Automated One-loop Computation in Quarkonium Process within NRQCD Framework

In last decades, it has been realized that the next-to-leading order corrections may become very important, and sometimes requisite, for some processes involving quarkoinum production or decay, e.g., $e^+e^- \to J/\psi + \eta_c$ and $J/\psi \to 3\gamma$. In this article, we review some basic steps to perform automated one-loop computations in quarkonium process within the Non-relativistic Quantum Chromodynamics (NRQCD) factorization framework, and we give an introduction to some related public tools or packages and their usages in each step. We start from generating Feynman diagrams and amplitudes with \textsc{FeynArts} for the quarkonium process, performing Dirac- and Color- algebras simplifications using \textsc{FeynCalc} and \textsc{FeynCalcFormLink}, and then to doing partial fractions on the linear-dependent propagators by \textsc{APart}, and finally to reducing the Tensor Integrals (TI) into Scalar Integrals (SI) or Master Integrals (MI) using Integration-By-Parts (IBP) method with the help of \textsc{Fire}. We will use a simple concrete example to demonstrate the basic usages of the corresponding packages or tools in each step.Comment: 8 pages, conference proceedings for ACAT 201

Effective mass splitting of neutron and proton and isospin emission in heavy-ion collisions

Within the framework of an isospin and momentum dependent transport model, the emissions of isospin particles (nucleons and light clusters) squeezed out in heavy-ion collisions are investigated as probes of the poorly known symmetry energy at high baryon density. Two different mass splittings of neutrons and protons in nuclear medium as $m_{n}^{\ast}>m_{p}^{\ast}$ and $m_{n}^{\ast}<m_{p}^{\ast}$ are used in the model and their influence on the isospin emission in heavy-ion collisions is discussed thoroughly. The competition between the stiffness and the momentum dependence of the symmetry potential on reaction dynamics are compared and systematically analyzed. It is found that the difference of the neutron and proton directed flows and the transverse momentum distribution of the neutron/proton ratio are sensitive to the stiffness of the symmetry energy, which can not be changed with the controversial effective mass splitting. The elliptic flows of free nucleons at high transverse momentum within mid-rapidity emission are a promising observable as distinguishing the nucleon effective mass splitting.Comment: 16 pages, 7 figure

Transverse emission of isospin ratios as a probe of high-density symmetry energy in isotopic nuclear reactions

Transverse emission of preequilibrium nucleons, light clusters (complex particles) and charged pions from the isotopic $^{112,124}$Sn+$^{112,124}$Sn reactions at a beam energy of 400\emph{A} MeV, to extract the high-density behavior of nuclear symmetry energy, are investigated within an isospin and momentum dependent transport model. Specifically, the double ratios of neutron/proton, triton/helium-3 and $\pi^{-}/\pi^{+}$ in the squeeze-out domain are analyzed systematically, which have the advantage of reducing the influence of the Coulomb force and less systematic errors. It is found that the transverse momentum distribution of isospin ratios strongly depend on the stiffness of nuclear symmetry energy, which would be a nice observable to extract the high-density symmetry energy. The collision centrality and the mass splitting of neutron and proton in nuclear medium play a significant role on the distribution structure of the ratios, but does not change the influence of symmetry energy on the spectrum.Comment: 5 figures, 13 page

Next-to-leading-order QCD corrections to gluon fragmentation into 1S0(1,8){}^1S_0^{(1,8)} quarkonia

Within the NRQCD factorization framework, we compute the next-to-leading-order QCD corrections to the gluon fragmentation into the ${}^1S_0^{(1,8)}$ Fock components of a quarkonium, at the lowest order in velocity expansion. We follow the operator definition of the fragmentation function advanced by Collins and Soper. The key technique underpinning our calculation is the sector decomposition method widely used in the area of multi-loop computation. It is found that the NLO QCD corrections have significant effects, and qualitatively modify the profiles of the corresponding leading-order fragmentation functions.Comment: 10 pages, 2 figures, 2 table

NN-Bright-Dark Soliton Solution to a Semi-Discrete Vector Nonlinear Schr\"odinger Equation

In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota's bilinear method. One- and two-bright-dark soliton solutions are explicitly presented for two-component semi-discrete NLS equation; two-bright-one-dark, and one-bright-two-dark soliton solutions are also given explicitly for three-component semi-discrete NLS equation. The asymptotic behavior is analysed for two-soliton solutions

Influence of the additional second neighbor hopping on the spin response in the t-J model

The influence of the additional second neighbor hopping t' on the spin response of the t-J model in the underdoped and optimally doped regimes is studied within the fermion-spin theory. Although the additional second neighbor hopping t' is systematically accompanied with the reduction of the dynamical spin structure factor and susceptibility, the qualitative behavior of the dynamical spin structure factor and susceptibility of the t-t'-J model is the same as in the case of t-J model. The integrated dynamical spin structure factor spectrum is almost t' independent, and the integrated dynamical spin susceptibility still shows the particularly universal behavior as $I(\omega,T)\propto {\rm arctan}[a_{1}\omega/T+a_{3}(\omega/T)^{3}]$.Comment: 12 pages, Latex, Four figures are included, final published version [accepted for publication in Phys. Rev. B (July 1 issue)