Chinese Physics C

Hadronic cross section of ${ {e^+e^-}}$ annihilation at bottomonium energy region

Xiang-Kun Dong, Xiao-Hu Mo, Ping Wang, Chang-Zheng Yuan

2020, 44(8): 083001. doi: 10.1088/1674-1137/44/8/083001

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Abstract:
The Born cross section and dressed cross section of

\begin{document}$ e^+e^-\to b\bar{b} $\end{document}

and the total hadronic cross section in

\begin{document}$ e^+e^- $\end{document}

annihilation in the bottomonium energy region are calculated based on the

\begin{document}$ R_b $\end{document}

values measured by the BaBar and Belle experiments. The data are used to calculate the vacuum polarization factors in the bottomonium energy region, and to determine the resonant parameters of the vector bottomonium(-like) states

\begin{document}$ Y(10750) $\end{document}

,

\begin{document}$ \Upsilon(5S) $\end{document}

, and

\begin{document}$ \Upsilon(6S) $\end{document}

.

Radiative decay of Ξ_b(6227) in a hadronic molecule picture

HongQiang Zhu, Yin Huang

2020, 44(8): 083101. doi: 10.1088/1674-1137/44/8/083101

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Abstract:
The baryon

\begin{document}$\Xi_b(6227)$\end{document}

with the quantum number

\begin{document}$J^P=1/2^{-}$\end{document}

is considered as a molecular state composed of a

\begin{document}$\Sigma_b$\end{document}

baryon and

\begin{document}$\bar{K}$\end{document}

meson. The partial decay widths of the

\begin{document}$\Sigma_b\bar{K}$\end{document}

molecular state into

\begin{document}$\Xi_b\gamma$\end{document}

and

\begin{document}$\Xi_b^{'}\gamma$\end{document}

final states through hadronic loops are evaluated with the help of the effective Lagrangians. The partial widths for the

\begin{document}$\Xi_b(6227)\to\gamma\Xi_b$\end{document}

and

\begin{document}$\Xi_b(6227)\to\gamma\Xi^{'}_b$\end{document}

transitions are evaluated at 1.50–1.02 keV and 17.56–24.91 keV, respectively, which may be accessible for the LHCb. Based on our results, we argue that an experimental determination of the radiative decay width of

\begin{document}$\Xi_b(6227)$\end{document}

is important for the understanding of its intrinsic properties.

Effective charge from lattice QCD

Z.-F. Cui, J.-L. Zhang, D. Binosi, F. De Soto, C. Mezrag, J. Papavassiliou, C. D. Roberts, J. Rodríguez-Quintero, J. Segovia, S. Zafeiropoulos

2020, 44(8): 083102. doi: 10.1088/1674-1137/44/8/083102

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Abstract:
Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD’s renormalisation-group-invariant process-independent effective charge,

\begin{document}$\hat\alpha(k^2)$\end{document}

. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale,

\begin{document}$m_0= 0.43(1)\;$\end{document}

GeV, this coupling saturates at infrared momenta:

\begin{document}$\hat\alpha(0)/\pi=0.97(4)$\end{document}

. Amongst other things:

\begin{document}$\hat\alpha(k^2)$\end{document}

is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by

\begin{document}$\hat\alpha(k^2)$\end{document}

suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.

Phenomenological advantages of the normal neutrino mass ordering

Shao-Feng Ge, Jing-yu Zhu

2020, 44(8): 083103. doi: 10.1088/1674-1137/44/8/083103

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Abstract:
The preference of the normal neutrino mass ordering from the recent cosmological constraint and the global fit of neutrino oscillation experiments does not seem like a wise choice at first glance since it obscures the neutrinoless double beta decay and hence the Majorana nature of neutrinos. Contrary to this naive expectation, we point out that the actual situation is the opposite. The normal neutrino mass ordering opens the possibility of excluding the higher solar octant and simultaneously measuring the two Majorana CP phases in future

\begin{document}$0 \nu 2 \beta$\end{document}

experiments. Especially, the funnel region will completely disappear if the solar mixing angle takes the higher octant. The combined precision measurement by the JUNO and Daya Bay experiments can significantly reduce the uncertainty in excluding the higher octant. With a typical

\begin{document}${\cal{O}}({\rm{meV}})$\end{document}

sensitivity on the effective mass

\begin{document}$|m_{ee}|$\end{document}

, the neutrinoless double beta decay experiment can tell if the funnel region really exists and hence exclude the higher solar octant. With the sensitivity further improved to sub-meV, the two Majorana CP phases can be simultaneously determined. Thus, the normal neutrino mass ordering clearly shows phenomenological advantages over the inverted one.

