP}^{\Re}$, which explicitly highlights the contribution of the real part of the interference term. Subsequently, we employ the three-body hadronic decay $B^{-} \rightarrow π^{+} π^{-} π^{-}$ within the Perturbative QCD (PQCD) approach as a primary case study to validate this theoretical framework. Furthermore, this method naturally eliminates the smooth, sign-preserving continuum background originating from broad scalar resonances like the $f_0(500)$. This generalized framework provides clean and robust theoretical guidance for recovering localized CP-violation signals that might otherwise be masked by coarse experimental binning at future high-luminosity colliders.

hep-ph↗

arXiv2025

Study of $Kπ$ final states from four-body deacy of $\bar{B}_{s}$ meason under perturbation QCD

In the perturbative QCD framework, we use the quasi-two-body method to study the CP violations and branching ratios in the $\bar B_{s} \rightarrow [ϕ(ρ^{0},ω)\rightarrow K^{+}K^{-}][K^{*0}\rightarrow K^{+}π^{-}]$ and $\bar B_{s} \rightarrow [ρ^{0}(ω,ϕ)\rightarrow (π^{+}π^{-})][K^{*0}\rightarrow K^{+}π^{-}]$ decay processes. Owing to the interference effects of $ρ^{0}$, $ω$, and $ϕ$, new strong phases associated with vector mesons will be generated, resulting in relatively large CP violation within the interference region. Moreover, we provide numerical comparisons of CP violation from resonance effects and non-resonance contributions. In order to provide better theoretical predictions for future experiments, we integrate CP violation over invariant mass to obtain the regional CP violation value. Furthermore, we have calculated the polarization fractions and branching ratios for different intermediate states in the four-body decay process, which may be influenced by vector interference effects. Additionally, we discuss the possibility of observing the predicted CP violation at the LHC.

hep-ph↗

arXiv2025

The role and contribution of resonance effect for the decay process of $\bar B^{0}_s \rightarrow π^{+}π^{-}P$

The size of the direct CP asymmetry generated during the weak decay of hadrons is attributed to the weak phase and some strong phases. The weak phase comes from the CKM matrix and a strong phase may result from the resonance effect which is produced by the mixing of vector meson $V\left\{ρ^{0}(770),ω(782),ϕ(1020)\right\}$ to $π^+ π^-$ meson pairs. $ρ^{0}(770)$ can decay directly into $π^+ π^-$ meson pairs, both $ω(782)$ and $ϕ(1020)$ can also decay into $π^+ π^-$ meson pairs with small contribution from isospin symmetry breaking. The main contribution for the middle state vector meson $ρ^{0}(770)-ω(782)-ϕ(1020)$ interference is the mix of $ρ^{0}(770)$, $ω(782)-ρ^{0}(770)$ and $ϕ(1020)-ρ^{0}(770)$. We calculate the CP asymmetry and decay branching ratio for $\bar{B}^0_{s} \rightarrow π^+ π^- π^0 (\bar K ^{0})$ in the framework of QCD factorization and compare them with previous work. We also add the analysis of $\bar{B}^0_{s} \rightarrow π^+ π^- η(η^{(')})$ decay process. The results show that the CP asymmetry of these four decay processes are significantly enhanced especially for the $\bar{B}^0_{s} \rightarrow π^+ π^- \bar K ^{0}$ decay process and the decay branching ratio also changes under resonance effect. These work might provide support for the experimental analysis of the $\bar B^{0}_s$ meson.

hep-ph↗

arXiv2025

The $CP$ violations and branching ratios for $B_c^+\to D_{(s)}^+π^+π^-(K^{+}K^{-})$ from interference of the vector mesons in Perturbative QCD

Within the framework of the perturbative QCD approach utilizing $K_T$ factorization, we have investigated the CP violations and branching ratios in the decay processes of $B_{c}^{+}\to D_{(s)} ^{+}V(V\rightarrowπ^{+}π^{-})$ and $B_{c}^{+}\to D_{(s)}^{+}V(V\rightarrow K^{+}K^{-})$, where V denotes three vector mesons $ρ^0$, $ω$, and $ϕ$. During the $V\to π^+π^-$ and $V\to K^+K^-$ decay processes, we incorporated the $ρ^{0}-ω-ϕ$ mixing mechanism to describe the amplitudes of these quasi-two-body decay processes. Within the interference regime of the three vector particles, we observed distinct changes in both CP violations and branching ratios. Furthermore, our study presents evidence for local CP violations and branching ratios that warrants further investigation through experiments.

