## 2018 Vol. 42, No. 4

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2018, 42(4): 042001. doi: 10.1088/1674-1137/42/4/042001

**Abstract:**

The success of hydrodynamics in high energy heavy-ion collisions leads to a flow paradigm, to understand the observed features of harmonic flow in terms of the medium collective expansion with respect to initial state geometrical properties. In this review, we present some essential ingredients in the flow paradigm, including the hydrodynamic modeling, the characterization of initial state geometry and the medium response relations. The extension of the flow paradigm to small colliding systems is also discussed.

2018, 42(4): 042002. doi: 10.1088/1674-1137/42/4/042002

**Abstract:**

The world's largest sample of J/ψ events, 1.31 billion events accumulated at the BESⅢ detector, provides a unique opportunity to investigate n and n' physics via two-body J/ψ radiative or hadronic decays. For many n' decay channels the low background data samples are up to three orders of magnitude larger than collected in any previous experiment. Here we review the most significant results on n and n' obtained at BESⅢ so far. The analyses range from detailed studies of common decay dynamics, observations of new radiative and Dalitz decays, and searches for rare/forbidden decays with sensitivity up to

*B*~10

^{-5}. Finally, prospects of forthcoming runs at the J/ψ peak for n and n' physics are discussed.

2018, 42(4): 043001. doi: 10.1088/1674-1137/42/4/043001

**Abstract:**

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used.

2018, 42(4): 043002. doi: 10.1088/1674-1137/42/4/043002

**Abstract:**

The exclusive Born cross sections of the production of D

^{0}, D

^{+}and D

_{s}

^{+}mesons in e

^{+}e

^{-}annihilation at 13 energy points between 3.970 and 4.260 GeV are obtained by applying corrections for initial state radiation and vacuum polarization to the observed cross sections measured by the CLEO-c experiment. Both the statistical and the systematic uncertainties for the obtained Born cross sections are estimated.

2018, 42(4): 043101. doi: 10.1088/1674-1137/42/4/043101

**Abstract:**

In order to investigate the possibility of the recently observed X(5568) being a 0

^{+}tetraquark state, we make an improvement to the study of the related various configuration states in the framework of the QCD sum rules. Particularly, to ensure the quality of the analysis, condensates up to dimension 12 are included to inspect the convergence of operator product expansion (OPE) and improve the final results of the studied states. We note that some condensate contributions could play an important role on the OPE side. By releasing the rigid OPE convergence criterion, we arrive at the numerical value 5.57

_{-0.23}

^{+0.35}GeV for the scalar-scalar diquark-antidiquark 0

^{+}state, which agrees with the experimental data for the X(5568) and could support its interpretation in terms of a 0

^{+}tetraquark state with the scalar-scalar configuration. The corresponding result for the axial-axial current is calculated to be 5.77

_{-0.33}

^{+0.44}GeV, which is still consistent with the mass of X(5568) in view of the uncertainty. The feasibility of X(5568) being a tetraquark state with the axial-axial configuration therefore cannot be definitely excluded. For the pseudoscalar-pseudoscalar and the vector-vector cases, their unsatisfactory OPE convergence make it difficult to find reasonable work windows to extract the hadronic information.

2018, 42(4): 043102. doi: 10.1088/1674-1137/42/4/043102

**Abstract:**

The light cone gauge with light cone variables is often used in pQCD calculations in relativistic heavy-ion collision physics. The Hard Thermal Loops (HTL) resummation is an indispensable technique for hot QCD calculation. It was developed in covariant gauges with conventional Minkowski varaiables; we shall extend this method to the light cone gauge. In the real time formalism, using the Mandelstam-Leibbrant prescription of (

*n*·

*K*)

^{-1}, we calculate the transverse and longitudinal components of the gluon HTL self energy, and prove that there are no infrared divergences. With this HTL self energy, we derive the HTL resummed gluon propagator in the light cone gauge. We also calculate the quark HTL self energy and the resummed quark propagator in the light cone gauge and find it is gauge independent. As application examples, we analytically calculate the damping rates of hard quarks and gluons with the HTL resummed gluon propagator in the light cone gauge and showed that they are gauge independent. The final physical results are identical to those computed in covariant gauge, as they should be.

2018, 42(4): 043103. doi: 10.1088/1674-1137/42/4/043103

**Abstract:**

I discuss the production mechanism of hidden-flavored hadrons at high energy. Using e

^{+}e

^{-}collisions and light-meson pair production in high energy exclusive processes, I demonstrate that hidden quark pairs do not necessarily participate in short-distance hard scattering. Implications are then explored in a few examples. Finally, I discuss the production mechanism of X(3872) in hadron collisions, where some misunderstandings have arisen in the literature.

