arXiv subjects

Michael Strickland

Publications and source records attributed to Michael Strickland.

At least 145 records · Page 8Linked to original sources

arXiv2013

Anisotropic Hydrodynamics for Rapidly Expanding Systems

We exactly solve the relaxation-time approximation Boltzmann equation for a system which is transversely homogeneous and undergoing boost-invariant longitudinal expansion. We compare the resulting exact numerical solution with approximate solutions available in the anisotropic hydrodynamics and second order viscous hydrodynamics frameworks. In all cases studied, we find that the anisotropic hydrodynamics framework is a better approximation to the exact solution than traditional viscous hydrodynamical approaches.

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arXiv2013

Charmonia and Bottomonia in a Magnetic Field

We study the effect of a static homogeneous external magnetic field on charmonium and bottomonium states. In an external magnetic field, quarkonium states do not have a conserved center-of-mass momentum. Instead there is a new conserved quantity called the pseudomomentum which takes into account the Lorentz force on the particles in the system. When written in terms of the pseudomomentum, the internal and center-of-mass motions do not decouple and, as a result, the properties of quarkonia depend on the states' center-of-mass momentum. We analyze the behavior of heavy particle-antiparticle pairs subject to an external magnetic field assuming a three dimensional harmonic potential and Cornell potential plus spin-spin interaction. In the case of the Cornell potential, we also take into account the mixing of the eta_c and J/psi states and eta_b and Upsilon states due to the background magnetic field. We then numerically calculate the dependence of the masses and mixing fractions on the magnitude of the background magnetic field and center-of-mass momentum of the state.

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arXiv2013

Testing viscous and anisotropic hydrodynamics in an exactly solvable case

We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying different non-equilibrium cases and comparing the exact kinetic-theory results to the second-order viscous hydrodynamics results we find that recent formulations of second-order viscous hydrodynamics agree better with the exact solution than the standard Israel-Stewart approach. Additionally, we find that, given the appropriate connection between the kinetic and anisotropic hydrodynamics relaxation times, anisotropic hydrodynamics provides a very good approximation to the exact relaxation time approximation solution.

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arXiv2013

Quark Number Susceptibilities from Two-Loop Hard Thermal Loop Perturbation Theory

We use the recently obtained two-loop hard thermal loop perturbation theory thermodynamics functions of a plasma of quarks and gluons to compute the diagonal second- and fourth-order quark number susceptibilities. The two-loop hard thermal loop perturbation theory thermodynamic functions used are reliable in the limit that the ratio of the quark chemical potential to temperature is small. Using this result, we are able to obtain (semi-)analytic expressions for the quark number susceptibilities at leading- and next-to-leading-order in hard thermal loop perturbation theory. We compare the hard thermal loop perturbation theory results with perturbative quantum chromodynamics calculations, a Polyakov-loop Nambu-Jona-Lasinio model calculation, and lattice quantum chromodynamics results.

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arXiv2013

Bulk Properties of a Fermi Gas in a Magnetic Field

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulae appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations, Omega = - P_parallel and P_perp = P_parallel - M B, with M = - d Omega/d B being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.

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arXiv2013

Two-loop HTL pressure at finite temperature and chemical potential

We calculate the two-loop pressure of a plasma of quarks and gluons at finite temperature and chemical potential using the hard thermal loop perturbation theory (HTLpt) reorganization of finite temperature/density quantum chromodynamics. The computation utilizes a high temperature expansion through fourth order in the ratio of the chemical potential to temperature. This allows us to reliably access the region of high temperature and small chemical potential. We compare our final result for the two-loop HTLpt pressure at finite temperature and chemical potential with perturbative quantum chromodynamics (QCD) calculations and available lattice QCD results.

