## 2018 Vol. 42, No. 10

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2018, 42(10): 103101. doi: 10.1088/1674-1137/42/10/103101

**Abstract:**

We extend the colored Zee-Babu model with a gauged

*U*(1)

_{B-L}symmetry, and a scalar singlet dark matter (DM) candidate S. The spontaneous breaking of

*U*(1)

_{B-L}leaves a residual

*Z*

_{2}symmetry that stabilizes the DM, and generates a tiny neutrino mass at the two-loop level with the color seesaw mechanism. After investigating the DM and flavor phenomenology of this model systematically, we further focus on its imprint on two cosmic-ray anomalies:The Fermi-LAT gamma-ray excess at the Galactic Center (GCE), and the PeV ultra-high energy (UHE) neutrino events at the IceCube. We found that the Fermi-LAT GCE spectrum can be well-fitted by DM annihilation into a pair of on-shell singlet Higgs mediators while being compatible with the constraints from the relic density, direct detections, and dwarf spheroidal galaxies, in the Milky Way. Although the UHE neutrino events at the IceCube could be accounted for by the resonance production of a TeV-scale leptoquark, the relevant Yukawa couplings have been severely limited by the current low-energy flavor experiments. We subsequently derive the IceCube limits on the Yukawa couplings by employing its latest six-year data.

2018, 42(10): 103102. doi: 10.1088/1674-1137/42/10/103102

**Abstract:**

In the littlest Higgs model with T-parity, we discuss the pair production of the T-odd top partner (

*T*_) that decays almost 100% into the top quark and the lightest T-odd particle (

*A*

_{H}). Considering the current constraints, we investigate the observability of the T-odd top partner pair production through the process

*pp*→

*T*_

*T*_→

*t*

*t*

*A*

_{H}

*A*

_{H}in the final states with two leptons at 14 TeV LHC. We analyze the signal significance and found that the lower limits on the T-odd top partner mass are approximately 1.2 TeV, 1.3 TeV, and 1.4 TeV at the 2

*σ*confidence level at 14 TeV LHC with an integrated luminosities of 30 fb

^{-1}, 100 fb

^{-1}, and 300 fb

^{-1}, respectively. This lower limit can be increased to approximately 1.5(1.6) TeV if we used 1000(3000) fb

^{-1}of the integrated luminosity.

2018, 42(10): 103103. doi: 10.1088/1674-1137/42/10/103103

**Abstract:**

A new method to test the valence quark distribution of nucleons obtained from the maximum entropy method using the Gottfried sum rule by performing the DGLAP equations with GLR-MQ-ZRS corrections and the original leading-order/next-to-leading-order (LO/NLO) DGLAP equations is outlined. The test relies on knowledge of the unpolarized electron-proton structure function

*F*

_{2}

^{ep}and the electron-neutron structure function

*F*

_{2}

^{en}and the assumption that Bjorken scaling is satisfied. In this work, the original Gottfried summation value obtained by the integrals of the structure function at different

*Q*

^{2}is in accordance with the theoretical value of 1/3 under the premise of light-quark flavor symmetry of the nucleon sea, whether it results from dynamical evolution equations or from global quantum chromodynamics fits of PDFs. Finally, we present the summation value of the LO/NLO DGLAP global fits of PDFs under the premise of light-quark flavor asymmetry of the nucleon sea. According to analysis of the original Gottfried summation value with two evolution equations at different

*Q*

^{2}, we find that the valence quark distributions of nucleons obtained by using the maximum entropy method are effective and reliable.

2018, 42(10): 103104. doi: 10.1088/1674-1137/42/10/103104

**Abstract:**

The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial

*SO*(3) Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the

**SD**Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and

**SD**Yang-Mills fields do not interact with one another.

2018, 42(10): 103105. doi: 10.1088/1674-1137/42/10/103105

**Abstract:**

In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the 3×3 flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalization-group (RG) equations in the tau-dominance approximation, and for the running behaviors of up-and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.

