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We study the N-partite coherences of GHZ and W states for free bosonic and fermionic fields when any n observers hover near the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. We derive the more general analytical expressions for N-partite coherence, encompassing both physically accessible and inaccessible coherences in the context of the dilaton black hole. It has been found that the coherence of the bosonic field is greater than that of the fermionic field, while the entanglement of the fermionic field is greater than that of the bosonic field in dilaton spacetime. Additionally, the coherence of the W state is greater than that of the GHZ state, whereas the entanglement of the GHZ state is greater than that of the W state in curved spacetime. These results suggest that we should utilize suitable quantum resources and different types of particles for relativistic quantum information tasks., Comment: 23 pages, 5 figures

This paper investigates the neutrino transition magnetic moment in the $U(1)_X$SSM. $U(1)_X$SSM is the $U(1)$ extension of Minimal Supersymmetric Standard Model (MSSM) and its local gauge group is extended to $SU(3)_C\times SU(2)_L \times U(1)_Y\times U(1)_X$. To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to the MSSM, which can explain the results of neutrino oscillation experiments. The neutrino transition magnetic moment is induced by electroweak radiative corrections. By applying effective Lagrangian method and on-shell scheme, we study the associated Feynman diagrams and the transition magnetic moment of neutrinos in the model. We fit experimental data for neutrino mass variances and mixing angle. Based on the range of data selection, the influences of different sensitive parameters on the results are analysed. The numerical analysis shows that many parameters have an effect on the neutrino transition moment, such as $g_X$, $M_2$, $\lambda_H$ and $g_{YX}$. For our numerical results, the order of magnitude of $\mu_{ij}$ is between $10^{-20}$ and $10^{-19}$.

Lepton flavor violation (LFV) represents a clear new physics (NP) signal beyond the standard model (SM). In this paper, we study LFV decays $Z\rightarrow l^{\pm}_{i}l^{\mp}_{j}$ in the B-L Supersymmetric Standard Model(B-LSSM). We calculate these processes separately in the mass eigenstate basis and the electroweak interaction basis, and the latter adopt the mass insertion approximation (MIA) method. The MIA clearly shows the effect of parameters on the LFV decays $Z\rightarrow l^{\pm}_{i}l^{\mp}_{j}$ in the analytic level, which provides a new way for us to analyze the LFV processes. At the same time, the corresponding constraints from the LFV decays $l^{-}_{j} \rightarrow l^{-}_{i} \gamma$ and $(g-2)_{\mu}$ are considered to analyze the numerical results.

In the $U(1)_X$SSM, we delve into the flavor violation of $h \rightarrow bs$, where $h$ is identified with the SM-like Higgs boson discovered at the LHC. As the U(1) extension of the minimal supersymmetric standard model (MSSM), the U(1)XSSM has new super fields such as right-handed neutrinos and three Higgs singlets. We conduct a thorough analysis of the underlying mechanisms and parameter dependencies of $h \rightarrow bs$ in the $U(1)_X$SSM. In the $U(1)_X$SSM, we discover that the Br$(h \rightarrow bs)$ for the Higgs decay to $bs$ could significantly differ from the expectation in the standard model (SM), depending on the values of the new parameters introduced in the model. Our research not only contributes to a deeper understanding of Higgs physics within the $U(1)_X$SSM, but also provides valuable guidance for new physics (NP).

It is well known that the muon magnetic dipole moment (MDM) has close relation with the new physics (NP) in the development of the Standard Model (SM). Combined with the Fermilab National Accelerator Laboratory (FNAL) and the Brookhaven National Laboratory (BNL) E821 result, the departure from the SM prediction is about 5.0 $\sigma$. We study the electroweak corrections from several type two-loop SUSY diagrams and the virtual SUSY particles include chargino, neutralino, scalar lepton and scalar neutrino. Based on the latest experimental constraints, we study the muon MDM under the next to the minimal supersymmetric extension of the SM with local B-L gauge symmetry (N-B-LSSM). The abundant numerical results verify that $\tan{\beta},~T_e,~M^2_L,~M^2_e,~M_{BB'}$ and $M^2_{eij}$ play an important role in muon MDM. $M^2_e,~\tan{\beta}$ and $T_e$ are sensitive parameters to muon MDM. From the data obtained in all the figures of the numerical results, most of the values of $a_{\mu}^{NBL}$ are in 2$\sigma$ interval, which can compensate the departure between the experiment data and the SM prediction.