hep-ph↗

arXiv2025

Direct CP violation in $\bar B_{s} \rightarrow K^{+}K^{-} K^{+}K^{-}$ decay process induced by interferences of the intermediate vector particles

We investigate CP violation in the decay process $\bar B_{s} \rightarrow V V \rightarrow K^{+}K^{-}K^{+}K^{-}$ within the framework of perturbative QCD, where V represents vector mesons $ϕ$, $ρ$, and $ω$. We analyze the mixing mechanism among $ϕ-ρ^{0}-ω$ and provide amplitudes for these decay processes. Moreover, we explore CP violation in the four-body decay process of $\bar{B}_{s}^{0} \rightarrow K^{+} K^{-} K^{+} K^{-}$ involving intermediate vector mesons and their mixing. Notably, significant CP violation is observed for specific two-vector meson intermediate states. Additionally, a substantial amount of CP violation arises from vector mixing when the invariant mass of $K^{+}K^{-}$ falls within a certain range. This study holds potential implications for future detection by the LHC experiment.

hep-ph↗

arXiv2024

CP asymmetry from the effect of the isospin symmetry breaking during B-meson decay

The direct CP asymmetry in quasi-two-body decays of $B \rightarrow (V\rightarrow π^{+}π^{-})P $ is investigated in the perturbative QCD method, where P represents a pseudoscalar meson and V refers to $ρ$, $ω$ and $ϕ$ mesons, respectively. We present the amplitude of the quasi-two-body decay process and investigate the effects of mixed resonances involving $ρ^{0}-ω$, $ρ^{0}-ϕ$ and $ω-ϕ$, while considering the impact of isospin symmetry breaking. We observe a significant CP asymmetry when the invariant mass of the $π^{+}π^{-}$ pair is within the resonance ranges of $ρ$, $ω$ and $ϕ$ mesons. Consequently, we proceed to quantify the regional CP asymmetry in these resonance regions. A significant difference is observed when comparing results obtained with and without interferences of the three vector mesons and isospin conservation. The CP asymmetry results obtained from the three-body decay process, without interference due to isospin conservation by the perturbative QCD method, are in agreement with the newly updated data acquired by the LHCb experiment.

hep-ph↗

arXiv2024

The resonance effect for the CP asymmetry associated with the process $ω\rightarrow π^{+}π^{-}π^{0}$

The direct CP asymmetry in the weak decay process of hadrons is commonly attributed to the weak phase of the CKM matrix and the indeterminate strong phase. We propose a way of creating a strong phase difference between two decay paths involving vector mesons $V= ω,ρ$ decaying to $π^{+}π^{-}π^{0}$ considering the G-parity suppressed decay process $ρ^{0} \rightarrow π^{+}π^{-}π^{0} $. It can lead to a significant CP asymmetry in the interference region. We consider the effects of $ω$ and $ρ$ mixing on their decays to $π^{+}π^{-}π^{0}$. Meanwhile, we calculate the CP asymmetry for the process $B\rightarrow π^{+}π^{-}π^{0}P$ (P refers to pseudoscalar meson) through $ω(ρ) \rightarrow π^{+}π^{-}π^{0}$. Besides, we also calculate the integral results of different phase space regions. We hope that our work can help provide some theoretical guidance for future experimental studies of CP asymmetry in these decays.

hep-ph↗

arXiv2023

Resonant contribution of the three-body decay process $\bar B_{s}\rightarrow K^{+}K^{-} P$ in perturbation QCD

We investigate the CP violation in the decay process $\bar B_{s} \rightarrow ϕ(ρ,ω) P \rightarrow K^{+}K^{-}P$ by considering the interference effects of $ϕ\rightarrow K^{+}K^{-}$, $ρ\rightarrow K^{+}K^{-}$ and $ω\rightarrow K^{+}K^{-}$ within the framework of perturbative QCD method (P refers to $π$, K, $η$ and $η'$ pseudoscalar mesons, respectively). We analyse the mixings of $ϕ-ρ^{0}$, $ϕ-ω$ and $ω-ρ^{0}$ and provide the amplitudes of the quasi-two-body decay processes. The CP violation for $\bar B_{s} \rightarrow K^{+}K^{-} P$ decay process is obvious at the ranges of the three vector mesons interferences. Meanwhile, the localised CP violation can be found for comparing with the experiment results from three-body decay process at the LHC in the near future.

