arXiv subjects
Publications and source records attributed to Xiao-Ming Xu.
Elastic parton-parton-parton scattering is briefly reviewed and is included in transport equations of quark-gluon matter. We solve the transport equations and get thermal states from initially produced quark-gluon matter. Both gluon matter and quark matter take early thermalization, but gloun matter has a shorter thermalization time than quark matter.
Elastic gluon-gluon-quark (gluon-gluon-antiquark) scattering is studied in perturbative QCD with 123 Feynman diagrams at the tree level. Individually squared amplitudes and interference terms of the Feynman diagrams are derived. With the elastic gluon-gluon-quark scattering and the elastic gluon-gluon-antiquark scattering transport equations are established. In the thermalization process of initially created quark-gluon matter, this matter is governed by elastic 2-to-2 scattering and elastic 3-to-3 scattering. Solutions of the transport equations show that initially created quark-gluon matter takes early thermalization, i.e., thermal states are established rapidly. Different thermalization times of gluon matter and quark matter are obtained.
The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.
Meson-charmonium dissociation reactions governed by the quark interchange are studied with temperature-dependent quark potentials. Quark-antiquark relative-motion wave functions and masses of charmonia and charmed mesons are determined by the central spin-independent part of the potentials or by the central spin-independent part and a smeared spin-spin interaction. The prominent temperature dependence of the masses is found. Based on the potentials, the wave functions, and the meson masses, we obtain temperature-dependent cross sections for fifteen pion-charmonium and rho-charmonium dissociation reactions. The numerical cross sections are parametrized for future applications in hadronic matter. The particular temperature dependence of the J/psi bound state leads to unusual behavior of the cross sections for endothermic J/psi dissociation reactions. The quantum numbers of psi' and chi_c can not make their difference in mass in the temperature region 0.6T_c < T < T_c, but can make the psi' dissociation different from the chi_c dissociation.
We divide the cross section for a meson-meson reaction into three parts. The first part is for the quark-interchange process, the second for quark-antiquark annihilation processes and the third for resonant processes. Master rate equations are established to yield time dependence of fugacities of pions, rhos, kaons and vetor kaons. The equations include cross sections for inelastic scattering of pions, rhos, kaons and vector kaons. Cross sections for quark-interchange-induced reactions, that were obtained in a potential model, are parametrized for convenient use. The number densities of pion and rho (kaon and vector kaon) are altered by quark-interchange processes in equal magnitudes but opposite signs. The master rate equations combined with the hydrodynamic equations for longitudinal and transverse expansion are solved with many sets of initial meson fugacities. Quark-interchange processes are shown to be important in the contribution of the inelastic meson-meson scattering to evolution of mesonic matter.
We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius $R$. Adopting the prisoner's dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of $R$, and for modest values of $R$, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of $R$ or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.
The elastic scattering of gqq, gqqbar and gqbarqbar and the thermalization of quark-gluon matter are studied. According to Feynman diagrams at the tree level, squared amplitudes for the elastic gqq scattering and the elastic gqqbar scattering are derived in perturbative QCD. Transport equations including the squared amplitudes for the elastic gqq, gqqbar and gqbarqbar scattering are established. Corresponding to anisotropic gluon and quark distributions created in central Au-Au collisions at RHIC, solutions of the transport equations show that thermalization time of quark matter can be shortened by the elastic gqq, gqqbar and gqbarqbar scattering.
We investigate an evolutionary prisoner's dilemma game among self-driven agents, where collective motion of biological flocks is imitated through averaging directions of neighbors. Depending on the temptation to defect and the velocity at which agents move, we find that cooperation can not only be maintained in such a system but there exists an optimal size of interaction neighborhood, which can induce the maximum cooperation level. When compared with the case that all agents do not move, cooperation can even be enhanced by the mobility of individuals, provided that the velocity and the size of neighborhood are not too large. Besides, we find that the system exhibits aggregation behavior, and cooperators may coexist with defectors at equilibrium.
We present a potential of which the short-distance part is given by one gluon exchange plus perturbative one- and two-loop corrections and of which the large-distance part exhibits a temperature-dependent constant value. The Schrodinger equation with this temperature-dependent potential yields a temperature dependence of the mesonic quark-antiquark relative-motion wave function and of meson masses. The temperature dependence of the potential, the wave function and the meson masses brings about temperature dependence of cross sections for the nonresonant reactions pi pi -> rho rho for I=2, KK -> K* K* for I=1, KK* -> K* K* for I=1, pi K -> rho K* for I=3/2, pi K* -> rho K* for I=3/2, rho K -> rho K* for I=3/2 and pi K* -> rho K for I=3/2. As the temperature increases, the rise or fall of peak cross sections is determined by the increased radii of initial mesons, the loosened bound states of final mesons, and the total-mass difference of the initial and final mesons. The temperature-dependent cross sections and meson masses are parametrized.