2018, 42(4): 043104. doi: 10.1088/1674-1137/42/4/043104

**Abstract:**

A thorough study reveals that the only key parameter for ψ (J/ψ, ψ') polarization at hadron colliders is the ratio <

*O*

^{ψ}(

^{3}

*S*

_{1}

^{[8]})>/<

*O*

^{ψ}(

^{3}

*P*

_{0}

^{[8]})> angle, if the velocity scaling rule holds. A slight variation of this parameter results in substantial change of the ψ polarization. We find that with equally good description of the yield data, this parameter can vary significantly. Fitting the yield data is therefore incapable of determining this parameter, and consequently, of determining the ψ polarization. We provide a universal approach to fixing the long-distance matrix elements (LDMEs) for J/ψ and ψ' production. Further, with the existing data, we implement this approach, obtain a favorable set of the LDMEs, and manage to reconcile the charmonia production and polarization experiments, except for two sets of CDF data on J/ψ polarization.

2018, 42(4): 043105. doi: 10.1088/1674-1137/42/4/043105

**Abstract:**

Electroweak WIMPs are under intense scrutiny from direct detection, indirect detection, and collider experiments. Nonetheless the pure (pseudo-Dirac) higgsino, one of the simplest such WIMPs, remains elusive. We present an up-to-date assessment of current experimental constraints on neutralino dark matter. The strongest bound on pure higgsino dark matter currently may arise from AMS-02 measurements of antiprotons, though the interpretation of these results has sizable uncertainty. We discuss whether future astrophysical observations could offer novel ways to test higgsino dark matter, especially in the challenging regime with order MeV mass splitting between the two neutral higgsinos. We find that heating of white dwarfs by annihilation of higgsinos captured via inelastic scattering could be one useful probe, although it will require challenging observations of distant dwarf galaxies or a convincing case to be made for substantial dark matter content in

*ω*Cen, a globular cluster that may be a remnant of a disrupted dwarf galaxy. White dwarfs and neutron stars give a target for astronomical observations that could eventually help to close the last, most difficult corner of parameter space for dark matter with weak interactions.

2018, 42(4): 043106. doi: 10.1088/1674-1137/42/4/043106

**Abstract:**

Motivated by the experimental measurements of D

^{0}radiative decay modes, we have proposed a model to study the D

^{0}→ K

^{*0}γ decay, by establishing a link with D

^{0}→ K

^{*0}V (V=ρ

^{0},

*ω*) decays through the vector meson dominance hypothesis. In order to do this properly, we have used the Lagrangians from the local hidden gauge symmetry approach to account for V

*γ*conversion. As a result, we have found the branching ratio

*B*[D

^{0}→ K

^{*0}

*γ*]=(1.55-3.44)×10

^{-4}, which is in fair agreement with the experimental values reported by the Belle and BaBar collaborations.

2018, 42(4): 043107. doi: 10.1088/1674-1137/42/4/043107

**Abstract:**

Inspired by the newly observed state X

^{*}(3860), we analyze the strong decay behaviors of some charmonium-like states, X

^{*}(3860), X(3872), X(3915), X(3930) and X(3940), with the

^{3}

*P*

_{0}model. We carry out our work based on the hypothesis that all of these states are charmonium systems. Our analysis indicates that, as a 0

^{++}charmonium state, X

^{*}(3860) can reproduce the experimental data. As for X(3872), it can tentatively be interpreted as the mixture of a m cc system and a D

^{*0}D

^{0}molecular state. If we consider X(3940) as a 3

^{1}

*S*

_{0}state, its total width in the present work is much lower than the experimental result. Thus, the 3

^{1}

*S*

_{0}charmonium state seems not to be a good candidate for X(3940). Furthermore, our analysis implies that it is reasonable to assign X(3915) and X(3930) to be the same state, 2

^{++}. However, combining our analysis with that in Refs.[14,71], we speculate that X(3915)/X(3930) might also be the mixture of a m cc system and a molecular state.

2018, 42(4): 044001. doi: 10.1088/1674-1137/42/4/044001

**Abstract:**

In the standard Big Bang nucleosynthesis (SBBN) model, the lithium puzzle has attracted intense interest over the past few decades, but still has not been solved. Conventionally, the approach is to include more reactions flowing into or out of lithium, and study the potential effects of those reactions which were not previously considered.

^{7}Be(d,

^{3}He)

^{6}Li is a reaction that not only produces

^{6}Li but also destroys

^{7}Be, which decays to

^{7}Li, thereby affecting

^{7}Li indirectly. Therefore, this reaction could alleviate the lithium discrepancy if its reaction rate is sufficiently high. However, there is not much information available about the

^{7}Be(d,

^{3}He)

^{6}Li reaction rate. In this work, the angular distributions of the

^{7}Be(d,

^{3}He)

^{6}Li reaction are measured at the center of mass energies

*E*

_{cm}=4.0 MeV and 6.7 MeV with secondary

^{7}Be beams for the first time. The excitation function of the

^{7}Be(d,

^{3}He)

^{6}Li reaction is first calculated with the computer code TALYS and then normalized to the experimental data, then its reaction rate is deduced. A SBBN network calculation is performed to investigate its influence on the

^{6}Li and

^{7}Li abundances. The results show that the

^{7}Be(d,

^{3}He)

^{6}Li reaction has a minimal effect on

^{6}Li and

^{7}Li because of its small reaction rate. Therefore, the

^{7}Be(d,

^{3}He)

^{6}Li reaction is ruled out by this experiment as a means of alleviating the lithium discrepancy.

