73 research outputs found

    Statistical Properties of the Linear Sigma Model

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    The statistical equilibrium properties of the linear sigma model are studied, with a view towards characterizing the field configurations employed as initial conditions for numerical simulations of the formation of disoriented chiral condensates in high-energy nuclear collisions. The field is decomposed into its spatial average (the order parameter) and the fluctuations (the quasi- particles) and enclosed in a rectangular box with periodic boundary conditions. The quantized quasi-particle modes are described approximately by Klein-Gordon dispersion relations containing an effective mass that depends on both the temperature and the magnitude of the order parameter. The thermal fluctuations are instrumental in shaping the effective potential governing the order parameter, and the evolution of its statistical distribution with temperature is discussed, as is the behavior of the associated effective masses. As the system is cooled the field fluctuations subside, causing a smooth change from the high-temperature phase in which chiral symmetry is approximately restored towards the normal phase. Of practical interest is the fact that the equilibrium field configurations can be sampled in a simple manner, thus providing a convenient means for specifying the initial conditions in dynamical simulations of the non-equilibrium relaxation of the chiral field. The corresponding correlation function is briefly considered and used to calculate the spectral strength of radiated pions. Finally, by propagating samples of initial configurations by the exact equation of motion, it has been ascertained that the treatment is sufficiently accurate to be of practical utility.Comment: 42 pages total, incl 18 figs using pstricks ([email protected]

    Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

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    We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc
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