2018, 42(10): 103106. doi: 10.1088/1674-1137/42/10/103106

**Abstract:**

We studied the electromagnetic form factors (EMFFs) of Λ

_{c}and the contributions of the quark and diquark currents to the EMFFs of Λ

_{c}in the space-like region in the Bethe-Salpeter equation approach with instantaneous approximation. In this picture, baryon Λ

_{c}can be regarded as a two-body

*c*(

*ud*) system. We found that for different values of parameters the contribution of quark and diquark currents to the EMFFs of Λ

_{c}is very different, while their total contribution to the EMFFs of Λ

_{c}is similar. The EMFFs of Λ

_{c}are similar to those of other baryons (proton, Ξ

^{-}, and Σ

^{+}) with a peak at

*ω*=1, where

*ω*=

*v*'·

*v*is the velocity transfer between the initial state (with velocity

*v*) and the final state (with velocity

*v*) of Λ

_{c}.

2018, 42(10): 103107. doi: 10.1088/1674-1137/42/10/103107

**Abstract:**

Following the discovery of the Higgs boson with a mass of approximately 125 GeV at the LHC, many studies have been performed from both the theoretical and experimental viewpoints to search for a new Higgs Boson that is lighter than 125 GeV. We explore the possibility of constraining a lighter neutral scalar Higgs boson

*h*

_{1}and a lighter pseudo-scalar Higgs boson

*a*

_{1}in the Next-to-Minimal Supersymmetric Standard Model by restricting the next-to-lightest scalar Higgs boson

*h*

_{2}to be the one observed at the LHC after applying the phenomenological constraints and those from experimental measurements. Such lighter particles are not yet completely excluded by the latest results of the search for a lighter Higgs boson in the diphoton decay channel from LHC data. Our results show that some new constraints on the Next-to-Minimal Supersymmetric Standard Model could be obtained for a lighter scalar Higgs boson at the LHC if such a search is performed by experimental collaborations and more data. The potentials of discovery for other interesting decay channels of such a lighter neutral scalar or pseudo-scalar particle are also discussed.

2018, 42(10): 103108. doi: 10.1088/1674-1137/42/10/103108

**Abstract:**

Flavor

*SU*(3) analysis of B meson charmless hadronic two light pseudoscalar decays can be formulated in two different ways. One is to construct the

*SU*(3) irreducible representation amplitude (IRA) according to effective Hamiltonian transformation properties, and the other is to draw the topological diagrams (TDA). We first point out that previous analyses of TDA and IRA approaches do not match in several aspects, in particular a few

*SU*(3) independent amplitudes have been overlooked in the TDA approach. This has caused confusions in the past and sometimes resulted in incorrect interpretation of data. We then demonstrate that only if these amplitudes are included, a consistent and unified picture can be obtained. With the new TDA amplitudes, all charmless hadronic decays of heavy meson must have nonzero direct CP symmetries as already predicted by the IRA approach. In addition to their notable impact on CP asymmetry, the new amplitudes are also important to extract new physics information.

2018, 42(10): 103109. doi: 10.1088/1674-1137/42/10/103109

**Abstract:**

The semi-constrained NMSSM (scNMSSM) extends the MSSM by a singlet field, and requires unification of the soft SUSY breaking terms in the squark and slepton sectors, while it allows that in the Higgs sector to be different. We try to interpret the muon g-2 in the scNMSSM, under the constraints of 125 GeV Higgs data, B physics, searches for low and high mass resonances, searches for SUSY particles at the LHC, dark matter relic density by WMAP/Planck, and direct searches for dark matter by LUX, XENON1T, and PandaX-Ⅱ. We find that under the above constraints, the scNMSSM can still (i) satisfy muon g-2 at 1

*σ*level, with a light muon sneutrino and light chargino; (ii) predict a highly-singlet-dominated 95 GeV Higgs, with a diphoton rate as hinted at by CMS data, because of a light higgsino-like chargino and moderate

*λ*; (iii) get low fine tuning from the GUT scale with small

*μ*

_{eff},

*M*

_{0},

*M*

_{1/2}, and

*A*

_{0}, with a lighter stop mass which can be as low as about 500 GeV, which can be further checked in future studies with search results from the 13 TeV LHC; (iv) have the lightest neutralino be singlino-dominated or higgsino-dominated, while the bino and wino are heavier because of high gluino bounds at the LHC and universal gaugino conditions at the GUT scale; (v) satisfy all the above constraints, although it is not easy for the lightest neutralino, as the only dark matter candidate, to get enough relic density. Several ways to increase relic density are discussed.