We study quantum steering and Bell nonlocality harvested by the local interaction of two Unruh-DeWitt detectors with the vacuum massless scalar field, both in the presence of gravitational waves and in Minkowski spacetime. It is shown that quantum steerability under the influence of gravitational waves can be greater than or less than quantum steerability in Minkowski spacetime, which means that the gravitational waves can amplify or degrade the harvested steering. In particular, a resonance effect occurs when the energy gap of the detector is tuned to the frequency of the gravitational wave. We also find that the harvesting-achievable separation range of vacuum steering can be expanded or reduced by the presence of gravitational waves, which depends on the energy gap, the gravitational wave frequency, and the duration of the gravitational wave action. It is interesting to note that two detector systems that satisfy the Bell inequality in most parameter spaces, regardless of the existence of gravitational waves, indicating that steering harvesting cannot be considered to be nonlocal., Comment: 19 pages, 3 figures

There is strong evidence for the existence of dark matter in a number of current experiments. We study dark matter using the $U(1)_X$SSM obtained from the $U(1)_X$ extension of the minimal supersymmetric standard model (MSSM). In the $U(1)_X$SSM, we use the right-handed neutrino as a dark matter candidate, whose lightest mass eigenstate has cold dark matter features. In this paper, the relic density of right-handed neutrino as dark matter is investigated. For dark matter scattering, both spin-independent and spin-dependent cross sections are studied. In the final numerical results obtained, some parameter spaces can satisfy the constraints of the relic density and dark matter direct detection experiments.

In this paper, we use the concepts of quantum entanglement and coherence to analyze the Unruh and anti-Unruh effects based on the model of Unruh-DeWitt detector. For the first time, we find that (i) the Unruh effect reduces quantum entanglement but enhances quantum coherence; (ii) the anti-Unruh effect enhances quantum entanglement but reduces quantum coherence. This surprising result refutes the notion that the Unruh effect can only destroy quantum entanglement and coherence simultaneously, and that the anti-Unruh can only protect quantum resources. Consequently, it opens up a new source for discovering experimental evidence supporting the existence of the Unruh and anti-Unruh effects., Comment: 12 pages, 2 figures

Complex quantum information tasks in a gravitational background require multipartite entanglement for effective processing. Therefore, it is necessary to investigate the properties of multipartite entanglement in a relativistic setting. In this paper, we study genuine N-partite entanglement of massless Dirac fields in the Schwarzschild-de Sitter (SdS) spacetime, characterized by the presence of a black hole event horizon (BEH) and a cosmological event horizon (CEH). We obtain the general analytical expression of genuine N-partite entanglement shared by n observers near BEH and m (n+m = N) observers near CEH. It is shown that genuine N-partite entanglement monotonically decreases with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. It is interesting to note that genuine N-partite entanglement is a non-monotonic function of the cosmological constant, meaning that the Hawking effect of the expanding universe can enhance quantum entanglement. This result contrasts with multipartite entanglement in single-event horizon spacetime, offering a new perspective on the Hawking effect in multi-event horizon spacetime., Comment: 14 pages, 3 figures

Charged lepton flavor violation (CLFV) represents a clear new physics (NP) signal beyond the standard model (SM). In this work, we investigate CLFV processes $l_j^-\rightarrow l_i^- \gamma$ utilizing mass insertion approximation(MIA) in the minimal supersymmetric extension of the SM with local B-L gauge symmetry (B-LSSM). The MIA method can provide a set of simple analytic formulae for the form factors and the associated effective vertices, so that the movement of the CLFV decays $l_j^-\rightarrow l_i^- \gamma$ with the sensitive parameters will be intuitively analyzed. Considering the SM-like Higgs boson mass and the muon anomalous dipole moment (MDM) within $4\sigma$, $3\sigma$ and $2\sigma$ regions, we discuss the corresponding constraints on the relevant parameter space of the model., Comment: to be published in Physical Review D

Charged lepton flavor violation (CLFV) represents a clear new physics (NP) signal beyond the standard model (SM). In this work, we investigate the CLFV decays of vector mesons $V\rightarrow l_i^{\pm}l_j^{\mp}$ with $V\in\{\phi, J/\Psi, \Upsilon(1S), \Upsilon(2S),\Upsilon(3S)\}$ in the $\mathrm{U}(1)_{X} \mathrm{SSM}$. Considering the SM-like Higgs boson mass within $3\sigma$ region, we discuss the corresponding constraints on the relevant parameter space of the model, which indicate this model can produce significant contributions to such CLFV decays. From the numerical analyses, the main sensitive parameters and CLFV sources originate from the non-diagonal elements correspond to the initial and final generations of the leptons. And the branching ratios to these CLFV processes can easily reach the present experimental upper bounds. Therefore, searching for CLFV processes of vector mesons may be an effective channel to study new physics.

