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P. J. Ellis

Publications and source records attributed to P. J. Ellis.

At least 19 recordsLinked to original sources
arXiv2004

Model Calculation of Effective Three-Body Forces

We propose a scheme for extracting an effective three-body interaction originating from a two-nucleon interaction. This is based on the Q-box method of Kuo and collaborators, where folded diagrams are obtained by differentiating a sum of non-folded diagrams with respect to the starting energy. To gain insight we have studied several examples using the Lipkin model where the perturbative approach can be compared with exact results. Numerically the three-body interactions can be significant and in a matrix example good accuracy was not obtained simultaneously for both eigenvalues with two-body interactions alone.

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arXiv2004

Role of Fluctuations in the Linear Sigma Model with Quarks

We study the thermodynamics of the linear sigma model with constituent quarks beyond the mean-field approximation. By integrating out the quark degrees of freedom we derive an effective action for the meson fields which is then linearized around the ground state including field fluctuations. We propose a new method for performing exact averaging of complicated functions over the meson field fluctuations. Both thermal and zero-point fluctuations are considered. The chiral condensate and the effective meson masses are determined self-consistently in a rigorous thermodynamic framework. At zero chemical potential the model predicts a chiral crossover transition which separates two distinct regimes: heavy quarks and light pions at low temperatures, but light quarks and heavy mesons at high temperatures. The crossover becomes a first order phase transition if the vacuum pion mass is reduced from its physical value.

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arXiv2004

Properties of the $ω$ Meson at Finite Temperature and Density

The mass shift, width broadening, and spectral density for the $ω$ meson in a heat bath of nucleons and pions is calculated using a general formula which relates the self-energy to the forward scattering amplitude. We use experimental data to saturate the scattering amplitude at low energies with resonances and include a background Pomeron term, while at high energies a Regge parameterization is used. The peak of the spectral density is little shifted from its vacuum position, but the width is considerably increased due to collisional broadening. At normal nuclear matter density and a temperature of 150 MeV the spectral density of the $ω$ meson has a width of 140 MeV. Zero temperature nuclear matter is also discussed.

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arXiv2002

Quark color superconductivity and the cooling of compact stars

The thermal conductivity of the color-flavor locked phase of dense quark matter is calculated. The dominant contribution to the conductivity comes from photons and Nambu-Goldstone bosons associated with the breaking of baryon number, both of which are trapped in the quark core. Because of their very large mean free path the conductivity is also very large. The cooling of the quark core arises mostly from the heat flux across the surface of direct contact with the nuclear matter. As the thermal conductivity of the neighboring layer is also high, the whole interior of the star should be nearly isothermal. Our results imply that the cooling time of compact stars with color-flavor locked quark cores is similar to that of ordinary neutron stars.

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arXiv2002

Dileptons and Photons from Coarse-Grained Microscopic Dynamics and Hydrodynamics Compared to Experimental Data

Radiation of dileptons and photons from high energy nuclear collisions provides information on the space-time evolution of the hot dense matter produced therein. We compute this radiation using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton and photon emission rates from perturbative QCD and from experimentally-based hadronic calculations are used. Comparisons are made to data on central Pb-Pb and Pb-Au collisions taken at the CERN SPS at a beam energy of 158 A GeV. Both hydrodynamics and UrQMD provide very good descriptions of the photon transverse momentum spectrum measured between 1 and 4 GeV, but slightly underestimate the low mass spectrum of e+e- pairs, even with greatly broadened rho and omega vector mesons. Predictions are given for the transverse momentum distribution of dileptons.

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arXiv2001

Properties of $ρ$ and $ω$ Mesons at Finite Temperature and Density as Inferred from Experiment

The mass shift, width broadening, and spectral density for the $ρ$ and $ω$ mesons in a heat bath of nucleons and pions are calculated using a general formula which relates the self-energy to the real and imaginary parts of the forward scattering amplitude. We use experimental data to saturate the scattering amplitude at low energies with resonances and include a background Pomeron term, while at high energies a Regge parameterization is used. The real part obtained directly is compared with the result of a dispersion integral over the imaginary part. The peaks of the spectral densities are little shifted from their vacuum positions, but the widths are considerably increased due to collisional broadening. Where possible we compare with the UrQMD model and find quite good agreement. At normal nuclear matter density and a temperature of 150 MeV the spectral density of the $ρ$ meson has a width of 345 MeV, while that for the $ω$ is in the range 90--150 MeV.

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arXiv2000

$π-N$ from an Extended Effective Field Theory

Third order chiral perturbation theory accounts for the $π-N$ scattering phase shift data out to energies slightly below the position of the $Δ$ resonance. The low energy constants are not accurately determined. Explicit inclusion of the $Δ$ field is favored.

