arXiv subjects

Tai-Fu Feng

Publications and source records attributed to Tai-Fu Feng.

At least 73 records · Page 4Linked to original sources

arXiv2023

GKZ-system of the 2-loop self energy with 4 propagators

Applying the system of linear partial differential equations derived from the Mellin-Barnes representation and the Miller transformation, we present the GKZ-system of the Feynman integral of the 2-loop self energy diagram with 4 propagators. The codimension of the derived GKZ-system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. In total 536 hypergeometric functions are obtained in the neighborhoods of the origin and infinity, in which 30 linearly independent hypergeometric functions whose convergent regions have nonempty intersection constitute a fundamental solution system in a proper subset of the whole parameter space.

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arXiv2023

Study on muon MDM and lepton EDM in BLMSSM via the mass insertion approximation

In the framework of the MSSM extension with local gauged baryon and lepton numbers (BLMSSM), we calculate the muon anomalous magnetic dipole moment (MDM) and lepton $(e, μ, τ)$ electric dipole moment (EDM), and discuss how the muon MDM and lepton EDM depend on the parameters within the mass insertion approximation. Among many parameters, $\tanβ$,~$g_L$,~$m_L$ and $μ_H$ are more sensitive parameters for $a^{BL}_μ$. Considering the experimental limitations, our best numerical result of $a^{BL}_μ$ is around $2.5 \times 10^{-9}$, which can well compensate the departure between the experiment data and Standard Model (SM) prediction. The CP violating phases in BLMSSM are more than those in the MSSM, including new parameters $θ_{μ_L}$ and $θ_{L}$. They can give large contributions, which play an important role in exploring the source of CP violation and probing new physics beyond SM.

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arXiv2022

The solution to the `$1/2$ vs $3/2$' puzzle

Using an almost complete relativistic method based on the Bethe-Salpeter equation, we study the mixing angle $θ$, the mass splitting $\bigtriangleup M$, the strong decay widths $Γ(D^{({\prime})}_1)$ and the weak production rates $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ of the $D_1(2420)$ and $D_1^{\prime}(2430)$. We find there is the strong cancellation between the $^1P_1$ and $^3P_1$ partial waves in $D_1^{\prime}(2430)$ with $θ\sim-35.3^{\circ}$, which leads to the `$1/2$ vs $3/2$' puzzle. The puzzle can not be overcome by adding only relativistic corrections since in a large parameter range where $\bigtriangleup M$ is linear varying and not small, the $θ$, $Γ(D^{({\prime})}_1)$ and $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ remain almost unchanged but conflict with data. While in a special range around the mass inverse point where $\bigtriangleup M=0$ and $θ=\pm 90^{\circ}$, they change rapidly but we find the windows where $\bigtriangleup M$, $Γ(D^{({\prime})}_1)$ and $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ are all consistent with data. The small $\bigtriangleup M$ confirmed by experiment, is crucial to solve the `$1/2$ vs $3/2$' puzzle.

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arXiv2022

Higgs boson decays $h\rightarrow Z γ$ and $h\rightarrow m_V Z$ in the $U(1)_X$SSM

We present a detailed analysis of the Higgs boson decays $h\rightarrow Z γ$ and $h\rightarrow m_V Z$ in the $U(1)_X$SSM, with $m_V$ denoting the meson ($ω,ρ,ϕ,J/ψ,Υ$). Using the effective Lagrangian method, we calculate the effective constants $C_{γZ}$ (CP-even) and $\tilde{C}_{γZ}$ (CP-odd) for the vertex $h γZ$, which are corrected by the new particle loop diagrams. Numerically, the ratio $Γ_{U(1)_X}(h\rightarrow Z γ)/Γ_{SM}(h\rightarrow Z γ)$ is between $1.02-1.35$. For the vector mesons $ω,ρ,ϕ$ and $J/ψ$, the ratios $Γ_{U(1)_X}(h\rightarrow m_V Z )/Γ_{SM}(h\rightarrow m_V Z)$ are mainly distributed in the range of ($1.01-1.45$). When $m_V$ represents $Υ$, the larger value of the ratio $Γ_{U(1)_X}(h\rightarrow ΥZ )/Γ_{SM}(h\rightarrow ΥZ)$ is mostly located in the range of ($1.002-1.30$). This work can provide a reference for specific types of decay processes which can be searched in LHC.