The different spatial curvatures of the universe affect the measurement of cosmological distances, which may also contribute to explaining the observed dimming of type Ia supernovae. This phenomenon may be caused by the opacity of the universe. Similarly, the opacity of the universe can lead to a bias in our measurements of curvature. Thus, it is necessary to measure cosmic curvature and opacity simultaneously. In this paper, we propose a new model-independent method to simultaneously measure the cosmic curvature and opacity by using the latest observations of HII galaxies acting as standard candles and the latest Hubble parameter observations. The machine learning method-Artificial Neural Network is adopted to reconstruct observed Hubble parameter $H(z)$ observations. Our results support a slightly opaque and flat universe at $1\sigma$ confidence level by using previous 156 HII regions sample. However, the negative curvature is obtained by using the latest 181 HII regions sample in the redshift range $z\sim 2.5$. More importantly, we obtain the simultaneous measurements with precision on the cosmic opacity $\rm\Delta\tau\sim 10^{-2}$ and curvature $\rm\Delta\Omega_K\sim 10^{-1}$. A strong degeneracy between the cosmic opacity and curvature parameters is also revealed in this analysis., Comment: 11 pages, 5 figures

Understanding the nature of repeating FRBs is crucial to probe the physics of FRBs. In this work, we analyze the statistics of waiting time between bursts of three repeating FRBs from four data sets. We find a universally pronounced dependency of the waiting times on the previous time interval (denoted as $\lambda_0$). We observe a temporal clustering where short waiting times tend to be followed by short ones, and long by long. This memory dependency is manifested in the conditional mean waiting time as well as in the conditional mean residual time to the next burst, both of which increase in direct proportion to $\lambda_0$. Consequently, the likelihood of experiencing a subsequent FRB burst within a given time window after the preceding burst is significantly influenced by the burst history. We reveal that, for the first time, these memory effects are present in the scale-invariant preconditioned waiting time distribution. We show that the memory effect provides a unified description of waiting times which may account for both the repeating FRBs and the apparent non-repeating FRBs (i.e. only observed one time). These results shed new light on the mechanism of FRBs.

The genuine entanglement of Dirac fields for an N-partite system is investigated in Schwarzschild spacetime and the analysis is carried out using the single-mode approximation. Due to the Hawking effect, quantum entanglement is divided into two parts physically accessible and inaccessible entanglement. We obtain a general analytic expression of genuine N-partite entanglement that includes all accessible and inaccessible entanglement in a Schwarzschild black hole. Unlike bosonic entanglement, the accessible N-partite entanglement of Dirac fields monotonically decreases to a nonzero value with the Hawking temperature. Interestingly, the inaccessible N-partite entanglement is a monotonic or non-monotonic function of the Hawking temperature, depending on the ratio between accessible and inaccessible modes, in contrast to bipartite or tripartite entanglement that is only a monotonic function of the Hawking temperature. Finally, we obtain two restrictive relationships for the quantum information of the black hole. This conclusion provides a new understanding of Hawking effect of the black hole., Comment: 14 pages, 1 figure

We study the redistribution of the fermionic steering and the relation among fermionic Bell nonlocality, steering, and entanglement in the background of the Garfinkle-Horowitz-Strominger dilaton black hole. We analyze the meaning of the fermionic steering in terms of the Bell inequality in curved spacetime. We find that the fermionic steering, which is previously found to survive in the extreme dilaton black hole, cannot be considered to be nonlocal. We also find that the dilaton gravity can redistribute the fermionic steering, but cannot redistribute Bell nonlocality, which means that the physically inaccessible steering is also not nonlocal. Unlike the inaccessible entanglement, the inaccessible steering may increase non-monotonically with the dilaton. Furthermore, we obtain some monogamy relations between the fermionic steering and entanglement in dilaton spacetime. In addition, we show the difference between the fermionic and bosonic steering in curved spacetime., Comment: 21 pages, 4 figures