Top quark pair production at complete NLO accuracy with NNLO+NNLL′ corrections in QCD

Michał Czakon, Andrea Ferroglia, Alexander Mitov, Davide Pagani, Andrew S. Papanastasiou, Benjamin D. Pecjak, Darren J. Scott, Ioannis Tsinikos, Xing Wang, Li Lin Yang, Marco Zaro

2020, 44(8): 083104. doi: 10.1088/1674-1137/44/8/083104

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Abstract:
We describe predictions for top quark pair differential distributions at hadron colliders, by combining the next-to-next-to-leading order quantum chromodynamics calculations and next-to-leading order electroweak corrections with double resummation at the next-to-next-to-leading logarithmic accuracy of threshold logarithms and small-mass logarithms. To the best of our knowledge, this is the first study to present such a combination, which incorporates all known perturbative information. Numerical results are presented for the invariant-mass distribution, transverse-momentum distribution, and rapidity distributions.

Tensor form factors of P→ P, S, V and A transitions within standard and covariant light-front approaches

Qin Chang, Xiao-Lin Wang, Li-Ting Wang

2020, 44(8): 083105. doi: 10.1088/1674-1137/44/8/083105

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Abstract:
We investigate the tensor form factors of

\begin{document}$ P\to P,\,S,\,V $\end{document}

, and A transitions within the standard light-front (SLF) and the covariant light-front (CLF) quark models (QMs). The self-consistency and Lorentz covariance of CLF QM are analyzed via these quantities, and the effects of zero-mode are discussed. For the

\begin{document}$ P\to V $\end{document}

and A transitions, besides the inconsistency between the results extracted via longitudinal and transverse polarization states, which is caused by the residual

\begin{document}$ \omega $\end{document}

-dependent spurious contributions, we find and analyze a “novel” self-consistence problem of the traditional CLF QM, caused by different strategies for dealing with the trace term in CLF matrix element. A possible solution to the problems of traditional CLF QM is discussed and confirmed numerically. Finally, the theoretical predictions for the tensor form factors of some

\begin{document}$ c\to q,\,s $\end{document}

and

\begin{document}$ b\to q,\,s\,,c $\end{document}

(

\begin{document}$ q = u,d $\end{document}

) induced

\begin{document}$ P\to P,\,S,\,V $\end{document}

and A transitions are updated within the CLF QM with a self-consistent scheme.

QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model

Xuanmin Cao, Hui Liu, Danning Li, Guanning Ou

2020, 44(8): 083106. doi: 10.1088/1674-1137/44/8/083106

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We study the phase transition between the pion condensed phase and normal phase, as well as chiral phase transition in a two flavor (

\begin{document}${\cal{N}}_f=2$\end{document}

) IR- improved soft-wall AdS/QCD model at finite isospin chemical potential

\begin{document}$\mu_I$\end{document}

and temperature T. By self-consistently solving the equations of motion, we obtain the phase diagram in the plane of

\begin{document}$\mu_I$\end{document}

and T. The pion condensation appears together with a massless Nambu-Goldstone boson

\begin{document}$m_{\pi_1}(T_c, \mu_I^c)=0$\end{document}

, which is very likely to be a second-order phase transition with mean-field critical exponents in the small

\begin{document}$\mu_I$\end{document}

region. When

\begin{document}$T=0$\end{document}

, the critical isospin chemical potential approximates to vacuum pion mass

\begin{document}$\mu_I^c \approx m_0$\end{document}

. The pion condensed phase exists in an arched area, and the boundary of the chiral crossover intersects the pion condensed phase at a tri-critical point. Qualitatively, the results are in good agreement with previous studies on lattice simulations and model calculations.