2018, 42(10): 104001. doi: 10.1088/1674-1137/42/10/104001

**Abstract:**

We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle efficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble consisting of events with two different efficiencies. By using the mean particle efficiencies, we find that the efficiency corrected cumulants show large deviations from the original inputs when the discrepancy between the two efficiencies is large. We further studied the effects of efficiency fluctuations for the cumulants of net-proton distributions by implementing the UrQMD events of Au+Au collisions at √

*s*

_{NN}=7.7 GeV in a realistic STAR detector acceptance. We consider the unequal efficiency in two sides of the Time Projection Chamber (TPC), multiplicity dependent efficiency, and the event-by-event variations of the collision vertex position along the longitudinal direction (

*V*

_{z}). When the efficiencies fluctuate dramatically within the studied event sample, the effects of efficiency fluctuations have significant impacts on the efficiency corrections of cumulants with the mean efficiencies. We find that this effect can be effectively suppressed by binning the entire event ensemble into various sub-event samples, in which the efficiency variations are relatively small. The final efficiency corrected cumulants can be calculated from the weighted average of the corrected factorial moments of the sub-event samples with the mean efficiencies.

2018, 42(10): 104101. doi: 10.1088/1674-1137/42/10/104101

**Abstract:**

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set Ⅱ represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated

*Q*values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental

*Q*values.

2018, 42(10): 104102. doi: 10.1088/1674-1137/42/10/104102

**Abstract:**

Rapidity-dependent transverse momentum spectra of negatively charged pions measured at different rapidities in proton-proton collisions at the Super Proton Synchrotron (SPS) at various energies within its Beam Energy Scan (BES) program are investigated by using one-and two-component standard distributions where the chemical potential and spin property of particles are implemented. The rapidity spectra are described by a double-Gaussian distribution. At the stage of kinetic freeze-out, the event patterns are structured by the scatter plots in the three-dimensional subspaces of velocity, momentum and rapidity. The results of the studies of the rapidity-independent transverse mass spectra measured at mid-rapidity in proton-proton collisions are compared with those based on the similar transverse mass spectra measured in the most central beryllium-beryllium, argon-scandium and lead-lead collisions from the SPS at its BES energies.

2018, 42(10): 104103. doi: 10.1088/1674-1137/42/10/104103

**Abstract:**

Based on an isospin-dependent transport model, the effects of the density-and momentum-dependent potentials are studied by simulating Au on Au collisions at 90, 120, 150 and 400 MeV/nucleon. It is found that the calculated results overestimate the experimental data on the directed flow and underestimate the data on the elliptic flow for protons. The impact of the density-and momentum-dependent potentials is observed in the mid-rapidity region of the final spectra. At 90 MeV/nucleon, the momentum-dependent potential has a larger impact on the observables than the density-dependent potential, and the elliptic flow has a higher value with the positive effective mass splitting. At 400 MeV/nucleon, however, the opposite is observed. The rapidity dependence of the elliptic flow for protons is sensitive to the symmetry energy. A soft symmetry energy corresponds to a higher value of the proton elliptic flow.

2018, 42(10): 104104. doi: 10.1088/1674-1137/42/10/104104

**Abstract:**

We develop a comprehensive dynamical framework, CIBJET, to calculate on an event-by-event basis the dependence of correlations between soft (

*p*

_{T}<2 GeV) and hard (

*p*

_{T}> 10 GeV) azimuthal flow angle harmonics on the color composition of near-perfect QCD fluids produced in high energy nuclear collisions at RHIC and LHC. CIBJET combines consistently predictions of event-by-event VISHNU2+1 viscous hydrodynamic fluid fields with CUJET3.1 predictions of event-by-event jet quenching. We find that recent correlation data favor a temperature dependent color composition including bleached chromo-electric

*q*(

*T*)+

*g*(

*T*) components and an emergent chromo-magnetic degrees of freedom

*m*(

*T*) consistent with non-perturbative lattice QCD information in the confinement/deconfinement temperature range.