We investigate the properties of quantum entanglement and mutual information in the multi-event horizon Schwarzschild-de Sitter (SdS) spacetime for massless Dirac fields. We obtain the expression for the evolutions of the quantum state near the black hole event horizon (BEH) and cosmological event horizon (CEH) in the SdS spacetime. Under the Nariai limit, the physically accessible entanglement and mutual information are maximized, and the physically inaccessible correlations are zero. With the increase in temperature of either horizon, the physically accessible correlations experience degradation. Notably, the initial state remains entangled and can be utilized in entanglement-based quantum information processing tasks, which differs form the scalar field case. Furthermore, the degradation of physically accessible correlations is more pronounced for small-mass black holes. In contrast, the physically inaccessible correlations separated by the CEH monotonically increase with the radiation temperature, and such correlations are not decisively influenced by the effect of particle creation at the BEH. Moreover, a similar phenomenon is observed for the inaccessible correlations separated by the BEH. This result differs from the single event spacetime, in which the physically inaccessible entanglement is a monotonic function of the Hawking temperature., Comment: 14 pages, 7 figures

In the present study, we investigate the decays of the top quark $t\rightarrow c\gamma$, $t\rightarrow cg$, $t\rightarrow cZ$ and $t\rightarrow ch$. They are extremely rare processes in the Standard Model (SM). As the $U(1)$ extension of the minimal supersymmetric standard model (MSSM), the $U(1)_X$SSM features new superfields such as the right-handed neutrinos and three Higgs singlets. We analyze the effects of different sensitive parameters on the results and make reasonable theorecial predictions, which provides a useful reference for future experimental development. Considering the constraint of the updated experimental data, the numerical results show that the branching ratios of all four processes $t\rightarrow c\gamma,~cg,~cZ,~ch$ can reach the same order of magnitude as their experimental upper limits. Among them, $\tan\beta$ has the most obvious effect on each process and is the main parameter. $g_X$, $g_{YX}$, $\mu$, $M_2$, $\lambda_H$, $M_{U23}^2$ and $M_{Q23}^2$ are important parameters for the processes, and have effects on the numerical results., Comment: pages 25, figures 27

Here, we study quantum coherence of N-partite GHZ (Greenberger-Horne-Zeilinger) and W states in the multiverse consisting of N causally disconnected de Sitter spaces. Interestingly, N-partite coherence increases monotonically as the curvature increases, while the Unruh effect destroys multipartite coherence in Rindler spacetime. Conversely, the curvature effect destroys quantum entanglement and discord, meaning that the curvature effect is beneficial to quantum coherence and harmful to quantum correlations in the multiverse. We find that, with the increase of n expanding de Sitter spaces, N-partite coherence of GHZ state increases monotonically for any curvature, while quantum coherence of the W state decreases or increases monotonically depending on the curvature. We find a distribution relationship, which indicates that the correlated coherence of N-partite W state is equal to the sum of all bipartite correlated coherence in the multiverse. Multipartite coherence exhibits unique properties in the multiverse, which argues that it may provide some evidence for the existence of the multiverse., Comment: 26 pages, 8 figures

$R_{D^{(*)}}$ is the ratio of branching ratio $\overline{B} \rightarrow D^{(*)}\tau\overline{\nu}_{\tau}$ to $\overline{B} \rightarrow D^{(*)}l\overline{\nu}_{l}~(l=e,~\mu)$. There is a gap of 2$\sigma_{exp}$ or more between its experimental value and the prediction under the standard model(SM). People extend the MSSM with the local gauge group $U(1)_X$ to obtain the $U(1)_X$SSM. Compared with MSSM, $U(1)_X$SSM has more superfields and effects. In $U(1)_X$SSM, we research the semileptonic decays $\overline{B} \rightarrow D^{(*)}l\overline{\nu}_{l}$ and calculate $R_{D^{(*)}}$. The numerical results of $R_{D^{(*)}}$ are further corrected under $U(1)_X$SSM, which are much better than the SM predictions. After correction, the theoretical value of $R_{D^{(*)}}$ can reach one $\sigma_{exp}$ range of the averaged experiment central value., Comment: 25 pages, 16 figures