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arXiv2022

Study the Higgs mass with the effective potential and Higgs decays in the $U(1)_X$SSM

As the U(1) extension of the minimal supersymmetric standard model, the $U(1)_X$SSM has new super fields such as right-handed neutrinos and three Higgs singlets. In the $U(1)_X$SSM, the lightest CP-even Higgs mass $m_{h^0}$ is researched through the Higgs effective potential with one loop corrections. We also calculate the Higgs decays $h^0\rightarrowγγ$, $h^0\rightarrow VV~(V=W,~Z)$, $h^0\rightarrow l\bar{l}Z$ and $h^0\rightarrow ν\barνZ$. The obtained results are reasonable, which are in favour of the study of the Higgs characteristic and the phenomenology of the $U(1)_X$SSM.

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arXiv2022

$Z$ boson decays $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ and Higgs boson decays $h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ with lepton flavor violation in a $U(1)$ extension of the MSSM

$U(1)_X$SSM is the extension of the minimal supersymmetric standard model (MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. We study lepton flavor violating (LFV) decays $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($Z\rightarrow eμ$, $Z\rightarrow eτ$, and $Z\rightarrow μτ$) and $h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($h\rightarrow eμ$, $h\rightarrow eτ$, and $h\rightarrow μτ$), in this model. In the numerical results, the branching ratios of $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are from $10^{-9}$ to $10^{-13}$ and the branching ratios of $h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are from $10^{-3}$ to $10^{-9}$, which can approach the present experimental upper bounds. Based on the latest experimental data, we analyze the influence of different sensitive parameters on the branching ratio, and make reasonable predictions for future experiments. The main sensitive parameters and LFV sources are the non-diagonal elements corresponding to the initial and final generations of leptons, which can be seen from the numerical analysis.

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arXiv2022

Feynman Integrals of Grassmannians

We embed Feynman integrals in the subvarieties of Grassmannians through homogenization of the integrands in projective space, then obtain GKZ-systems satisfied by those scalar integrals. The Feynman integral can be written as linear combinations of the hypergeometric functions of a fundamental solution system in neighborhoods of regular singularities of the GKZ-system, whose linear combination coefficients are determined by the integral on an ordinary point or some regular singularities. Taking some Feynman diagrams as examples, we elucidate in detail how to obtain the fundamental solution systems of Feynman integrals in neighborhoods of regular singularities. Furthermore we also present the parametric representations of Feynman integrals of the 2-loop self-energy diagrams which are convenient to embed in the subvarieties of Grassmannians.

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arXiv2022

Muon conversion to an eletron in nuclei in the $B-L$ symmetric SSM

In a few years, the COMET experiment at J-PARC and the Mu2e experiment at Fermilab will probe the $μ-e$ conversion rate in the vicinity of $\mathcal{O}(10^{-17})$ for an Al target with high experimental sensitivity. Within the framework of the minimal supersymmetric extension of the Standard Model with local $B-L$ gauge symmetry (B-LSSM), we analyze the lepton flavor violating (LFV) process of $μ-e$ conversion in nuclei. Considering the constraint of the experimental upper limit of the LFV rare decay $μ\rightarrow eγ$, the $μ-e$ conversion rates in nuclei within the B-LSSM can achieve $\mathcal{O}(10^{-12})$, which is 5 orders of magnitude larger than the future experimental sensitivity at the Mu2e and COMET experiments and may be detected in the near future.

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arXiv2022

Lepton flavor violating decays $l_j\rightarrow{l_iγ}$ in the $U(1)_X$SSM model within the Mass Insertion Approximation

Three singlet new Higgs superfields and right-handed neutrinos are added to MSSM to obtain $U(1)_X$SSM model. Its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. In the framework of $U(1)_X$SSM, we study muon anomalous magnetic moment and lepton flavor violating decays $l_j\rightarrow{l_iγ}(j=2,3;i=1,2)$ within the Mass Insertion Approximation(MIA). Through the MIA method, we can find the parameters that directly affect the analytical result of the lepton flavor violating decays $l_j\rightarrow{l_iγ}$, which make our work more convenient. We want to provide a set of simple analytic formulas for the form factors and the associated effective vertices, that may be very useful for future phenomenological studies of the lepton flavor violating decays. According to the accuracy of the numerical results which the influence of different sensitive parameters, we come to the conclusion that the non-diagonal elements which correspond to the generations of the initial lepton and final lepton are main sensitive parameters and lepton flavor violation(LFV) sources. This work can provide a clear signal of new physics(NP).

