arXiv subjects

S. P. Klevansky

Publications and source records attributed to S. P. Klevansky.

46 records · Page 3Linked to original sources

arXiv1997

Developing Transport Theory to Study the Chiral Phase Transition

Chiral symmetry is an important aspect of QCD. Modelling this via the Nambu-Jona-Lasinio model, we construct a complete relativistic transport theory for quarks and mesons. The collision integral is analysed in a systematic 1/N_c approximation, and via this, it is shown that one can naturally incorporate mesonic degrees of freedom plus the hadronization of quarks and antiquarks into mesons into the field theoretic description. Time permitting, some simulation results, on the level of the Vlasov equation and also including collisions in a relaxation time approach, will be discussed.

hep-ph↗

arXiv1997

Confinement in the Coulomb Gauge Model

The Coulomb gauge model of QCD is studied with the introduction of a confining potential into the scalar part of the vector potential. Using a Green function formalism, we derive the self-energy for this model, which has both scalar and vector parts, $Σ^S(p)$ and $Σ^V(p)$. A rotation of these variables leads to the so-called gap and energy equations. We then analyse the divergence structure of these equations. As this depends explicitly on the form of potential, we give as examples both the linear plus Coulomb and quadratically confining potentials. The nature of the confining single particle Green function is investigated, and shown to be divergent due to the infrared singularities caused by the confining potential. Solutions to the gap equation for the simpler case of quadratic confinement are found both semi-analytically and numerically. At finite temperatures, the coupled set of equations are solved numerically in two decoupling approximations. Although chiral symmetry is found only to be exactly restored as $T\to\infty$, the chiral condensate displays a steep drop over a somewhat small temperature range.

hep-ph↗

arXiv1997

Developing Transport Theory to Systematically Include Mesons And Hadronization

Transport theory for the Nambu--Jona-Lasinio (NJL) model is examined. The collision term is investigated in a first approach in a coupling strength expansion. It can be demonstrated that this leads to a form easily recognized from the Boltzmann equation if the quasiparticle approximation is used. It is seen that enforcing a quasiparticle approximation suppresses the three body creation and annihilation processes that would otherwise be present. Including mesons and hadronization consistently in a $1/N_c$ expansion is discussed briefly. Some comments on the numerical simulation of the Vlasov equation and the relaxation time approximation to the collision term are made.

hep-ph↗

arXiv1996

Elastic Scattering and Transport Coefficients for a Quark Plasma in $SU_f(3)$ at Finite Temperatures

The temperature dependence of the elastic scattering processes $qq'\to qq'$ and $q\bar q'\to q\bar q'$, with $q, q' = u, d, s$ is studied as a function of the scattering angle and the center of mass energy of the collision within the framework of the $SU_f(3)$ Nambu--Jona--Lasinio model. Critical scattering at threshold is observed in the $q\bar q'\to q\bar q'$ process, leading to an enhancement of the cross section as occurs in the phenomenon of critical opalescence. Transport properties such as viscosity, mean free paths and thermal relaxation times are calculated. Strangeness enhancement is investigated via the chemical relaxation times, which are found to be considerably higher than those calculated via perturbative QCD. A comparison with the experimental values for the strangeness enhancement in $S+S$ collisions leads to an upper limit of 4~fm/$c$ for the lifetime of the plasma.

hep-ph↗

arXiv1995

One Loop Integrals at Finite Temperature and Density

The technique of decomposing Feynman diagrams at the one loop level into elementary integrals is generalized to the imaginary time Matsubara formalism. The three lowest integrals, containing one, two and three fermion lines, are provided in a form that separates out the real and imaginary parts of these complex functions, according to the input arguments, in a fashion that is suitable for numerical evaluation. The forms given can be evaluated for arbitrary values of temperature, particle mass, particle momenta and chemical potential.

hep-ph↗

arXiv1995

Hadronization in the SU(3) Nambu-Jona-Lasinio Model

The hadronization process for quarks combining into two mesons, q\bar q\to MM' at temperature T is described within the SU(3) Nambu- Jona-Lasinio model with finite current quark masses. Invariant matrix elements, cross-sections and transition rates are calculated to leading order in a 1/N_c expansion. Four independent classes, u\bar d, u\bar s, u\bar u and s\bar s\to hadrons are analysed, and the yield is found to be dominated by pion production. Threshold behaviour is determined by the exothermic or endothermic nature of the processes constituting the hadronization class. A strong suppression of transition rates is found at the pionic Mott temperature T_{Mπ}=212 MeV, at which the pion becomes a resonant state. The mean time for hadronization is calculated to be 2-4 fm/c near the Mott temperature. The calculation of strangeness changing processes indicates that hadronization accounts for a 1% increase in the absolute value of the kaon to pion ratio at T=150 MeV.

hep-ph↗

arXiv1995

CHIRALLY INVARIANT TRANSPORT EQUATIONS FOR QUARK MATTER

Transport equations for quark matter are derived in the mean field approximation for the Nambu -- Jona-Lasinio Lagrangian. Emphasis is put on the chiral limit (zero current quark masses) and the consequences of the chiral symmetry are investigated in detail. Our approach is based on the spinor decomposition of the Wigner function. Kinetic equations for the quark densities and for the spin are derived. We find that the latter is constrained by the requirement of the axial current conservation.

hep-ph↗

arXiv1995

$λϕ^{4}$ non equilibrium dynamics and kinetic field theory

Off-shellness and inhomogeneities are in the non-equilibrium dynamics of the lambda phi^4 model are studied using the closed timepath formalism reformulated as kinetic field theory. We take into account initial correlations up to the 4-point functions. The model is shown to exhibit a SO(1,1) symmetry broken by interactions and initial conditions. The divergence of the corresponding Noethercurrent is calculated and the Ward-Takahashi relations for the broken symmetry are given. They constitute a set of generalized integrated kinetic equations for the general n-point functions. We demonstrate that energy-momentum conservation follows from the transport equations. As an application we discuss inhomogeneities and general non-equilibrium conditions in the free field model. In our solution we identify the casimir-effect.

hep-th↗

arXiv1994

Pi-Pi scattering lengths at finite temperature

The $s$-wave $π-π$ scattering lengths $a^I(T)$ at finite temperature $T$ and isospin $I=0,2$ are calculated within the SU(2) Nambu--Jona-Lasinio model. $a^2(T)$ displays a singularity at the Mott temperature $T_M$, defined as $m_π(T_M) = 2m_q(T_M)$, while $a^0(T)$ is singular in addition at the lower temperature $T_d$, where $m_σ(T_d) = 2m_π(T_d)$, $m_σ$ and $m_π$ being the masses of the $σ$ and $π$ mesons, respectively. Numerically we find $T_d = 198$MeV and $T_M=215$MeV. We speculate on possible experimental consequences.

hep-ph↗

arXiv1994

Hadronization cross--sections at the chiral phase transition of a quark plasma

Hadronization at finite temperature $T$ is discussed in the framework of the Nambu--Jona-Lasinio model. The differential cross-section for the conversion of a quark--antiquark pair into two pions to first order in a $1/N_c$ expansion is calculated as a function of the c.m.~energy $s$ and temperature $T$. In particular, approaching the temperature $T_c$ of the chiral phase transition, the hadronization cross-section diverges like $\ln |1-{T\over T_c}|$.

hep-ph↗