2018, 42(4): 044101. doi: 10.1088/1674-1137/42/4/044101

**Abstract:**

We perform calculations for the B

_{s}

^{0}→ J/ψπ

^{0}f

_{0}(980) and B

_{s}

^{0}→ J/ψπ

^{0}a

_{0}(980) reactions, showing that the first is isospin-suppressed while the second is isospin-allowed. The reaction proceeds via a triangle mechanism, with B

_{s}

^{0}→J/ψK

^{*}K +c.c., followed by the decay K

^{*}→Kπ and a further fusion of KK into the f

_{0}(980) or a

_{0}(980). We show that the mechanism develops a singularity around the π

^{0}f

_{0}(980) or π

^{0}a

_{0}(980) invariant mass of 1420 MeV, where the π

^{0}f

_{0}and π

^{0}a

_{0}decay modes are magnified and also the ratio of π

^{0}f

_{0}to π

^{0}a

_{0}production. Using experimental information for the B

_{s}

^{0}→ J/ψK

^{*}K +c.c. decay, we are able to obtain absolute values for the reactions studied which fall into the experimentally accessible range. The reactions proposed and the observables evaluated, when contrasted with actual experiments, should be very valuable to obtain information on the nature of the low lying scalar mesons.

2018, 42(4): 044102. doi: 10.1088/1674-1137/42/4/044102

**Abstract:**

The present work is a continuation of our previous paper[J.-G. Deng, et al., Chin. Phys. C,

**41**:124109 (2017)]. In the present work, the

*α*decay half-life of the unknown nucleus

^{296}Og is predicted within the two-potential approach and the hindrance factors of all 20 even-even nuclei in the same region as

^{296}Og, i.e. proton number 82 <

*Z*< 126 and neutron number 152 <

*N*< 184, from

^{250}Cm to

^{294}Og, are extracted. The prediction is 1.09 ms within a factor of 5.12. In addition, based on the latest experimental data, a new set of parameters of

*α*decay hindrance factors for the even-even nuclei in this region, considering the shell effect and proton-neutron interaction, are obtained.

2018, 42(4): 044103. doi: 10.1088/1674-1137/42/4/044103

**Abstract:**

Isovector neutron-proton (np) pairing and particle-number fluctuation effects on the spectroscopic factors (SF) corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS (SBCS) discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in

*N*=

*Z*nuclei, and must then be taken into account.

2018, 42(4): 045101. doi: 10.1088/1674-1137/42/4/045101

**Abstract:**

In this paper, we describe quasinormal modes (QNMs) for gravitational perturbations of Einstein-Gauss-Bonnet black holes (BHs) in higher dimensional spacetimes, and derive the corresponding parameters of such black holes in three types of spacetime (flat, de Sitter (dS) and anti-de Sitter (AdS)). Our attention is concentrated on discussing the (in)stability of Einstein-Gauss-Bonnet AdS BHs through the temporal evolution of all types of gravitational perturbation fields (tensor, vector and scalar). It is concluded that the potential functions in vector and scalar gravitational perturbations have negative regions, which suppress quasinormal ringing. Furthermore, the influences of the Gauss-Bonnet coupling parameter

*α*, the number of dimensions

*n*and the angular momentum quantum number

*l*on the Einstein-Gauss-Bonnet AdS BHs quasinormal spectrum are analyzed. The QNM frequencies have greater oscillation and lower damping rate with the growth of

*α*. This indicates that QNM frequencies become increasingly unstable with large

*α*. Meanwhile, the dynamic evolutions of the perturbation field are compliant with the results of computation from the Horowitz and Hubeny method. Because the number of extra dimensions is connected with the string scale, the relationship between

*α*and properties of Einstein-Gauss-Bonnet AdS BHs might be beneficial for the exploitation of string theory and extra-dimensional brane worlds.

2018, 42(4): 045102. doi: 10.1088/1674-1137/42/4/045102

**Abstract:**

In our previous work[1], a new kind of inflation model was proposed, which has the interesting property that its perturbation equation of motion gets a correction of

*k*

^{4}, due to the non-linearity of the kinetic term. Nonetheless, the scale-invariance of the power spectrum remains valid, both in large-

*k*and small-

*k*limits. In this paper, we investigate in detail the spectral index, the index running and the tensor/scalar ratio in this model, especially in the potential-driven case, and compare the results with the current PLANCK/BICEP observational data. We also discuss the tensor spectrum in this case, which is expected to be tested by future observations of primordial gravitational waves.

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

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