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arXiv2022

Pair production of neutral Higgs particles in the B-LSSM

Higgs pair production provides a unique handle for measuring the strength of Higgs self interaction and constraining the shape of the Higgs potential. Including radiative corrections to the trilinear couplings of $CP$-even Higgs, we investigate the cross section of the lightest neutral Higgs pair production in gluon fusion at the Large Hadron Collider in the supersymmetric extensions of the standard model. Numerical results indicate that the correction to the cross section is about 11\% in the B-LSSM, while is only about 4\% in the MSSM. Considering the constraints of the experimental data of the lightest Higgs, we find that the gauge couplings of $U(1)_{B-L}$ and the ratio of the nonzero vacuum expectation values of two singlets also affect strongly the theoretical evaluations on the production cross section in the B-LSSM.

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arXiv2022

Nuclear $0\nu2β$ decays in $B-L$ symmetric SUSY model and in TeV scale left-right symmetric model

In this paper we take B-L supersymmetric standard model (B-LSSM) and TeV scale left-right symmetric model (LRSM) as two representations of the two kinds of new physics models to study the nuclear neutrinoless double beta decays ($0\nu2β$) so as to see the senses onto these two kinds of models when the decays are taken into account additionally. Within the parameter spaces allowed by all the exist experimental data, the decay half-life of the nucleus $^{76}$Ge and $^{136}$Xe, $T^{0ν}_{1/2}$($^{76}$Ge, $^{136}$Xe), is precisely calculated and the results are presented properly. Based on the numerical results, we conclude that the room of LRSM type models for the foreseeable future experimental observations on the decays is greater than that of B-LSSM type models.

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arXiv2022

Muon anomalous magnetic dipole moment in the $μν$SSM

Recently, the Muon g-2 experiment at Fermilab has measured the muon anomalous magnetic dipole moment (MDM), $a_μ=(g_μ-2)/2$, which reported that the new experimental average increases the tension between experiment and the standard model (SM) prediction to 4.2$σ$. In this work, we reanalyse the muon anomalous MDM at two-loop level in the $μ$ from $ν$ Supersymmetric Standard Model ($μν$SSM) combined with the updated experimental average. The $μν$SSM can explain the current tension between the experimental measurement and the SM theoretical prediction for the muon anomalous MDM, constrained by the 125 GeV Higgs boson mass and decays, the rare decay $\bar{B}\rightarrow X_sγ$ and so on. We also investigate the anomalous MDM of the electron and tau lepton, $a_e=(g_e-2)/2$ and $a_τ=(g_τ-2)/2$, at two-loop level in the $μν$SSM. In addition, the 125 GeV Higgs boson decays to a pair of charged leptons in the $μν$SSM are also analysed.

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arXiv2022

The study of lepton EDMs in $U(1)_X$ SSM

The minimal supersymmetric extension of the standard model (MSSM) is extended to the $U(1)_X$SSM, whose local gauge group is $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_X$. To obtain the $U(1)_X$SSM, we add the new superfields to the MSSM, namely: three Higgs singlets $\hatη,~\hat{\barη},~\hat{S}$ and right-handed neutrinos $\hatν_i$. The CP violating effects are considered to study the lepton electric dipole moment(EDM) in $U(1)_X$SSM. The CP violating phases in $U(1)_X$SSM are more than those in the standard model(SM). In this model, some new parameters $(θ_S, θ_{BB^{\prime}}, θ_{BL})$ as CP violating phases are considered, so there are new contributions to lepton EDMs. It is conducive to exploring the source of CP violation and probing new physical beyond SM.