Rare ${{\Lambda_b \rightarrow \Lambda l^+ l^- }}$ decay in the Bethe-Salpeter equation approach

Liang-Liang Liu, Xian-Wei Kang, Zhen-Yang Wang, Xin-Heng Guo

2020, 44(8): 083107. doi: 10.1088/1674-1137/44/8/083107

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Abstract:
We study the rare decays

\begin{document}$\Lambda_b \rightarrow \Lambda l^+ l^-~(l=e,\mu, \tau)$\end{document}

in the Bethe-Salpeter equation approach. We find that the branching ratio is

\begin{document}${\rm Br}(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\times 10^{6} = 1.051 \sim 1.098$\end{document}

in our model. This result agrees with the experimental data well. In the same parametric region, we find that the branching ratio is

\begin{document}${\rm Br}(\Lambda_b \rightarrow \Lambda e^+ e^-(\tau^+ \tau^-) )\times 10^{6} = 0.252 \sim 0.392 ~(0.286 \sim 0.489)$\end{document}

.

Lattice study of two-photon decay widths for scalar and pseudo-scalar charmonium

Ying Chen, Ming Gong, Ning Li, Chuan Liu, Yu-Bin Liu, Zhaofeng Liu, Jian-Ping Ma, Yu Meng, Chao Xiong, Ke-Long Zhang, (CLQCD Collaboration)

2020, 44(8): 083108. doi: 10.1088/1674-1137/44/8/083108

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Abstract:
This exploratory study computes two-photon decay widths of pseudo-scalar (

\begin{document}$ \eta_c $\end{document}

) and scalar (

\begin{document}$ \chi_{c0} $\end{document}

) charmonium using two ensembles of

\begin{document}$ N_f = 2 $\end{document}

twisted mass lattice QCD gauge configurations. The simulation is performed using two lattice ensembles with lattice spacings

\begin{document}$ a = 0.067 $\end{document}

fm with size

\begin{document}$ 32^3\times{64} $\end{document}

and

\begin{document}$ a = 0.085 $\end{document}

fm with size

\begin{document}$ 24^3\times{48} $\end{document}

. The decay widths for the two charmonia are obtained within the expected ballpark, but are however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.

Quark-hadron phase transition in DGP including BD brane

Tayeb Golanbari, Terife Haddad, Abolhassan Mohammadi, M. A. Rasheed, Kh. Saaidi

2020, 44(8): 083109. doi: 10.1088/1674-1137/44/8/083109

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Abstract:
A Dvali–Gabadadze–Porrati (DGP) brane-world model with perfect fluid brane matter including a Brans-Dicke (BD) scalar field on brane was utilized to investigate the problem of the quark-hadron phase (QHP) transition in early evolution of the Universe. The presence of the BD scalar field arises with several modified terms in the Friedmann equation. Because the behavior of the phase transition strongly depends on the basic evolution equations, even a small change in these relations might lead to interesting results about the time of transition. The phase transition is investigated in two scenarios, namely the first-order phase transition and smooth crossover phase transition. For the first-order scenario, which is used for the intermediate temperature regime, the evolution of the physical quantities, such as temperature and scale factor, are investigated before, during, and after the phase transition. The results show that the transition occurs in about a micro-second. In the following part, the phenomenon is studied by assuming a smooth crossover transition, where the lattice QCD data is utilized to obtain a realistic equation for the state of the matter. The investigation for this part is performed in the high and low-temperature regimes. Using the trace anomaly in the high-temperature regime specifies a simple equation of state, which states that the quark-gluon behaves like radiation. However, in the low-temperature regime, the trace anomaly is affected by discretization effects, and the hadron resonance gas model is utilized instead. Using this model, a more realistic equation of state is found in the low-temperature regime. The crossover phase transition in both regimes is considered. The results determine that the transition lasts around a few micro-seconds. Further, the transition in the low-temperature regime occurs after the transition in the high-temperature regime.

Scotogenic dark symmetry as a residual subgroup of Standard Model symmetries

Salvador Centelles Chuliá, Ricardo Cepedello, Eduardo Peinado, Rahul Srivastava

2020, 44(8): 083110. doi: 10.1088/1674-1137/44/8/083110

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We demonstrate that a scotogenic dark symmetry can be obtained as a residual subgroup of the global

\begin{document}$U(1)_{B-L}$\end{document}

symmetry already present in the Standard Model. In addition, we propose a general framework in which the

\begin{document}$U(1)_{B-L}$\end{document}

symmetry is spontaneously broken into an even

\begin{document}${\cal{Z}}_{2n}$\end{document}

subgroup, setting the general conditions for neutrinos to be Majorana and for dark matter stability to exist in terms of the residual

\begin{document}${\cal{Z}}_{2n}$\end{document}

. As an example, under this general framework, we build a class of simple models where, in a scotogenic manner, the dark matter candidate is the lightest particle running inside the mass loop of a neutrino. The global

\begin{document}$U(1)_{B-L}$\end{document}

symmetry in our framework, being anomaly free, can also be gauged in a straightforward manner leading to a richer phenomenology.