STAR collaboration has offered eminent nuclear modification factor of J/psi at high p_T and midrapidity produced in Cu-Cu collisions at \sqrt {s_{NN}}= 200 GeV. Recalling a prediction we can understand that the feature of high-p_T nuclear modification factor is related to c\bar c produced by 2-to-1 and 2-to-2 partonic processes in deconfined matter particularly in the prethermal stage and to the recombination of c and \bar c. The nuclear modification factor at high p_T is sensitive to the earliest form of deconfined matter that does not have a temperature.
Meson-meson nonresonant reactions governed by the quark-interchange mechanism are studied in a potential that is derived from QCD. S-wave elastic phase shifts for I=2 ππand I=3/2 K πscattering are obtained with wave functions determined by the central spin-independent term of the potential. The reactions include inelastic scatterings of two mesons in the ground-state pseudoscalar octet and the ground-state vector nonet. Cross sections for reactions involving pion, rho, K and K^* indicate that mesonic interactions in matter consisting of only K and K^* can be stronger than mesonic interactions in matter consisting of only pions and rhos and the reaction of I=3/2 πK^* \to ρK is most important among the endothermic nonresonant reactions. By the quark-interchange mechanism we can offer \sqrt s-dependences of phi absorption cross sections in collisions with pion and rho and relevant average cross sections what are very small for the reaction of I=1 πϕ\to K^* K^* and remarkably large for the reaction of I=1 ρϕ\to K^* K^*. It is found from the \sqrt s-dependences of cross sections that rho and K^* creation cross sections can be larger than their absorption cross sections, respectively.
Meson-meson reactions A(q_1 \bar{q}_1) + B(q_2 \bar{q}_2) to q_1 + \bar{q}_1 + q_2 + \bar{q}_2 in high-temperature hadronic matter are found to produce an appreciable amount of quarks and antiquarks freely moving in hadronic matter and to establish a new mechanism for deconfinement of quarks and antiquarks in hadronic matter.
Thermalization of quark-gluon matter is studied with a transport equation that includes contributions of 2-to-2 and 3-to-3 elastic scatterings. Thermalization time is related to the squared amplitudes for the elastic scatterings that are calculated in perturbative QCD.
Thermalization of quark matter and antiquark matter is studied with quark-quark-antiquark as well as quark-antiquark-antiquark elastic scatterings. Squared amplitudes of qqqbar to qqqbar and qqbarqbar to qqbarqbar at order alpha_s^4 are derived in perturbative QCD. Solved by a new technique, solutions of transport equations with the squared amplitudes indicate that the scatterings qqqbar to qqqbar and qqbarqbar to qqbarqbar shorten the thermalization time of quark matter and antiquark matter. It is emphasized that three-parton and other multi-parton scatterings become important at the high parton number density achieved in RHIC Au-Au collisions.
We predict that initially produced chi_cJ mesons at low transverse momentum in the central rapidity region are almost dissociated by nucleons and antinucleons in hadronic matter produced in central Au+Au collisions at RHIC energies sqrt {s_{NN}}= 130 and 200 GeV. In calculations the nucleon and antinucleon distributions in hadronic matter are results of evolution from their freeze-out distributions which well fit the experimental p_T spectra of proton and antiproton. Any measured chi_cJ mesons at low p_T are generated from deconfined matter and give an explicit proof of regeneration mechanism (recombination mechanism).
Three-gluon to three-gluon scatterings lead to rapid thermalization of gluon matter created in central Au-Au collisions at RHIC energies. Thermalization of quark matter is studied from three-quark to three-quark scatterings.
Triple-quark elastic scattering amplitudes from perturbative QCD are first calculated and then used in a transport equation to study the thermalization of quark matter. By examining momentum isotropy to which the transport equation leads, we can determine thermalization time and offer an initial thermal quark distribution function. With an anisotropic initial quark distribution, which is relevant to quark matter initially created in a central Au-Au collision at \sqrt {s_{NN}}=200 GeV, the transport equation gives a time of the order of 1.8 fm/c for quark matter itself to thermalize by the triple-quark scatterings.
Triple-gluon elastic scatterings are briefly reviewed since the scatterings explain the early thermalization puzzle in Au-Au collisions at RHIC energies. A numerical solution of the transport equation with the triple-gluon elastic scatterings demonstrates gluon momentum isotropy achieved at a time of the order of 0.65 fm/c. Triple-gluon scatterings lead to a short thermalization time of gluon matter.