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arXiv2022

The newly observed state $D_{s0}(2590)^{+}$

We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the $S$ matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $D^*(2010)\to Dπ$, we study the newly observed $D_{s0}(2590)^{+}$ with supposing it to be the state $D_s(2^1S_0)^+$, we find its decay width $Γ$ is highly sensitive to the $D_{s0}(2590)^{+}$ mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we studied the overlap integral over the wave functions of initial and final states, here we parameterized it as $X$ which is model-independent, and the ratio $Γ/{|{\vec P_f}|^3}$, both are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $X_{D_s(2S) \to D^*K}=0.25\sim 0.41$ and $Γ/{|{\vec P_f}|^3}=0.81\sim1.77$ MeV$^{-2}$ are smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) \to Dπ}=0.540\pm0.009$, the current data $X^{ex}_{D_s(2S) \to D^*K}=0.585^{+0.015}_{-0.035}$ is too big to be an reasonable value, so it is early to say $D_{s0}(2590)^{+}$ is the conventional $D_s(2^1S_0)^+$ meson.

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arXiv2022

Lepton flavor violating decays $τ\rightarrow{Pl}$ in the $U(1)_X$SSM model

$U(1)_X$SSM is the extension of the minimal supersymmetric standard model(MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to MSSM. In the framework of $U(1)_X$SSM, we study lepton flavor violating decays $τ\rightarrow{Pl}(P=π,~η,~η^\prime;~l=μ,~e)$. According to the latest experimental data of $τ\rightarrow{Pe}$ and $τ\rightarrow{Pμ}$, the influence of different sensitive parameters on the results is analyzed to make a reasonable prediction for future experiments. From the numerical analysis, the non-diagonal elements which correspond to the generations of the initial lepton and final lepton are main sensitive parameters and lepton flavor violation(LFV) sources. This work can provide a basis for finding the existence of new physics(NP).

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arXiv2022

Study muon g-2 at two-loop level in the $U(1)_X$SSM

The new experiment data of muon g-2 is reported by the workers at Fermilab National Accelerator Laboratory(FNAL). Combined with the previous Brookhaven National Laboratory(BNL) E821 result, the departure from the standard model prediction is about 4.2 $σ$. It strengthens our faith in the new physics. $U(1)_X$SSM is the U(1) extension of the minimal supersymmetric standard model, where we study the electroweak corrections to the anomalous magnetic dipole moment of muon from the one-loop diagrams and some two-loop diagrams possessing important contributions. These two-loop diagrams include Barr-Zee type, rainbow type and diamond type. The virtual supersymmetric particles in these two-loop diagrams are chargino, scalar neutrino, neutralino, scalar lepton, which are supposed not very heavy to make relatively large corrections. We obtain the Wilson coefficients of the dimension 6 operators inducing the anomalous magnetic dipole moment of muon. The numerical results can reach $25\times 10^{-10}$ and even larger.

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arXiv2021

Electric dipole moments of neutron and heavy quarks c, t in CP violating $U(1)_X$SSM

We study and analyze the electric dipole moments (EDMs) of neutron and heavy quarks c, t in a CP-violating (CPV) supersymmetric U(1) extension of the standard model called $U(1)_X$SSM, whose local gauge group is $U(1)_X\times SU(3)_C\times SU(2)_L \times U(1)_Y$. The contributions from the one loop diagrams and the Weinberg operators are taken into account with the new introduced CPV phases beyond the minimum supersymmetric standard model(MSSM) being non-zero. Our numerical results show that in $U(1)_X$SSM the neutron EDM can be smaller than its experimental upper bound $1.8\times10^{-26}$ e$\cdot$cm without a small CPV phase. The magnitudes of EDMs of heavy quarks c and t can reach $10^{-24}$ e$\cdot$cm. and $10^{-22}$ e$\cdot$cm respectively. This is favorable to the study of CPV.

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arXiv2021

Muon $(g-2)$ in the B-LSSM

The difference between the updated experimental result on the muon anomalous magnetic dipole moment and the corresponding theoretical prediction of the standard model on that is about $4.2$ standard deviations. In this work, we calculate the muon anomalous MDM at the two-loop level in the supersymmetric $B-L$ extension of the standard model. Considering the experimental constraints on the lightest Higgs boson mass, Higgs boson decay modes $h\rightarrow γγ,\;WW,\;ZZ,\; b\bar b,\;τ\barτ$, B rare decay $\bar B\rightarrow X_sγ$, and the transition magnetic moments of Majorana neutrinos, we analyze the theoretical predictions of the muon anomalous magnetic dipole moment in the $B-L$ supersymmetric model. The numerical analyses indicate that the tension between the experimental measurement and the standard model prediction is remedied in the $B-L$ supersymmetric model.

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