arXiv subjects

Michael Strickland

Publications and source records attributed to Michael Strickland.

At least 199 records · Page 11Linked to original sources

arXiv2005

Visualizing Color Plasma Instabilities

I discuss recent advances in the understanding of non-equilibrium gauge field dynamics in plasmas which have particle distributions which are locally anisotropic in momentum space. In contrast to locally isotropic plasmas such anisotropic plasmas have a spectrum of soft unstable modes which are characterized by exponential growth of transverse (chromo)-magnetic fields at short times. The long-time behavior of such instabilities depends on whether or not the gauge group is abelian or non-abelian. I will report on recent numerical simulations which attempt to determine the long-time behavior of an anisotropic non-abelian plasma within hard-loop effective theory. For novelty I will present an interesting method for visualizing the time-dependence of SU(2) gauge field configurations produced during our numerical simulations.

hep-ph↗

arXiv2005

Hard-loop dynamics of non-abelian plasma instabilities

I discuss recent advances in the understanding of non-equilibrium gauge field dynamics in plasmas which have particle distributions which are locally anisotropic in momentum space. In contrast to locally isotropic plasmas such anisotropic plasmas have a spectrum of soft unstable modes which are characterized by exponential growth of transverse (chromo)-magnetic fields at short times. The long-time behavior of such instabilities depends on whether or not the gauge group is abelian or non-abelian. Here I will report on recent numerical simulations which attempt to determine the long-time behavior of an anisotropic non-abelian plasma within hard-loop effective theory.

hep-ph↗

arXiv2005

Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation

Non-Abelian plasma instabilities have been proposed as a possible explanation for fast isotropization of the quark-gluon plasma produced in relativistic heavy-ion collisions. We study the real-time evolution of these instabilities in non-Abelian plasmas with a momentum-space anisotropy using a hard-loop effective theory that is discretized in the velocities of hard particles. We extend our previous results on the evolution of the most unstable modes, which are constant in directions transverse to the direction of anisotropy, from gauge group SU(2) to SU(3). We also present first full 3+1-dimensional simulation results based on velocity-discretized hard loops. In contrast to the effectively 1+1-dimensional transversely constant modes we find subexponential behaviour at late times.

hep-ph↗

arXiv2005

Hard-Loop Dynamics of Non-Abelian Plasma Instabilities

Non-Abelian plasma instabilities may be responsible for the fast apparent quark-gluon thermalization in relativistic heavy-ion collisions if their exponential growth is not hindered by nonlinearities. We study the real-time evolution of instabilities in an anisotropic non-Abelian plasma with an SU(2) gauge group in the hard-loop approximation. We find exponential growth of non-Abelian plasma instabilities both in the linear and in the strongly nonlinear regime, with only a brief phase of subexponential behavior in between.

hep-ph↗

arXiv2004

Progress in Anisotropic Plasma Physics

In 1959 Weibel demonstrated that when a QED plasma has a temperature anisotropy there exist unstable transverse magnetic excitations which grow exponentially fast. In this paper we will review how to determine the growth rates for these unstable modes in the weak-coupling and ultrarelativistic limits in which the collective behavior is describable in terms are so-called "hard-loops". We will show that in this limit QCD is subject to instabilities which are analogous to the Weibel instability in QED. The presence of such instabilities dominates the early time evolution of a highly anisotropic plasma; however, at longer times it is expected that these instabilities will saturate (condense). I will discuss how the presence of non-linear interactions between the gluons complicates the determination of the saturated state. In order to discuss this I present the generalization of the Braaten-Pisarski isotropic hard-thermal-loop effective action to a system with a temperature anisotropy in the parton distribution functions. The resulting hard-loop effective action can be used to determine the time and energy scales associated with the possible saturation (condensation) of the gluonic modes. We will also discuss the effects of anisotropies on observables, in particular on the heavy quark energy loss.

hep-ph↗

arXiv2004

Collisional Energy Loss of a Heavy Quark in an Anisotropic Quark-Gluon Plasma

We compute the leading-order collisional energy loss of a heavy quark propagating through a quark-gluon plasma in which the quark and gluon distributions are anisotropic in momentum space. Following the calculation outlined for QED in an earlier work we indicate the differences encountered in QCD and their effect on the collisional energy loss results. For a 20 GeV bottom quark we show that momentum space anisotropies can result in the collisional heavy quark energy loss varying with the angle of propagation by up to 50%. For low velocity quarks we show that anisotropies result in energy gain instead of energy loss with the energy gain focused in such a way as to accelerate particles along the anisotropy direction thereby reducing the momentum-space anisotropy. The origin of this negative energy loss is explicitly identified as being related to the presence of plasma instabilities in the system.

hep-ph↗

arXiv2004

Hard-Loop Effective Action for Anisotropic Plasmas

We generalize the hard-thermal-loop effective action of the equilibrium quark-gluon plasma to a non-equilibrium system which is space-time homogeneous but for which the parton momentum distribution is anisotropic. We show that the manifestly gauge-invariant Braaten-Pisarski form of the effective action can be straightforwardly generalized and we verify that it then generates all n-point functions following from collisionless gauge-covariant transport theory for a homogeneous anisotropic plasma. On the other hand, the Taylor-Wong form of the hard-thermal-loop effective action has a more complicated generalization to the anisotropic case. Already in the simplest case of anisotropic distribution functions, it involves an additional term that is gauge invariant by itself, but nontrivial also in the static limit.

