Elliptic flow of thermal photons in relativistic nuclear collisions

We predict the transverse momentum (p(T)) dependence of elliptic flow of thermal photons for Au + Au collisions at the BNL Relativistic Heavy Ion Collider. We model the system hydrodynamically, with a thermalized quark-gluon plasma at early times followed by hadronization and decoupling. Photons are emitted throughout the expansion history. Contrary to hadron elliptic flow, which increases monotonically with p(T), the elliptic flow nu2(p(T)) of thermal photons is predicted to first rise and then fall again. Photon elliptic flow at high p(T) reflects the quark momentum anisotropy at early times when it is small, while at low p(T) it mirrors the large pion momentum anisotropy during the late hadronic emission stage. An interesting structure is predicted at intermediate p(T) approximately 0.4 GeV/c, where photon elliptic flow reflects the momenta and the (compared to pions) reduced nu2 of heavy vector mesons in the late hadronic phase.     

Elliptic flow at large transverse momenta from quark coalescence

We show that hadronization via quark coalescence enhances hadron elliptic flow at large p(perpendicular) relative to that of partons at the same transverse momentum. Therefore, compared to earlier results based on covariant parton transport theory, more moderate initial parton densities dN/deta(b=0) approximately 1500-3000 can explain the differential elliptic flow v(2)(p(perpendicular)) data for Au+Au reactions at sqrt[s]=130 and 200A GeV from BNL RHIC. In addition, v(2)(p(perpendicular)) could saturate at about 50% higher values for baryons than for mesons. If strange quarks have weaker flow than light quarks, hadron v(2) at high p(perpendicular) decreases with relative strangeness content.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

中能重离子反应中的在平面流和椭圆流

利用同位旋相关的量子分子动力学模型研究了⁴⁰Ca+⁴⁰Ca系统在能量从30MeV/u到150MeV/u的在平面流和椭圆流.发现随着入射能量的增加,在平面流出现从负到正的跃迁,而椭圆流则随入射能量的增大而减少并且出现从正到负的跃迁.椭圆流和在平面流对于入射能量和碰撞参数较为敏感,相反对于对称能和核态方程却不太敏感.最后对于不同质量的碎块的依赖性关系我们还作了进一步仔细的研究.     

Globally polarized quark-gluon plasma in noncentral A + A collisions

Produced partons have a large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage of noncentral heavy-ion collisions. Parton scattering is shown to polarize quarks along the same direction due to spin-orbital coupling. Such global quark polarization will lead to many observable consequences, such as left-right asymmetry of hadron spectra and global transverse polarization of thermal photons, dileptons, and hadrons. Hadrons from the decay of polarized resonances will have an azimuthal asymmetry similar to the elliptic flow. Global hyperon polarization is studied within different hadronization scenarios and can be easily tested.     

Notes on the Elliptic Ruijsenaars Operators

We construct the spaces that the elliptic Ruijsenaars operators act on. It is shown that they are extensible to nonnegative selfadjoint operators on a space of square integrable functions, or preserve a finite dimensional vector space of entire functions. These facts are shown in terms of the R-operators which satisfy the Yang–lBaxter equation. The elliptic Ruijsenaars operators are considered as the elliptic analogues of the Macdonald operators or the difference analogues of the Lamé operators.     

Recent results from parton-cascade/microscopic transport

The parton-cascade model is a microscopic transport approach in the study of the space-time evolution of the quark–gluon plasma produced in relativistic heavy-ion collisions and its experimental manifestations. In the following, parton-cascade calculations on elliptic flow and thermalization will be discussed. Dynamical evolution is shown to be important for the production of elliptic flow including the scaling and the breaking of the scaling of elliptic flow. The degree of thermalization is estimated using both an elastic parton-cascade and a radiative transport model. A longitudinal to transverse pressure ratio of P _L /P _T ≈0.8 is shown to be expected in the central cell in central collisions. This provides information on viscous corrections to the ideal hydrodynamical approach.     

200GeV AuAu碰撞中前快度区的微分椭圆流

Identified particle elliptic flow results are presented for the Au+Au reaction at s_NN=200GeV as a function of transverse momentum and pseudorapidity. Data at pseudorapidities η≈0,1, and 3.4 were obtained using the two BRAHMS spectrometers. Differential v₂ (η,p_t) values for a given particle type are found to be essentially constant over the covered pseudorapidity range, in contrast to the integral v₂ values which have previously been observed to decrease at forward rapidities. A softening of the particle spectra at forward angles is found to account for at least part of the integral v₂ falloff. The data are found to be consistent with existing constituent quark scaling systematics.     

动量相关势对直接流和椭圆流的影响

利用极端相对论量子分子动力学(UrQMD)模型,研究了两种不同强度的动量相关势对中子、质子、氢同位素和带电荷粒子等四种粒子直接流和椭圆流的影响.计算结果表明,在不可压缩系数K0一定的情况下,直接流几乎不敏感于动量相关势的变化,而高动量粒子的椭圆流v2则敏感于高动量处动量相关势强度的大小及其动量依赖.考虑高动能区强度较强...     