$U(1)_X$SSM is a non-universal Abelian extension of the Minimal Supersymmetric Standard Model (MSSM) and its local gauge group is extended to $SU(3)_C\times SU(2)_L \times U(1)_Y\times U(1)_X$. Based on the latest data of neutral meson mixing and experimental limitations, we investigate the process of $B^{0}-\bar{B^{0}}$ mixing in $U(1)_X$SSM. Using the effective Hamiltonian method, the Wilson coefficients and mass difference $\triangle m_{B}$ are derived. The abundant numerical results verify that $~v_S,~M^2_D,~\lambda_C,~{\mu},~M_2,~\tan{\beta},~g_{YX},~M_1$ and $~\lambda_H$ are sensitive parameters to the process of $B^{0}-\bar{B^{0}}$ mixing. With further measurement in the experiment, the parameter space of the $U(1)_X$SSM will be further constrained during the mixing process of $B^{0}-\bar{B^{0}}$.

It is well known that nonlocal coherence reflects nonclassical correlations better than quantum entanglement. Here, we analyze nonlocal coherence harvesting from the quantum vacuum to particle detectors adiabatically interacting with a quantum scalar field in Minkowski spacetime. We find that the harvesting-achievable separation range of nonlocal coherence is larger than that of quantum entanglement. As the energy gap grows sufficiently large, the detectors harvest less quantum coherence, while the detectors could extract more quantum entanglement from the vacuum state. Compared with the linear configuration and the scalene configuration, we should choose the model of equilateral triangle configuration to harvest tripartite coherence from the vacuum. Finally, we find a monogamous relationship, which means that tripartite l1-norm of coherence is essentially bipartite types., Comment: 18 pages, 5 figures

We study lepton flavor violating (LFV) decays $B_d\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($B_d\rightarrow e{\mu}$, $B_d\rightarrow e{\tau}$ and $B_d\rightarrow {\mu}{\tau}$) in the $U(1)_X$SSM, which is the $U(1)_X$ extension of the minimal supersymmetric standard model(MSSM). The local gauge group of $U(1)_X$SSM is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. These processes are strictly forbidden in the standard model(SM), but these LFV decays are a signal of new physics(NP). We use the Mass Insertion Approximation(MIA) to find sensitive parameters that directly influence the result of the branching ratio of LFV decay $B_d\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$. Combined with the latest experimental results, we analyze the relationship between different sensitive parameters and the branching ratios of the three processes. According to the numerical analysis, these elements are very restricted from the non observation of CLFV.

Increasing the interaction between light and mechanical resonators is an ongoing endeavor in the field of cavity optomechanics. Optical microcavities allow for boosting the interaction strength through their strong spatial confinement of the optical field. In this work, we follow this approach by realizing a sub-wavelength-long, free-space optomechanical microcavity on-chip fabricated from an (Al,Ga)As heterostructure. A suspended GaAs photonic crystal mirror is acting as a highly reflective mechanical resonator, which together with a distributed Bragg reflector forms an optomechanical microcavity. We demonstrate precise control over the microcavity resonance by change of the photonic crystal parameters. The interplay between the microcavity mode and a guided resonance of the photonic crystal modifies the cavity response and results in a stronger dynamical backaction on the mechanical resonator compared to conventional optomechanical dynamics., Comment: 11 pages, 6 figures + Supplementary Material with 10 pages, 12 figures, 2 tables

In this paper, we study the lepton flavor violating decays of the $l_j\rightarrow l_i \gamma\gamma$ (j=2, 3; i=1, 2) processes under the $U(1)_X$SSM. The $U(1)_X$SSM is the addition of three singlet new Higgs superfields and right-handed neutrinos to the minimal supersymmetric standard model (MSSM). Based on the latest experimental constraints of $l_j\rightarrow l_i \gamma\gamma$, we analyze the effects of different sensitive parameters on the results and made reasonable predictions for future experimental development. Numerical analysis shows that many parameters have a greater or lesser effect on lepton flavor violation(LFV), but the main sensitive parameters and sources leading to LFV are the non-diagonal elements involving the initial and final leptons. This work could provide a basis for the discovery of the existence of new physics (NP).