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arXiv2000

Kaon Condensation in Proto-Neutron Star Matter

We study the equation of state (EOS) of kaon-condensed matter including the effects of temperature and trapped neutrinos. It is found that the order of the phase transition to a kaon-condensed phase, and whether or not Gibbs' rules for phase equilibrium can be satisfied in the case of a first order transition, depend sensitively on the choice of the kaon-nucleon interaction. The main effect of finite temperature, for any value of the lepton fraction, is to mute the effects of a first order transition, so that the thermodynamics becomes similar to that of a second order transition. Above a critical temperature, found to be at least 30--60 MeV depending upon the interaction, the first order transition disappears. The phase boundaries in baryon density versus lepton number and baryon density versus temperature planes are delineated. We find that the thermal effects on the maximum gravitational mass of neutron stars are as important as the effects of trapped neutrinos, in contrast to previously studied cases in which the matter contained only nucleons or in which hyperons and/or quark matter were considered. Kaon-condensed EOSs permit the existence of metastable neutron stars, because the maximum mass of an initially hot, lepton-rich protoneutron star is greater than that of a cold, deleptonized neutron star. The large thermal effects imply that a metastable protoneutron star's collapse to a black hole could occur much later than in previously studied cases that allow metastable configurations.

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arXiv2000

An Effective Model for Hot Gluodynamics

We consider an effective Lagrangian containing contributions from glueball and gluon degrees of freedom with a scale-invariant coupling between the two. The thermodynamic potential is calculated taking into account thermal fluctuations of both fields. The glueball mean field dominates at low temperature, while the high temperature phase is governed by low-mass gluon-like excitations. The model shows some similarities to the lattice results in the pure glue sector of QCD. In particular, it exhibits a strong first order phase transition at a critical temperature of approximately 265 MeV when reasonable parameters are taken.

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arXiv1999

Baryon Masses in Chiral Perturbation Theory with Infrared Regularization

The baryon masses are examined in SU(3) chiral perturbation theory to third order using the recently proposed infrared regularization scheme. Fourth order is estimated by evaluating the dominant diagram. With this regularization the magnitude of the loop integrals is reduced so that the convergence of the series appears to be better than in the heavy baryon approach.

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arXiv1997

An Effective Lagrangian with Broken Scale and Chiral Symmetry IV: Nucleons and Mesons at Finite Temperature

We study the finite temperature properties of an effective chiral Lagrangian which describes nuclear matter. Thermal fluctuations in both the nucleon and the meson fields are considered. The logarithmic and square root terms in the effective potential are evaluated by expansion and resummation with the result written in terms of the exponential integral and the error function, respectively. In the absence of explicit chiral symmetry breaking a phase transition restores the symmetry, but when the pion has a mass the transition is smooth. The nucleon and meson masses as a functions of density and temperature are discussed.

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arXiv1996

An Effective Lagrangian with Broken Scale and Chiral Symmetry III: Mesons at Finite Temperature

We investigate the finite temperature behavior of the meson sector of an effective Lagrangian which describes nuclear matter. A method is developed for evaluating the logarithmic terms in the effective potential which involves expansion and resummation; the result is written in terms of the exponential integral. In the absence of explicit chiral symmetry breaking, a phase transition restores the symmetry at a temperature of 190 MeV; when the pion has a mass the transition is smooth. At a much higher temperature a first order phase transition restores scale symmetry.

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arXiv1996

Strangeness in Stellar Matter

A protoneutron star is formed immediately after the gravitational collapse of the core of a massive star. At birth, the hot and high density matter in such a star contains a large number of neutrinos trapped during collapse. Trapped neutrinos generally inhibit the presence of exotic matter -- hyperons, a kaon condensate, or quarks. However, as the neutrinos diffuse out in about 10-15 s, the threshold for the appearance of strangeness is reduced; hence, the composition and the structure of the star can change significantly. The effect of exotic, negatively-charged, strangeness-bearing components is always to soften the equation of state, and the possibility exists that the star collapses to a black hole at this time. This could explain why no neutron star has yet been seen in the remnant of supernova SN1987A, even though one certainly existed when neutrinos were detected on Feb. 23, 1987. With new generation neutrino detectors it is feasible to test different theoretical scenarios observationally.

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arXiv1996

Numerical Approximation to the Thermodynamic Integrals

We approximate boson thermodynamic integrals as polynomials in two variables chosen to give the correct limiting expansions and to smoothly interpolate into other regimes. With 10 free parameters, an accuracy of better than 0.009\% is achieved for the pressure, internal energy density and the number density. We also revisit the fermion case, originally addressed by Eggleton, Faulkner and Flannery (1973), and substantially improve the accuracy of their fits.

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arXiv1995

An Effective Lagrangian with Broken Scale and Chiral Symmetry II: Pion Phenomenology

We extend an effective Lagrangian embodying broken scale and chiral symmetry to include explicit chiral symmetry breaking and an additional chiral invariant term which allows for an axial coupling constant greater than unity. We also include a chiral Lagrangian for the isotriplet vector mesons which leads to a renormalization of the pion field. The properties of nuclear matter and nuclei, low energy $πN$ scattering and the behavior of quantities such as the pion mass and axial coupling at finite density are discussed.

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arXiv1995

Role of Hyperon Negative Energy Sea in Nuclear Matter

We have examined the contribution of the filled negative energy sea of hyperons to the energy/particle in nuclear matter at the one and two loop levels. While this has the potential to be significant, we find a strong cancellation between the one and two loop contributions for our chosen parameters so that hyperon effects can be justifiably neglected.

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