hep-ph↗

arXiv2023

CP asymmetry from resonance effect of B meson decay process with $π$ and K final states

We introduce the new resonance of $V\rightarrow K^{+}K^{-}$ $(V=ϕ, ρ, ω)$, which produces some new strong phase associated with vector meson resonance and thus can cause relatively large CP asymmetry at the range of interferences. There are the resonances of $ϕ\rightarrow K^{+}K^{-}$, $ρ\rightarrow K^{+}K^{-}$ and $ω\rightarrow K^{+}K^{-}$ due to the mixing of vector mesons $ϕ$, $ρ$, $ω$. We calculate the CP asymmetry from the decay modes of $B \rightarrow KKπ(K)$. Meanwhile, the localised CP asymmetries are presented and some detailed analysis can be found. The CP asymmetry from the decay mode of ${B}^{-}\rightarrow ϕπ^{-}\rightarrow K^{+}K^{-}π^{-}$ is also presented in our framework which is well consisted with LHC experiment. The introduced CP asymmetry can provide a favorable theoretical support for the experimental exploration in the future.

hep-ph↗

arXiv2022

Analysis of localized CP asymmetry in $\bar{B}_{s}^{0} \rightarrow π^+π^-π^{0}(K^{0})$

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 of isospin symmetry breaking. To better compared with the data from experimental in the future, we integrate CP asymmetry over the invariant mass and obtain localized CP asymmetry value for the decay $\bar{B}_{s}^{0} \rightarrow π^+π^-π^{0} (K^{0})$. We find that there is an evident signal about CP asymmetry at invariant mass value $m(π^{+}π^{-})$ below the mass of $ρ(770)^{0}$ with the decay $\bar{B}_{s}^{0} \rightarrow π^+π^{-}π^{0}$.

hep-ph↗

arXiv2022

Direct $CP$ violation of three bodies decay process from the resonance effect

The physical state of $ρ$-$ω$-$ϕ$ mesons can be mixed by the unitary matrix. The decay processes of $ω\rightarrow π^{+}π^{-}$ and $ϕ\rightarrow π^{+}π^{-}$ are from the isospin symmetry breaking. The $ρ-ω$, $ρ-ϕ$ and $ω-ϕ$ interferences lead to resonance contribution to produce the strong phases. The $CP$ asymmetry is considered from above isospin symmetry breaking due to the new strong phase for the first order. It has been found the $CP$ asymmetry can be enhanced greatly for the decay process of $B^{0}\rightarrowπ^+π^{-}η^{(')}$ when the invariant masses of the $π^+π^{-}$ pairs are in the area around the $ω$ resonance range and the $ϕ$ resonance range in perturbative QCD. We also discuss the possibility to search the predicted $CP$ violation at the LHC.

hep-ph↗

arXiv2021

Hunting for direct CP violation in $\bar{B}_s^0 \to {π^+}{π^-}K^{*0}$

In perturbative QCD approach, based on the first order of isospin symmetry breaking, we study the direct $CP$ violation in the decay of $\bar{B}_s^0\toρ(ω)K^{*0}\to {π^+}{π^-}K^{*0}$. An interesting mechanism is applied to enlarge the $CP$ violating asymmetry involving the charge symmetry breaking between $ρ$ and $ω$. We find that the $CP$ violation is large by the $ρ-ω$ mixing mechanism when the invariant masses of the $π^+π^-$ pairs is in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\toρ(ω)K^{*0}\to{π^+}{π^-}K^{*0}$, the maximum $CP$ violation can reach $-59.12\%$. Furthermore, taking $ρ-ω$ mixing into account, we calculate the branching ratio for $\bar{B}_s^0 \rightarrow ρ(ω) K^{*0}$. We also discuss the possibility of observing the predicted $CP$ violation asymmetry at the LHC.