Heavy flavor dissociation in framework of multi-body Dirac equations

Shuzhe Shi, Jiaxing Zhao, Pengfei Zhuang

2020, 44(8): 084101. doi: 10.1088/1674-1137/44/8/084101

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We study heavy flavor properties at finite temperature in the framework of a relativistic potential model. Using an improved method to solve the three-body Dirac equation, we determine a universal set of model parameters for both mesons and baryons by fitting heavy flavor masses in vacuum. Taking heavy quark potential from lattice QCD simulations in hot medium, we systematically calculate heavy flavor binding energies and averaged sizes as functions of the temperature. The meson and baryons are separately sequentially dissociated in the quark-gluon plasma, and the mesons can survive at higher temperatures owing to the stronger potential between quark-antiquark pairs than that between quark-quark pairs.

Identifying hidden charm pentaquark signal from non-resonant background in electron–proton scattering

Zhi Yang, Xu Cao, Yu-Tie Liang, Jia-Jun Wu

2020, 44(8): 084102. doi: 10.1088/1674-1137/44/8/084102

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In this study, we analyze the electroproduction of the LHCb pentaquark states with the assumption that they are resonant states. Our main concern is to investigate the final state distribution in the phase space to extract a feeble pentaquark signal from a large non-resonant background. The results indicate that the signal to background ratio will increase significantly with a proper kinematic cut, which will be beneficial for future experimental analysis.

Investigation of neutron density distribution of ²⁰⁸Pb nucleus when the proton density is constrained to its experimental distribution

A. R. Abdulghany

2020, 44(8): 084103. doi: 10.1088/1674-1137/44/8/084103

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Abstract:
In this study, two novel improvements for the theoretical calculation of neutron distributions are presented. First, the available experimental proton distributions are used as a constraint rather than inferred from the calculation. Second, the recently proposed distribution formula, d3pF, is used for the neutron density, which is more detailed than the usual shapes, for the first time in a nuclear structure calculation. A semi-microscopic approach for binding energy calculation is considered in this study. However, the proposed improvements can be introduced to any other approach. The ground state binding energy and neutron density distribution of ²⁰⁸Pb nucleus are calculated by optimizing the binding energy considering three different distribution formulae. The implementation of the proposed improvements leads to qualitative and quantitative improvements in the calculation of the binding energy and neutron density distribution. The calculated binding energy agrees with the experimental value, and the calculated neutron density exhibits fluctuations within the nuclear interior, which corresponds with the predictions of self-consistent approaches.

2νββ-decay to first 2⁺ states with partial isospin symmetry restoration from spherical QRPA calculations

Dong-Liang Fang, Amand Faessler

2020, 44(8): 084104. doi: 10.1088/1674-1137/44/8/084104

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Abstract:
Using partially restored isospin symmetry, we calculate the nuclear matrix elements for a special decay mode of a two-neutrino double beta decay – the decay to the first 2⁺ excited states. Employing the realistic CD–Bonn nuclear force, we analyze the dependence of the nuclear matrix elements on the isovector and isoscalar parts of proton–neutron particle–particle interactions. The dependence on the different nuclear matrix elements is observed, and the results are explained. We also provide the phase space factors using numerical electron wavefunctions and properly chosen excitation energies. Finally, we present our results for the half-lives of this decay mode for different nuclei.

Single-particle resonant states with Green’s function method

Cheng Chen, Zhipan Li, Yuxiao Li, Tingting Sun

2020, 44(8): 084105. doi: 10.1088/1674-1137/44/8/084105

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Abstract:
This study employs the relativistic mean field theory with the Green's function method to study the single-particle resonant states. In contrast to our previous work [Phys. Rev. C, 90: 054321 (2014)], the resonant states are identified by searching for the poles of Green's function or the extremes of the density of states. This new approach is highly effective for all kinds of resonant states, no matter whether they are broad or narrow. The dependence on the space size for the resonant energies, widths, and the density distributions in the coordinate space has been checked and was found to be very stable. Taking ¹²⁰Sn as an example, four new broad resonant states

\begin{document}$ 2g_{7/2} $\end{document}

,

\begin{document}$ 2g_{9/2} $\end{document}

,

\begin{document}$ 2h_{11/2} $\end{document}

, and

\begin{document}$ 1j_{13/2} $\end{document}

were observed, and the accuracy for the width of the very narrow resonant state

\begin{document}$ 1h_{9/2} $\end{document}

was highly improved to

\begin{document}$ 1\times 10^{-8} $\end{document}

MeV. Further, our results are very close to those obtained using the complex momentum representation method and the complex scaling method.

