## 2017 Vol. 41, No. 8

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2017, 41(8): 083001. doi: 10.1088/1674-1137/41/8/083001

**Abstract:**

A detailed theoretical derivation of the cross sections of e

^{+}e

^{-}→e

^{+}e

^{-}and e

^{+}e

^{-}→μ

^{+}μ

^{-}around the J/ψ resonance is reported. The resonance and interference parts of the cross sections, related to J/ψ resonance parameters, are calculated. Higher-order corrections for vacuum polarization and initial-state radiation are considered. An arbitrary upper limit of radiative correction integration is involved. Full and simplified versions of analytic formulae are given with precision at the level of 0.1% and 0.2%, respectively. Moreover, the results obtained in the paper can be applied to the case of the ψp resonance.

2017, 41(8): 083101. doi: 10.1088/1674-1137/41/8/083101

**Abstract:**

We investigate the rare baryonic

*λ*

_{b}→

*λ*l

^{+}l

^{-}decays in a non-universal Z' model, which is one of the well-motivated extensions of the standard model (SM). Considering the effects of Z'-mediated flavour-changing neutral currents (FCNCs) we analyse the differential decay rate, forward-backward asymmetries and lepton polarisation asymmetries for the

*λ*

_{b}→

*λ*l

^{+}l

^{-}decays. We find significant deviations from their SM predictions, which could indicate new physics arising from the Z' gauge boson.

2017, 41(8): 083102. doi: 10.1088/1674-1137/41/8/083102

**Abstract:**

We investigate instanton effects on the heavy-quark potential, including its spin-dependent part, based on the instanton liquid model. Starting with the central potential derived from the instanton vacuum, we obtain the spin-dependent part of the heavy-quark potential. We discuss the results of the heavy-quark potential from the instanton vacuum. Finally, we solve the nonrelativistic two-body problem, associated with the heavy-quark potential from the instanton vacuum. The instanton effects on the quarkonia spectra are marginal but are required for quantitative description of the spectra.

2017, 41(8): 083103. doi: 10.1088/1674-1137/41/8/083103

**Abstract:**

In this article, we assign the m Y(4390) and m Y(4220) to be the vector molecular states DD

_{1}(2420) and D

^{*}D

_{0}

^{*}(2400), respectively, and study their masses and pole residues in detail with the QCD sum rules. The present calculations only favor assigning the m Y(4390) to be the DD

_{1}(1

^{——}) molecular state.

2017, 41(8): 083104. doi: 10.1088/1674-1137/41/8/083104

**Abstract:**

In this article, we study the strong interaction of the vertices

*∑*

_{b}

*NB*and

*∑*

_{c}

*ND*using the three-point QCD sum rules under two different Dirac structures. Considering the contributions of the vacuum condensates up to dimension 5 in the operation product expansion, the form factors of these vertices are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which gives the coupling constants. Our analysis indicates that the coupling constants for these two vertices are

*G*

_{∑bNB}=0.43±0.01 GeV

^{-1}and G

_{∑cND}=3.76±0.05 GeV

^{-1}.

2017, 41(8): 083105. doi: 10.1088/1674-1137/41/8/083105

**Abstract:**

By employing the perturbative QCD (PQCD) factorization approach, we study the quasi-two-body B

_{(s)}

^{0}→ η

_{c}(2

*S*)π

^{+}π

^{-}decays, where the pion pair comes from the

*S*-wave resonance

*f*

_{0}(

*X*). The Breit-Wigner formula for the

*f*

_{0}(500) and

*f*

_{0}(1500) resonances and the Flatté model for the

*f*

_{0}(980) resonance are adopted to parameterize the time-like scalar form factors in the two-pion distribution amplitudes. As a comparison, Bugg's model is also used for the wide

*f*

_{0}(500) in this work. For decay rates, we found the following PQCD predictions:(a)

*B*(B

_{s}

^{0}→η

_{c}(2

*S*)

*f*

_{0}(

*X*)[π

^{+}π

^{-}]

_{s})= ≤ ft (2.67

_{-1.08}

^{+1.78})×10

^{-5}when the contributions from

*f*

_{0}(980) and

*f*

_{0}(1500) are all taken into account; (b)

*B*(B

^{0}→η

_{c}(2

*S*)

*f*

_{0}(500)[π

^{+}π

^{-}]

_{s})= ≤ ft (1.40

_{-0.56}

^{+0.92})×10

^{-6}in the Breit-Wigner model and ≤ ft (1.53

^{+0.97}

_{-0.61}ight)×10

^{-6}in Bugg's model.

2017, 41(8): 083106. doi: 10.1088/1674-1137/41/8/083106

**Abstract:**

The non-relativistic wave function framework is applied to study the production and decay of exotic hadrons, which can be effectively described as bound states of other hadrons. Employing the factorized formulation, with the help of event generators, we investigate the production of exotic hadrons in multiproduction processes at high energy hadron colliders. This study provides crucial information for the measurements of the relevant exotic hadrons.