hep-ph↗

arXiv2020

Isospin symmetry breaking effects for the mode ${B}\rightarrow ππ(K)$ in Perturbative QCD

We calculate the direct $CP$ violation for the decay process of ${B}^{0}\rightarrow π^{0}π^{0}$, ${B}^{+}\rightarrow π^{0}π^{+}$, ${B}^{0}\rightarrow K^{0}π^{0}$ and ${B}^{+}\rightarrow K^{+}π^{0}$ via isospin symmetry breaking effects from the $π^{0}-η-η'$ mixing mechanism in perturbative QCD approach. Isospin symmetry breaking originates from the electroweak interaction and the u-d quark mass difference through the strong interaction which are known to be tiny. However, we find that isospin symmetry breaking at the leading order changes the $CP$ violation from the new strong phases. Our calculation results for the $CP$ violation are within or including the range of experimental results. We also compare our results with those from the QCD factorization and the perturbative QCD schemes without regard to isospin symmetry breaking effects.

hep-ph↗

arXiv2019

Direct $CP$ violation for $\bar{B}_s^0 \to ϕ{π^+}{π^-}$ in Perturbative QCD

In perturbative QCD approach, we study the direct $CP$ violation in the decay of $\bar{B}_s^0\toρ(ω)ϕ\to {π^+}{π^-}ϕ$ via isospin symmetry breaking. An interesting mechanism involving the charge symmetry violating between $ρ$ and $ω$ is applied to enlarge the $CP$ violating asymmetry. We find that the $CP$ violation can be enhanced by the $ρ-ω$ mixing mechanism when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\toρ(ω)ϕ\to{π^+}{π^-}ϕ$, the maximum $CP$ violation can reach $5.98\%$. The possibility of detecting the $CP$ violation is also presented.

hep-ph↗

arXiv2019

Direct $CP$ violation from isospin symmetry breaking effects in PQCD

We investigate the direct $CP$ violation for the decay process of $\bar{B}_{s}\rightarrow P(V)π^{0}$ (P,V refer to the pseudoscalar meson and vector meson, respectively) via isospin symmetry breaking effects from the $π^{0}-η-η'$ mixing mechanism in PQCD factorization approach. Isospin symmetry breaking arises from the electroweak interaction and the u-d quark mass difference by the strong interaction which are known to be tiny. However, we find that isospin symmetry breaking at the leading order shifts the $CP$ violation due to the new strong phases.

hep-ph↗

arXiv2018

Effect of resonance for $CP$ asymmetry of the decay process $\bar{B}_{s}\rightarrow Pπ^+π^-$ in perturbative QCD

In the framework of Perturbative QCD (PQCD) approach we study the direct $CP$ asymmetry for the decay channel $\bar{B}_{s}\rightarrow Pπ^+π^-$ around the resonance range via the $ρ-ω$ mixing mechanism (where P refer to pseudoscalar meson). We find that the $CP$ asymmetry can be enhanced by $ρ-ω$ mixing when the masses of the $π^+π^-$ pairs are at the area of $ρ-ω$ resonance, and the maximum $CP$ asymmetry can reach 59{\%} for the relevant decay channels.

hep-ph↗

arXiv2017

$CP$ violation induced by the double resonance for pure annihilation decay process in Perturbative QCD

In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in the pure annihilation decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$ induced by the $ρ$ and $ω$ double resonance effect. Generally, the $CP$ violation is small in the pure annihilation type decay process. However, we find that the $CP$ violation can be enhanced by double $ρ-ω$ interference when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$, the maximum $CP$ violation can reach 28.64{\%}.

hep-ph↗

arXiv2016

$CP$ violation for $B^+_{c}\rightarrow D_{(s)}^+π^+π^-$ in Perturbative QCD

In the perturbative QCD (PQCD) approach we study the direct $CP$ violation in $B^+_{c}\rightarrow D_{(s)}^+ρ^0(ω) \rightarrow D_{(s)}^+π^+π^-$ via the $ρ-ω$ mixing mechanism. We find that the $CP$ violation can be enhanced by $ρ-ω$ mixing when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process $B^+_{c}\rightarrow D^+ρ^0(ω) \rightarrow D^+π^+π^-$, the maximum $CP$ violation can reach 7.5 {\%}.

hep-ph↗