Deconfinement transition: a three dimensional model

We present a three–dimensional model for quark matter with a density dependent quark–quark (confining) potential, which allows to describe a sort of deconfinement transition as the system evolves from a low density assembly of bound structures to a high density free Fermi gas of quarks. We consider different confining potentials, some of which successfully utilized in hadron spectroscopy. We find that a proper treatment of the many–body correlations induced by the medium is essential to disentangle the different nature of the two (hadronic and deconfined) phases of the system. For this purpose the ground state energy per particle and the pair correlation function are investigated. Received: 10 June 1998 / Revised version: 24 September 1998     

超相对论Au+Au碰撞中椭圆流的时间依赖

用相对论量子分子动力学(RQMD)模型模拟了质心系束能量为s_NN=200GeV的Au+Au非对心碰撞, 研究了椭圆流对末态粒子冻出时间的关系. 研究了在不同的阶段, 椭圆流对末态粒子位置的关系. 结果表明椭圆流随冻出时间的单调递减, 椭圆流对横向半径的关系随冻出时间发生变化. 用压力梯度对所得结果进行了分析. 径向速度用来表征压力梯度.     

Hadron Multiplicities in Pb＋Pb Collisions at the Large Hadron Collider and Pomeron Loop Effects

We study the pseudo-rapidity distribution of hadron multiplicities of high energy Pb＋Pb collisions by using color glass condensate dynamics at LHC/ALICE in the fixed coupling case. It is found that after including the pomeron loop effects the charged hadron multiplicities at central rapidity are about 1500 for central Pb＋Pb collisions, which are significantly smaller than the saturation based calculations, ～ 1700 ÷ 2500 and compatible with that based on a study of multiplicities in the fragmentation region.     

Some implications of the quark model for high energy scattering

The expressions for total scattering cross sections obtained from the quark model are expressed in a simple form which shows the dependence of the results on the assumptions. The results are shown to depend only on the value of six constants or “charges” defined for each hadron and to be otherwise independent of the structure. Any model which gives the same values of these charges gives the same result as the quark model. In particular, the results for processes which have odd signature t-channel quantum numbers hold in a quark model even with arbitrary mixtures of additional quarkantiquark pairs in the hadron wave function, provided that B, Y, and I are conserved.     

The phase transition to the quark-gluon plasma and its effect on hydrodynamic flow

It is shown that in ideal relativistic hydrodynamics a phase transition from hadron to quark and gluon degrees of freedom in the nuclear matter equation of state leads to a minimum in the excitation function of the transverse collective flow.     

Universal scaling of the elliptic flow data at RHIC

Recent PHOBOS measurements of the excitation function for the pseudo-rapidity dependence of the elliptic flow in Au + Au collisions at RHIC have posed a significant theoretical challenge. Here we show that these differential measurements, as well as the RHIC measurements on transverse momentum satisfy a universal scaling relation predicted by the Buda-Lund model, based on exact solutions of perfect fluid hydrodynamics. We also show that the recently found transverse kinetic energy scaling of the elliptic flow is a special case of this universal scaling.     

Understanding of radial and elliptic expansion with quark number scaling and blast wave model in 200 GeV Au+Au at RHIC-PHENIX

Measurement of azimuthal anisotropy is one of the most important study because of its relation to the initial stage. Especially, the elliptical anisotropy which is measured as the second coefficient of Fourier expansion of particle azimuthal distribution is believed to carry the information about the initial geometrical anisotropy. It seems the identified hadron v ₂ depends on the number of quark contents of the hadron. The experimental result of quark number scaling of v ₂ suggests quark level collectivity in the hot dense matter and quark coalescence mechanism to form hadron from quark matter via quark-gluon phase transition. The measured v ₂ and p _T spectra are analyzed with various assumptions based on the blast wave model in order to understand the freeze-out temperature and collective flow after the system expansion.     

强子作为非拓扑孤粒子的SU（5）大统—模型（Ⅰ）

提出一种新的包含三代已知轻子与夸克的ＳＵ（５）大统—模型．按本模型，强子可看作由夸克形成的非拓扑孤粒子；轻子与夸克本质上是相同的，它们之间的差别是由对称性自发破缺造成的；在强子内部，夸克质量很小，其性质与已知夸克相同；在强子外部，夸克的性质与已知轻子相同，只是质量很重，并将很快衰变．本文除了定义严格守恒的电荷Ｑ０、费米子数Ｆ０外，还在孤粒子内部定义了近似守恒的内色荷、内电荷、内费米子数．已知ＳＵ（５）大统—模型的（Ｌ－Ｂ）守恒相应于本模型的Ｆ０守恒。