2017, 41(8): 083107. doi: 10.1088/1674-1137/41/8/083107

**Abstract:**

The unobserved

*J*

^{P}=0

^{-}radial excitation D

_{s}(2

^{1}

*S*

_{0}) is anticipated to have mass 2650 MeV (denoted as D

_{s}(2650)). Study of hadronic production is an important way to identify highly excited states. We study hadronic production of D

_{s}(2650) from higher excited resonances in a

^{3}

*P*

_{0}model. Relevant hadronic partial decay widths are found to be very small, which implies it is difficult to observe D

_{s}(2650) in hadronic decays of higher excited resonances. Hadronic decay widths of radially excited D

_{s}(3

*P*) have also been estimated. The total decay widths of four D

_{s}(3

*P*) are large, but the branching ratios in the D

_{s}(2650)

*η*channel are very small, which implies that it seems impossible to observe D

_{s}(2650) in hadronic decays of D

_{s}(3

*P*). The dominant decay channels of the four D

_{s}(3

*P*) have been pointed out, and D

_{1}(2420), D

_{1}(2430), m D

_{2}

^{*}(2460), m D(2550), m D(2600), m (1

^{1}D

_{2})D(2750) and m D

_{3}

^{*}(2760) are possible to observe in hadronic production from D

_{s}(3

*P*).

2017, 41(8): 084101. doi: 10.1088/1674-1137/41/8/084101

**Abstract:**

Within the framework of a multiphase transport model, we study the production and properties of Ω and

*φ*in Au + Au collisions with a new set of parameters for √

^{s}NN=200 GeV and with the original set of parameters for √

^{s}NN=11.5 GeV. The AMPT model with string melting provides a reasonable description at √

^{s}NN=200 GeV, while the default AMPT model describes the data well at √

^{s}NN=11.5 GeV. This indicates that the system created at top RHIC energy is dominated by partonic interactions, while hadronic interactions become important at lower beam energy, such as √

^{s}NN=11.5 GeV. The comparison of

*N*(Ω

^{+}+Ω

^{-})/[2

*N*(

*φ*)] ratio between data and calculations further supports the argument. Our calculations can generally describe the data of nuclear modification factor as well as elliptic flow.

2017, 41(8): 084102. doi: 10.1088/1674-1137/41/8/084102

**Abstract:**

We examine the evolution of quark-gluon plasma (QGP) droplets with viscous hydrodynamics and analyze the pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss (HBT) interferometry in a granular source model consisting of viscous QGP droplets. The shear viscosity of the QGP droplet speeds up and slows down the droplet evolution in the central and peripheral regions of the droplet, respectively. The effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change little for granular sources with and without viscosity. On the other hand, the influence of viscosity on HBT radius

*R*

_{out}is considerable. It makes

*R*

_{out}decrease in the granular source model. We determine the model parameters of granular sources using the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii together, and investigate the effects of viscosity on the model parameters. The results indicate that the granular source model may reproduce the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii in heavy-ion collisions of Au-Au at √

^{s}NN=200 GeV and Pb-Pb at √

^{s}NN=2.76 TeV in different centrality intervals. The viscosity of the droplet leads to an increase in the initial droplet radius and a decrease of the source shell parameter in the granular source model.

2017, 41(8): 084103. doi: 10.1088/1674-1137/41/8/084103

**Abstract:**

The properties of the ground and excited-state (

*γ*-and

*β*-bands) of

^{168-178}Hf nuclei have been studied. The ratio

*r*(I+2/I) and

*E*

*γ*(I→ I-2)/I have been calculated as a function of the spin (I) to determine the ground-state evolution. The results indicate that these isotopes have a rotational property

*SU*(3). The energy levels for the ground-state,

*γ*-and

*β*-bands of

^{168-178}Hf have been calculated using the Interacting Boson Model and Semi Empirical Formula (SEF). The parameters of the best fit to the measured data are determined. The behavior of energy and B(E2) ratios in the ground state band are examined.

2017, 41(8): 084104. doi: 10.1088/1674-1137/41/8/084104

**Abstract:**

The systematics of kinematic moment of inertia

*J*

^{(1)}and dynamic moment of inertia

*J*

^{(2)}of superdeformed (SD) bands in

*A*~130, 150, 190 mass regions have been studied. We have obtained the values of

*J*

^{(1)}and

*J*

^{(2)}for all the SD bands observed in the

*A*~130, 150, 190 mass regions by using the experimental intraband E2 transition energies. The result of this work includes the variation of

*J*

^{(1)}with the product of valence proton and neutron numbers (

*N*

_{p}

*N*

_{n}). The phenomenon of band mixing has been observed in the

*A*~130, 150 mass regions and band crossing has been observed in the

*A*~190 mass region. The systematics also includes the variation of

*J*

^{(2)}with the product of valence proton and neutron numbers (

*N*

_{p}

*N*

_{n}). Evidence of staggering behaviour has been observed in all three

*A*~130, 150 and 190 mass regions. We present for the first time the variation of

*J*

^{(1)}and

*J*

^{(2)}of SD bands in the

*A*~130, 150, 190 mass regions with

*N*

_{p}

*N*

_{n}.