2018, 42(10): 104105. doi: 10.1088/1674-1137/42/10/104105

**Abstract:**

The time-dependent Hartree-Fock approach in three dimensions is employed to study the multi-nucleon transfer reaction

^{132}Sn +

^{208}Pb at various incident energies above the Coulomb barrier. Probabilities for different transfer channels are calculated by using the particle-number projection method. The results indicate that neutron stripping (transfer from the projectile to the target) and proton pick-up (transfer from the target to the projectile) are favored. De-excitation of the primary fragments is treated by using the state-of-art statistical code GEMINI++. Primary and final production cross sections of the target-like fragments (with

*Z*=77 to

*Z*=87) are investigated. The results reveal that fission decay of heavy nuclei plays an important role in the de-excitation process of nuclei with

*Z*>82. It is also found that the final production cross sections of neutron-rich nuclei depend only slightly on the incident energy, while those of neutron-deficient nuclei depend strongly on the incident energy.

2018, 42(10): 105101. doi: 10.1088/1674-1137/42/10/105101

**Abstract:**

We discuss the Hamiltonian formulation of gravity in four-dimensional spacetime under Bondi-like coordinates {

*v,r,x*

^{a},

*a*=2,3}. In Bondi-like coordinates, the three-dimensional hypersurface is a null hypersurface, and the evolution direction is the advanced time

*v*. The internal symmetry group SO(1,3) of the four-dimensional spacetime is decomposed into SO(1,1), SO(2), and T

^{±}(2), whose Lie algebra

**(1,3) is decomposed into**

*so***(1,1),**

*so***(2), and t**

*so*^{±}(2) correspondingly. The SO(1,1) symmetry is very obvious in this type of decomposition, which is very useful in

**(1,1) BF theory. General relativity can be reformulated as the four-dimensional coframe (**

*so**e*

_{μ}

^{I}) and connection (

*ω*

_{μ}

^{IJ}) dynamics of gravity based on this type of decomposition in the Bondi-like coordinate system. The coframe consists of two null 1-forms

*e*

^{-},

*e*

^{+}and two spacelike 1-forms

*e*

^{2},

*e*

^{3}. The Palatini action is used. The Hamiltonian analysis is conducted by Dirac's methods. The consistency analysis of constraints has been done completely. Among the constraints, there are two scalar constraints and one two-dimensional vector constraint. The torsion-free conditions are acquired from the consistency conditions of the primary constraints about

*π*

_{IJ}

^{μ}. The consistency conditions of the primary constraints

*π*

_{IJ}

^{0}=0 can be reformulated as Gauss constraints. The conditions of the Lagrange multipliers have been acquired. The Poisson brackets among the constraints have been calculated. There are 46 constraints including 6 first-class constraints

*π*

_{IJ}

^{0}=0 and 40 second-class constraints. The local physical degrees of freedom is 2. The integrability conditions of Lagrange multipliers

*n*

_{0},

*l*

_{0}, and

*e*

_{0}

^{A}are Ricci identities. The equations of motion of the canonical variables have also been shown.

2018, 42(10): 105102. doi: 10.1088/1674-1137/42/10/105102

**Abstract:**

We study the quasinormal modes (QNMs) of a Schwarzschild black hole immersed in an electromagnetic (EM) universe. The immersed Schwarzschild black hole (ISBH) originates from the metric of colliding EM waves with double polarization[Class. Quantum Grav. 12, 3013 (1995)]. The perturbation equations of the scalar fields for the ISBH geometry are written in the form of separable equations. We show that these equations can be transformed to the confluent Heun's equations, for which we are able to use known techniques to perform analytical quasinormal (QNM) analysis of the solutions. Furthermore, we employ numerical methods (Mashhoon and 6

^{th}-order Wentzel-Kramers-Brillouin (WKB)) to derive the QNMs. The results obtained are discussed and depicted with the appropriate plots.

**ISSN** 1674-1137 **CN** 11-5641/O4

Original research articles, Ietters and reviews Covering theory and experiments in the fieids of

- Particle physics
- Nuclear physics
- Particle and nuclear astrophysics
- Cosmology

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