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arXiv2013

Hydrodynamics of anisotropic quark and gluon fluids

The recently developed framework of anisotropic hydrodynamics is generalized to describe the dynamics of coupled quark and gluon fluids. The quark and gluon components of the fluids are characterized by different dynamical anisotropy parameters. The dynamical equations describing such mixtures are derived from kinetic theory with the collisional kernel treated in the relaxation- time approximation allowing for different relaxation times for quarks and gluons. Baryon number conservation is enforced in the quark and anti-quark components of the fluid, but overall parton number non-conservation is allowed in the system. The resulting equations are solved numerically in the (0+1)-dimensional boost-invariant case at zero and finite baryon density.

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arXiv2013

Thermal Bottomonium Suppression

I discuss recent calculations of the thermal suppression of bottomonium states in relativistic heavy ion collisions. I present results for the inclusive Upsilon(1s) and Upsilon(2s) suppression as a function of centrality. I compare with recent preliminary CMS data available at central rapidities and make predictions at forward rapidities which are within the acceptance of the ALICE dimuon spectrometer.

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arXiv2013

The chromo-Weibel instability in an expanding background

In this proceedings contribution we review recent calculations of the dynamics of the chromo-Weibel instability in the quark gluon plasma. This instability is present in gauge theories with a one-particle distribution function which is momentum-space anisotropic in the local rest frame. The conditions necessary for triggering this instability can be present already in the color-glass-condensate initial state or dynamically generated by the rapid longitudinal expansion of the matter created in a heavy-ion collision. Using the hard-loop framework we study the case that the one-particle distribution function possesses an arbitrary initial momentum anisotropy that increases in time due to longitudinal free streaming. The resulting three-dimensional dynamical equations for the chromofield evolution are solved numerically. We find that there is regeneration of the longitudinal pressure due to unstable plasma modes; nevertheless, the system seems to maintain a high-degree of momentum-space anisotropy. Despite this anisotropy, we find that there is rapid longitudinal thermalization of the plasma due to the non-linear mode couplings inherent in the unstable evolution.

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arXiv2013

Quarkonia in the Quark Gluon Plasma

In this paper we review recent progress towards understanding the nature of quarkonia in the quark-gluon plasma. We review the theory necessary to understand the melting of bound states due to color-screening, including lattice results for the heavy quark potential, lattice results on the correlation functions related to the relevant spectral functions, and the emergence of a complex-valued potential in high-temperature quantum chromodynamics. We close with a brief survey of phenomenological models of quarkonium suppression in relativistic heavy ion collisions.

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arXiv2013

Anisotropic hydrodynamics -- basic concepts

Due to the rapid longitudinal expansion of the quark-gluon plasma created in relativistic heavy ion collisions, potentially large local rest frame momentum-space anisotropies are generated. The magnitude of these momentum-space anisotropies can be so large as to violate the central assumption of canonical viscous hydrodynamical treatments which linearize around an isotropic background. In order to better describe the early-time dynamics of the quark gluon plasma, one can consider instead expanding around a locally anisotropic background which results in a dynamical framework called anisotropic hydrodynamics. In this proceedings contribution we review the basic concepts of the anisotropic hydrodynamics framework presenting viewpoints from both the phenomenological and microscopic points of view.

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arXiv2013

Longitudinal thermalization via the chromo-Weibel instability

Non-Abelian plasma instabilities play an important role in the non-equilibrium dynamics of a weakly coupled quark-gluon plasma. Using the discretized hard loop framework we calculate the time evolution of soft gluonic fields in a longitudinally free streaming background. Extrapolating our results to energies probed in relativistic heavy-ion collisions we find a pressure anisotropy that persists for a few fm/c. However, the chromofields quickly develop a Boltzmann longitudi- nal energy spectrum, suggesting fast longitudinal thermalization of the quark gluon plasma even though it remains momentum-space anisotropic. In this proceedings contribution we review our recent numerical results, present new results for the scaling of the isotropization time with the initial current fluctuation amplitude, and present tests of the gauge invariance of the extracted longitudinal spectra.