Perturbation solutions of relativistic viscous hydrodynamics for longitudinally expanding fireballs

Ze-Fang Jiang, Duan She, C. B. Yang, Defu Hou

2020, 44(8): 084107. doi: 10.1088/1674-1137/44/8/084107

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The solutions of the relativistic viscous hydrodynamics for longitudinally expanding fireballs are investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and the Euler conservation equations for the viscous fluid are derived in Rindler coordinates, by assuming that the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the longitudinal expanding framework are presented. The specific temperature profile shows symmetric Gaussian shape in the Rindler coordinates. Further, we compare the results from the Israel-Stewart approximation with the results from the Bjorken and the Navier-Stokes approximations, in the presence of the longitudinal acceleration expansion effect. We found that the Israel-Stewart approximation gives a good description of the early stage evolutions than the Navier-Stokes theory.

Isospin dependence of projectile fragmentation at hundreds of MeV/u

Jun Su, Long Zhu, Chenchen Guo, Feng-Shou Zhang

2020, 44(8): 084106. doi: 10.1088/1674-1137/44/8/084106

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By modeling the fragmentation process using a dynamic model and permitting only evaporation in the statistical code, the main features of a projectile fragmentation at 600 MeV/u were considered in our previous study [Phys. Rev. C, 98: 014610 (2018)]. In this study, we extend this to the isospin dependence of a projectile fragmentation at several hundreds of MeV/u. We searched for isospin observables related to the isospin fractionation to extract the symmetry energy, and found that at the pre-equilibrium stage of the collisions an isospin diffusion will take place and affect the isospin of the final fragments. The isospin fractionation plays a part during the fragmenting stage. Compared to the soft symmetry energy, the stiff symmetry energy provides a smaller repulsive force for neutrons and an attractive force for the protons in a neutron-rich system at a subnormal density, and hence causes a smaller isospin asymmetry of the gas phase, leaving a more neutron-rich liquid phase. An observable robust isospin is proposed to extract the slope of the symmetry energy at normal density based on the isospin dependence of the projectile fragmentation at hundreds of MeV/u.

Expected LHAASO sensitivity to decaying dark matter signatures from dwarf galaxies gamma-ray emission

Dong-Ze He, Xiao-Jun Bi, Su-Jie Lin, Peng-Fei Yin, Xin Zhang

2020, 44(8): 085001. doi: 10.1088/1674-1137/44/8/085001

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Abstract:
As a next-generation complex extensive air shower array with a large field of view, the large high altitude air shower observatory (LHAASO) is very sensitive to the very-high-energy gamma rays from ~300 GeV to 1 PeV and may thus serve as an important probe for the heavy dark matter (DM) particles. In this study, we make a forecast for the LHAASO sensitivities to the gamma-ray signatures resulting from DM decay in dwarf spheroidal satellite galaxies (dSphs) within the LHAASO field of view. Both individual and combined limits for 19 dSphs incorporating the uncertainties of the DM density profile are explored. Owing to the large effective area and strong capability of the photon-proton discrimination, we find that LHASSSO is sensitive to the signatures from decaying DM particles above

\begin{document}${\cal{O}}(1)$\end{document}

TeV. The LHAASO sensitivity to the DM decay lifetime reaches

\begin{document}${\cal{O}} (10^{26}) \sim {\cal{O}} (10^{28})$\end{document}

s for several decay channels at the DM mass scale from 1 TeV to 100 TeV.