Previous studies have shown that the Hawking effect always destroys quantum correlations and the fidelity of quantum teleportation in the Schwarzschild black hole. Here, we investigate the fidelity of quantum teleportation of Dirac fields between users in Schwarzschild spacetime. We find that, with the increase of the Hawking temperature, the fidelity of quantum teleportation can monotonically increases, monotonically decreases, or non-monotonically increases, depending on the choice of the initial state, which means that the Hawking effect can create net fidelity of quantum teleportation. This striking result banishes the extended belief that the Hawking effect of the black hole can only destroy the fidelity of quantum teleportation. We also find that quantum steering cannot fully guarantee the fidelity of quantum teleportation in Schwarzschild spacetime. This new unexpected source may provide a new idea for the experimental evidence of the Hawking effect., Comment: 16 pages, 3 figures

Detecting the structure of spacetime with quantum technologies has always been one of the frontier topics of relativistic quantum information. Here, we analytically study the generation and redistribution of Gaussian entanglement of the scalar fields in an expanding spacetime. We consider a two-mode squeezed state via a Gaussian amplification channel that corresponds to the time-evolution of the state from the asymptotic past to the asymptotic future. Therefore, the dynamical entanglement of the Gaussian state in an expanding universe encodes historical information about the underlying spacetime structure, suggesting a promising application in observational cosmology. We find that quantum entanglement is more sensitive to the expansion rate than the expansion volume. According to the analysis of quantum entanglement, choosing the particles with the smaller momentum and the optimal mass is a better way to extract information about the expanding universe. These results can guide the simulation of the expanding universe in quantum systems., Comment: 17 pages, 4 figures

We propose the concept of pair-wise coherence to study the relation between the l1 norm of coherence and the quantum interference in Young's multi-photon multi-path experiments, where the input photons may be entangled each other. We find that only the local coherence of each single photon can make quantum interference and the collective coherence between photons has no contribution to quantum interference. The visibility of interference fringe is commonly less than the l1norm of coherence of the corresponding input state, suggesting that the l1 norm of coherence is only the necessary but not sufficient condition for quantum interference. We also find that the maximal fringe visibility can reach one. The optimal input states for producing the maximal visibility are presented., Comment: 12 pages, 2 figures

We study the genuine tripartite entanglement (GTE), one-tangle and two-tangle of W state of fermionic fields in the background of a Schwarzschild black hole. We find that, with the increase of the Hawking temperature, the GTE of W state first decreases and then tends to zero, while the GTE of GHZ state first decreases and then freezes. We also find that the Hawking effect can completely destroy the two-tangle of W state, whilie one-tangle first decreases and then appears freezing phenomenon with the growth of the Hawking temperature. These results are helpful to guide us to select appropriate quantum states and quantum resources to deal with relativistic quantum information tasks., Comment: 7 pages, 4 figures

People extend the MSSM with the local gauge group $U(1)_X$ to obtain the $U(1)_X$SSM. In the framework of the $U(1)_X$SSM, we study the flavor transition process $b\rightarrow{s\gamma}$ with the mass insertion approximation (MIA). By the MIA method and some reasonable parameter assumptions, we can intuitively find the parameters that have obvious effect on the analytic results of the flavor transition process $b\rightarrow{s\gamma}$. By means of the influences of different sensitive parameters, we can obtain reasonable results to better fit the experimental data.

We study Gaussian quantum steering in the Schwarzschild-de Sitter (SdS) spacetime that is endowed with both a black hole event horizon (BEH) and a cosmological event horizon (CEH), giving rise to two different Hawking temperatures. It is shown that the Hawking effect of the black hole always reduces the quantum steering, but the Hawking effect of the expanding universe does not always play the same role. For the first time, we find that the Hawking effect can improve quantum steering. We also find that the observer who locates in the BEH has stronger steerability than the observer who locates in CEH. Further, we study the steering asymmetry, and the conditions for two-way, one-way and no-way steering in the SdS spacetime. Finally, we study the Gaussian quantum steering in the scenario of effective equilibrium temperature. We show that quantum steering reduces monotonically with the effective temperature but now increases monotonically with the Hawking temperature of the black hole, which banishes the belief that the Hawking effect can only destroy quantum steering., Comment: 21 pages, 7 figures

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 $(e, \mu, \tau)$ 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, $\tan{\beta}$,~$g_L$,~$m_L$ and $\mu_H$ are more sensitive parameters for $a^{BL}_{\mu}$. Considering the experimental limitations, our best numerical result of $a^{BL}_{\mu}$ 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 $\theta_{\mu_L}$ and $\theta_{L}$. They can give large contributions, which play an important role in exploring the source of CP violation and probing new physics beyond SM.