hep-ph↗

arXiv2004

Three-loop Phi-derivable Approximation in QED

In this paper we examine Phi-derivable approximations in QED. General theorems tell us that the gauge dependence of the n-loop Phi-derivable approximation shows up at order g^(2n) where g is the coupling constant. We consider the gauge dependence of the two-loop Phi-derivable approximation to the Debye mass and show that it is of order e^4 as expected. We solve the three-loop Phi-derivable approximation in QED by expanding sum-integrals in powers of e^2 and m/T, where m is the Debye mass which satisfies a variational gap equation. The results for the pressure and the Debye mass are accurate to order e^5.

hep-ph↗

arXiv2004

Collective modes of an Anisotropic Quark-Gluon Plasma II

We continue our exploration of the collective modes of an anisotropic quark gluon plasma by extending our previous analysis to arbitrary Riemann sheets. We demonstrate that in the presence of momentum-space anisotropies in the parton distribution functions there are new relevant singularities on the neighboring unphysical sheets. We then show that for sufficiently strong anisotropies that these singularities move into the region of spacelike momentum and their effect can extend down to the physical sheet. In order to demonstrate this explicitly we consider the polarization tensor for gluons propagating parallel to the anisotropy direction. We derive analytic expressions for the gluon structure functions in this case and then analytically continue them to unphysical Riemann sheets. Using the resulting analytic continuations we numerically determine the position of the unphysical singularities. We then show that in the limit of infinite contraction of the distribution function along the anisotropy direction that the unphysical singularities move onto the physical sheet and result in real spacelike modes at large momenta for all "out-of-plane" angles of propagation.

hep-ph↗

arXiv2003

Collective Modes of an Anisotropic Quark-Gluon Plasma

We analyze the collective modes of high-temperature QCD in the case when there is an anisotropy in the momentum-space distribution function for the gluons. We perform a tensor decomposition of the gluon self-energy and solve the dispersion relations for both stable and unstable modes. Results are presented for a class of anisotropic distribution functions which can be obtained by stretching or squeezing an isotropic distribution function along one direction in momentum space. We find that there are three stable modes and either one or two unstable modes depending on whether the distribution function is stretched or squeezed. The presence of unstable modes which have exponential growth can lead to a more rapid thermalization and isotropization of the soft modes in a quark gluon plasma and therefore may play an important role in the dynamical evolution.

hep-ph↗

arXiv2003

Energy Loss of a Heavy Fermion in an Anisotropic QED Plasma

We compute the leading-order collisional energy loss of a heavy fermion propagating in a QED plasma with an electron distribution function which is anisotropic in momentum space. We show that in the presence of such anisotropies there can be a significant directional dependence of the heavy fermion energy loss with the effect being quite large for highly-relativistic velocities. We also repeat the analysis of the isotropic case more carefully and show that the final result depends on the intermediate scale used to separate hard and soft contributions to the energy loss. We then show that the canonical isotropic result is obtained in the weak-coupling limit. For intermediate-coupling we use the residual scale dependence as a measure of our theoretical uncertainty. We also discuss complications which could arise due to the presence of unstable soft photonic modes and demonstrate that the calculation of the energy loss is safe.

hep-ph↗

arXiv2003

Two-loop HTL Thermodynamics with Quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.

hep-ph↗

arXiv2002

The Equation of State for Dense QCD and Quark Stars

We calculate the equation of state for degenerate quark matter to leading order in hard-dense-loop (HDL) perturbation theory. We solve the Tolman-Oppenheimer-Volkov equations to obtain the mass-radius relation for dense quark stars. Both the perturbative QCD and the HDL equations of state have a large variation with respect to the renormalization scale for quark chemical potential below 1 GeV which leads to large theoretical uncertainties in the quark star mass-radius relation.

hep-ph↗

arXiv2002

HTL Perturbation Theory to Two Loops

We calculate the pressure for pure-glue QCD at high temperature to two-loop order using hard-thermal-loop (HTL) perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum energy density and the HTL mass parameter. We determine the HTL mass parameter by a variational prescription. The resulting predictions for the pressure fail to agree with results from lattice gauge theory at temperatures for which they are available.

hep-ph↗

arXiv2001

Mass Expansions of Screened Perturbation Theory

The thermodynamics of massless phi^4-theory is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the Lagrangian. We analytically calculate the pressure and entropy to three-loop order and the screening mass to two-loop order, expanding in powers of m/T. The truncated m/T-expansion results are compared with numerical SPT results for the pressure, entropy and screening mass which are accurate to all orders in m/T. It is shown that the m/T-expansion converges quickly and provides an accurate description of the thermodynamic functions for large values of the coupling constant.

hep-ph↗

arXiv2001

Screened Perturbation Theory to Three Loops

The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast to the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.

hep-ph↗

arXiv2000

Self-consistent renormalization group flow

A self-consistent renormalization group flow equation for the scalar lambda phi^4 theory is analyzed and compared with the local potential approximation. The two prescriptions coincide in the sharp cutoff limit but differ with a smooth cutoff. The dependence of the critical exponent nu on the smoothness parameter and the field of expansion is explored. An optimization scheme based on the minimum sensitivity principle is employed to ensure the most rapid convergence of nu with the level of polynomial truncation.

hep-th↗

arXiv2000

The Massive Thermal Basketball Diagram

The "basketball diagram" is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a phi^4 interaction to three-loop order.

hep-ph↗