Uplifting of AdS type to quintessence-like potential induced by frozen large-scale Lorentz violation

Hanyu Zhai, Jiayin Shen, Xun Xue

2020, 44(8): 085101. doi: 10.1088/1674-1137/44/8/085101

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The quintessence-like potential of vacuum energy can meet the requirements from both quantum gravity and the accelerating expansion of the universe. The anti-de Sitter (AdS) vacuum in string theory must be lifted to the meta-stable dS vacuum with a positive vacuum energy density to explain the accelerating expansion of the universe. Based on possible large-scale Lorentz violation, we define an effective cosmological constant that depends not only on the bare cosmological constant but also on the Lorentz violation effect. We find that the evolution of the effective cosmological constant exhibits the behavior of the quintessence potential when the bare cosmological constant originates from the string landscape, in contrast to the existence of a local minimum during evolution when the bare cosmological constant is supplied by the swampland. The critical value of the bare cosmological constant is approximately zero for the behavior transition. The frozen large-scale Lorentz violation can uplift the AdS vacua to an effective quintessence-like one in this sense.

Electron and positron spectra in three-dimensional spatial-dependent propagation model

Zhen Tian, Wei Liu, Bo Yang, Xue-Dong Fu, Hai-Bo Xu, Yu-Hua Yao, Yi-Qing Guo

2020, 44(8): 085102. doi: 10.1088/1674-1137/44/8/085102

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Abstract:
The spatial-dependent propagation (SDP) model has been demonstrated to account for the spectral hardening of both primary and secondary Cosmic Rays (CRs) nuclei above about 200 GV. In this work, we further apply this model to the latest AMS-02 observations of electrons and positrons. To investigate the effect of different propagation models, both homogeneous diffusion and SDP are compared. In contrast to the homogeneous diffusion, SDP brings about harder spectra of background CRs and thus enhances background electron and positron fluxes above tens of GeV. Thereby, the SDP model could better reproduce both electron and positron energy spectra when introducing a local pulsar. The influence of the background source distribution is also investigated, where both axisymmetric and spiral distributions are compared. We find that considering the spiral distribution leads to a larger contribution of positrons for energies above multi-GeV than the axisymmetric distribution. In the SDP model, when including a spiral distribution of sources, the all-electron spectrum above TeV energies is thus naturally described. In the meantime, the estimated anisotropies in the all-electrons spectrum show that in contrary to the homogeneous diffusion model, the anisotropy under SDP is well below the observational limits set by the Fermi-LAT experiment, even when considering a local source.

The running curvaton

Lei-Hua Liu, Wu-Long Xu

2020, 44(8): 085103. doi: 10.1088/1674-1137/44/8/085103

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Abstract:
In this paper, we propose a homogeneous curvaton mechanism that operates during the preheating process and in which the effective mass is running (i.e., its potential consists of a coupling term and an exponential term whose contribution is subdominant thereto). This mechanism can be classified into either narrow resonance or broad resonance cases, with the spectral index of the curvaton consituting the deciding criteria. The inflationary potential is that of chaotic inflation (i.e., a quadratic potential), which could result in a smooth transition into the preheating process. The entropy perturbations are converted into curvature perturbations, which we validate using the

\begin{document}$ \delta N $\end{document}

formalism. By neglecting the exponential term's contribution to the curvaton potential, we calculate the power spectrum

\begin{document}$ P_\zeta $\end{document}

and the nonlinear non-Gaussian parameter

\begin{document}$ f_{NL} $\end{document}

. Our calculations analytically show that these two observables are independent of the inflaton potential. Finally, when the curvaton decays (and the inflaton field vanishes), the exponential potential approaches a constant value similar to that of the cosmological constant, which may play the role of dark energy.

Observational constraints on Rastall gravity from rotation curves of low surface brightness galaxies

Meirong Tang, Zhaoyi Xu, Jiancheng Wang

2020, 44(8): 085104. doi: 10.1088/1674-1137/44/8/085104

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Rastall gravity is a modification of Einstein's general relativity in which the energy-momentum conservation is not satisfied and depends on the gradient of the Ricci curvature. It is currently in dispute whether Rastall gravity is equivalent to general relativity (GR). In this work, we constrain the theory using the rotation curves of low surface brightness (LSB) spiral galaxies. By fitting the rotation curves of LSB galaxies, we obtain parameter

\begin{document}$\beta$\end{document}

of the Rastall gravity. The

\begin{document}$\beta$\end{document}

values of LSB galaxies satisfy the weak energy condition (WEC) and strong energy condition (SEC). Combining the

\begin{document}$\beta$\end{document}

values of type Ia supernovae and the gravitational lensing of elliptical galaxies on Rastall gravity, we conclude that Rastall gravity may be equivalent to general relativity.

2020 Vol. 44, No. 8