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arXiv2012

Instabilities of an anisotropically expanding non-Abelian plasma: 3D+3V discretized hard-loop simulations

We study the (3+1)-dimensional evolution of non-Abelian plasma instabilities in the presence of a longitudinally expanding background of hard particles using the discretized hard loop framework. The free streaming background dynamically generates a momentum-space anisotropic distribution which is unstable to the rapid growth of chromomagnetic and chromoelectric fields. These fields produce longitudinal pressure that works to isotropize the system. Extrapolating our results to energies probed in ultrarelativistic heavy-ion collisions we find, however, that a pressure anisotropy persists for a few fm/c. In addition, on time scales relevant to heavy-ion collisions we observe continued growth of plasma instabilities in the strongly non-Abelian regime. Finally, we find that the longitudinal energy spectrum is well-described by a Boltzmann distribution with increasing temperature at intermediate time scales.

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arXiv2012

Bottomonia in the Quark Gluon Plasma

I review recent calculations of the suppression of bottomonium states in heavy ion collisions. A non-relativistic potential is used which is complex valued. This allows one to extract the binding energies and decay widths of the ground and excited states of bottomonium as a function of the typical plasma particle momentum and momentum-space anisotropy. The decay widths determined are used as input and integrated over space-time taking into account the dynamical evolution of the typical particle momentum and momentum-space anisotropy. The suppression of Upsilon(1s), Upsilon(2s), Upsilon(3s), chi_b1, and chi_b2 is obtained as a function of centrality, rapidity, and transverse momentum. The obtained results are compared with data from the STAR and CMS collaborations.

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arXiv2012

Highly anisotropic dissipative hydrodynamics

The quark gluon plasma generated in ultrarelativistic heavy ion collisions may possess sizable momentum-space anisotropies that cause the longitudinal and transverse pressures in the local rest frame to be significantly different. We review recent attempts to derive a dynamical framework that can reliably describe systems that possess a high degree of momentum-space anisotropy. The dynamical framework that has been developed can describe the evolution of the quark gluon plasma ranging from the longitudinal free-streaming limit to the ideal hydrodynamical limit.

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arXiv2012

Chromoelectric oscillations in a dynamically evolving anisotropic background

We study the oscillations of a uniform longitudinal chromoelectric field in a dynamically-evolving momentum-space anisotropic background in the weak field limit. Evolution equations for the background are derived by taking moments of the Boltzmann equation in two cases: (i) a fixed relaxation time and (ii) a relaxation time that is proportional to the local inverse transverse momentum scale of the plasma. The second case allows us to reproduce 2nd-order viscous hydrodynamical dynamics in the limit of small shear viscosity to entropy ratio. We then linearize the Boltzmann-Vlasov equation in a dynamically-evolving background and obtain an integro-differential evolution equation for the chromoelectric field. We present numerical solutions to this integro-differential equation for a variety of different initial conditions and shear viscosity to entropy density ratios. The dynamical equations obtained are novel in that they include a non-trivial time-dependent momentum-space anisotropic background and the effect of collisional damping for the first time.

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arXiv2012

Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)-dimensional boost invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte-Carlo Glauber initial conditions. For this purpose we have developed two numerical implementations: one which is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions; and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the lab-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity to entropy ratio, proper time, and impact parameter.

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arXiv2012

Thermal Bottomonium Suppression at RHIC and LHC

In this paper we consider the suppression of bottomonium states in ultrarelativistic heavy ion collisions. We compute the suppression as a function of centrality, rapidity, and transverse momentum for the states Upsilon(1s), Upsilon(2s), Upsilon(3s), chi_b1, and chi_b2. Using this information, we then compute the inclusive Upsilon(1s) suppression as a function of centrality, rapidity, and transverse momentum including feed down effects. Calculations are performed for both RHIC sqrt(s_NN)=200 GeV Au-Au collisions and LHC sqrt(s_NN)=2.76 TeV Pb-Pb collisions. From the comparison of our theoretical results with data available from the STAR and CMS Collaborations we are able to constrain the shear viscosity to entropy ratio to be in the range 0.08 < eta/S < 0.24. Our results are consistent with the creation of a high temperature quark-gluon plasma at both RHIC and LHC collision energies.

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