2017, 41(8): 084105. doi: 10.1088/1674-1137/41/8/084105

**Abstract:**

Level structures of

^{85}Br have been investigated using the shell-model code nushellx within a large model space containing the neutron-core excitations across the

*N*=50 closed shell. The calculated results have been compared with the available experimental data. Reasonable agreement between the experimental and calculated values is obtained, which indicates that the neutron-core excitations are essential to reproduce the level structures of

^{85}Br. The systematic features of neutron-core excitations in the

*N*=50 isotones are investigated.

2017, 41(8): 085101. doi: 10.1088/1674-1137/41/8/085101

**Abstract:**

Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of

*c*, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.

2017, 41(8): 086001. doi: 10.1088/1674-1137/41/8/086001

**Abstract:**

We have studied optimization of the design of a barrel-shaped pixelated tracker for given spatial boundaries. The optimization includes choice of number of layers and layer spacing. Focusing on tracking performance only, momentum resolution is chosen as the figure of merit. The layer spacing is studied based on Gluckstern's method and a numerical geometry scan of all possible tracker layouts. A formula to give the optimal geometry for curvature measurement is derived in the case of negligible multiple scattering to deal with trajectories of very high momentum particles. The result is validated by a numerical scan method, which could also be implemented with any track fitting algorithm involving material effects, to search for the optimal layer spacing and to determine the total number of layers for the momentum range of interest under the same magnetic field. The geometry optimization of an inner silicon pixel tracker proposed for BESⅢ is also studied by using a numerical scan and these results are compared with Geant4-based simulations.

2017, 41(8): 087001. doi: 10.1088/1674-1137/41/8/087001

**Abstract:**

The particle motion equation for a Radio Frequency (RF) quadrupole is derived. The motion equation shows that the general transform matrix of a RF quadrupole with length less than or equal to 0.5

*β*

*λ*(

*β*is the relativistic velocity of particles and

*λ*is wavelength of radio frequency electromagnetic field) can describe the particle motion in an arbitrarily long RF quadrupole. By iterative integration, the general transform matrix of a discrete RF quadrupole is derived from the motion equation. The transform matrix is in form of a power series of focusing parameter

*B*. It shows that for length less than

*β*

*λ*, the series up to the 2

^{nd}order of

*B*agrees well with the direct integration results for

*B*up to 30, while for length less than 0.5

*β*

*λ*, the series up to 1

^{st}order is already a good approximation of the real solution for

*B*less than 30. The formula of the transform matrix can be integrated into linac or beam line design code to deal with the focusing of discrete RF quadrupoles.

2017, 41(8): 087002. doi: 10.1088/1674-1137/41/8/087002

**Abstract:**

Estimation and correction of the optics errors in an operational storage ring is always vital to achieve the design performance. To achieve this task, the most suitable and widely used technique, called linear optics from closed orbit (LOCO) is used in almost all storage ring based synchrotron radiation sources. In this technique, based on the response matrix fit, errors in the quadrupole strengths, beam position monitor (BPM) gains, orbit corrector calibration factors etc. can be obtained. For correction of the optics, suitable changes in the quadrupole strengths can be applied through the driving currents of the quadrupole power supplies to achieve the desired optics. The LOCO code has been used at the Indus-2 storage ring for the first time. The estimation of linear beam optics errors and their correction to minimize the distortion of linear beam dynamical parameters by using the installed number of quadrupole power supplies is discussed. After the optics correction, the performance of the storage ring is improved in terms of better beam injection/accumulation, reduced beam loss during energy ramping, and improvement in beam lifetime. It is also useful in controlling the leakage in the orbit bump required for machine studies or for commissioning of new beamlines.

2017, 41(8): 087003. doi: 10.1088/1674-1137/41/8/087003

**Abstract:**

A gas cluster ion beam (GCIB) system with cluster energy up to 12 keV has been designed. To facilitate pumping of the nozzle chamber and increased pressure of the gas source up to 10 atm, pulse mode was used for the gas feeding. Argon was employed as the working gas. To separate monomers from clusters, both electromagnet and retarding electrode were utilized. A maximal pulsed cluster current of 90 nA has been achieved. The shape of pulsed ion beam currents has been analyzed in detail at different applied magnetic and retarding electric fields.

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

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

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