300 research outputs found

    The Cluster Expansion for the Self-Gravitating gas and the Thermodynamic Limit

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    We develop the cluster expansion and the Mayer expansion for the self-gravitating thermal gas and prove the existence and stability of the thermodynamic limit N, V to infty with N/V^{1/3} fixed. The essential (dimensionless) variable is here eta = [G m^2 N]/[V^{1/3} T] (which is kept fixed in the thermodynamic limit). We succeed in this way to obtain the expansion of the grand canonical partition function in powers of the fugacity. The corresponding cluster coefficients behave in the thermodynamic limit as [eta/N]^{j-1} c_j where c_j are pure numbers. They are expressed as integrals associated to tree cluster diagrams. A bilinear recurrence relation for the coefficients c_j is obtained from the mean field equations in the Abel form. In this way the large j behaviour of the c_j is calculated. This large j behaviour provides the position of the nearest singularity which corresponds to the critical point (collapse) of the self-gravitating gas in the grand canonical ensemble. Finally, we discuss why other attempts to define a thermodynamic limit for the self-gravitating gas fail.Comment: LaTex 12 pages, 1 figure .p

    Stability of the Scalar Potential and Symmetry Breaking in the Economical 3-3-1 Model

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    A detailed study of the criteria for stability of the scalar potential and the proper electroweak symmetry breaking pattern in the economical 3-3-1 model, is presented. For the analysis we use, and improve, a method previously developed to study the scalar potential in the two-Higgs-doublet extension of the standard model. A new theorem related to the stability of the potential is stated. As a consequence of this study, the consistency of the economical 3-3-1 model emerges.Comment: to be published in EPJ C, 13 page

    Role of Sterile Neutrino Warm Dark Matter in Rhenium and Tritium Beta Decays

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    Sterile neutrinos with mass in the range of one to a few keV are important as extensions of the Standard Model of particle physics and are serious dark matter (DM) candidates. This DM mass scale (warm DM) is in agreement with both cosmological and galactic observations. We study the role of a keV sterile neutrino through its mixing with a light active neutrino in Rhenium 187 and Tritium beta decays. We pinpoint the energy spectrum of the beta particle, 0 < T_e < (Q_{beta} - m_s), as the region where a sterile neutrino could be detected and where its mass m_s could be measured. This energy region is at least 1 keV away rom the region suitable to measure the mass of the light active neutrino, located near the endpoint Q_{beta} . The emission of a keV sterile neutrino in a beta decay could show up as a small kink in the spectrum of the emitted beta particle. With this in view, we perform a careful calculation of the Rhenium and Tritium beta spectra and estimate the size of this perturbation by means of the dimensionless ratio R of the sterile neutrino to the active neutrino contributions. We comment on the possibility of searching for sterile neutrino signatures in two experiments which are currently running at present, MARE and KATRIN, focused on the Rhenium 187 and Tritium beta decays respectively.Comment: 16 pages, 10 figures. Version to appear in Nucl. Phys. B. Results and conclusions unchange

    Kaon Production and Kaon to Pion Ratio in Au+Au Collisions at \snn=130 GeV

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    Mid-rapidity transverse mass spectra and multiplicity densities of charged and neutral kaons are reported for Au+Au collisions at \snn=130 GeV at RHIC. The spectra are exponential in transverse mass, with an inverse slope of about 280 MeV in central collisions. The multiplicity densities for these particles scale with the negative hadron pseudo-rapidity density. The charged kaon to pion ratios are K+/π=0.161±0.002(stat)±0.024(syst)K^+/\pi^- = 0.161 \pm 0.002 {\rm (stat)} \pm 0.024 {\rm (syst)} and K/π=0.146±0.002(stat)±0.022(syst)K^-/\pi^- = 0.146 \pm 0.002 {\rm (stat)} \pm 0.022 {\rm (syst)} for the most central collisions. The K+/πK^+/\pi^- ratio is lower than the same ratio observed at the SPS while the K/πK^-/\pi^- is higher than the SPS result. Both ratios are enhanced by about 50% relative to p+p and pˉ\bar{\rm p}+p collision data at similar energies.Comment: 6 pages, 3 figures, 1 tabl

    Evolution of the differential transverse momentum correlation function with centrality in Au+Au collisions at sNN=200\sqrt{s_{NN}} = 200 GeV

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    We present first measurements of the evolution of the differential transverse momentum correlation function, {\it C}, with collision centrality in Au+Au interactions at sNN=200\sqrt{s_{NN}} = 200 GeV. {\it C} exhibits a strong dependence on collision centrality that is qualitatively similar to that of number correlations previously reported. We use the observed longitudinal broadening of the near-side peak of {\it C} with increasing centrality to estimate the ratio of the shear viscosity to entropy density, η/s\eta/s, of the matter formed in central Au+Au interactions. We obtain an upper limit estimate of η/s\eta/s that suggests that the produced medium has a small viscosity per unit entropy.Comment: 7 pages, 4 figures, STAR paper published in Phys. Lett.

    Phi meson production in Au+Au and p+p collisions at sqrt (s)=200 GeV

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    We report the STAR measurement of Phi meson production in Au+Au and p+p collisions at sqrt (s)=200 GeV. Using the event mixing technique, the Phi spectra and yields are obtained at mid-rapidity for five centrality bins in Au+Au collisions and for non-singly-diffractive p+p collisions. It is found that the Phi transverse momentum distributions from Au+Au collisions are better fitted with a single-exponential while the p+p spectrum is better described by a double-exponential distribution. The measured nuclear modification factors indicate that Phi production in central Au+Au collisions is suppressed relative to peripheral collisions when scaled by the number of binary collisions. The systematics of versus centrality and the constant Phi/K- ratio versus beam species, centrality, and collision energy rule out kaon coalescence as the dominant mechanism for Phi production.Comment: 6 pages, 3 figures, submitted to Phys. Rev. Let

    Longitudinal scaling property of the charge balance function in Au + Au collisions at 200 GeV

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    We present measurements of the charge balance function, from the charged particles, for diverse pseudorapidity and transverse momentum ranges in Au + Au collisions at 200 GeV using the STAR detector at RHIC. We observe that the balance function is boost-invariant within the pseudorapidity coverage [-1.3, 1.3]. The balance function properly scaled by the width of the observed pseudorapidity window does not depend on the position or size of the pseudorapidity window. This scaling property also holds for particles in different transverse momentum ranges. In addition, we find that the width of the balance function decreases monotonically with increasing transverse momentum for all centrality classes.Comment: 6 pages, 3 figure

    Energy and system size dependence of \phi meson production in Cu+Cu and Au+Au collisions

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    We study the beam-energy and system-size dependence of \phi meson production (using the hadronic decay mode \phi -- K+K-) by comparing the new results from Cu+Cu collisions and previously reported Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented are from mid-rapidity (|y|<0.5) for 0.4 < pT < 5 GeV/c. At a given beam energy, the transverse momentum distributions for \phi mesons are observed to be similar in yield and shape for Cu+Cu and Au+Au colliding systems with similar average numbers of participating nucleons. The \phi meson yields in nucleus-nucleus collisions, normalised by the average number of participating nucleons, are found to be enhanced relative to those from p+p collisions with a different trend compared to strange baryons. The enhancement for \phi mesons is observed to be higher at \sqrt{s_NN} = 200 GeV compared to 62.4 GeV. These observations for the produced \phi(s\bar{s}) mesons clearly suggest that, at these collision energies, the source of enhancement of strange hadrons is related to the formation of a dense partonic medium in high energy nucleus-nucleus collisions and cannot be alone due to canonical suppression of their production in smaller systems.Comment: 20 pages and 5 figure
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