Thermal quark production in ultra-relativistic nuclear collisions

We calculate thermal production of u, d, s, c and b quarks in ultra-relativistic heavy ion collisions. The following processes are taken into account: thermal gluon decay (g to ibar i), gluon fusion (g g to ibar i), and quark-antiquark annihilation (jbar j to ibar i), where i and j represent quark species. We use the thermal quark masses, $m_i^2(T)\simeq m_i^2 + (2g^2/9)T^2$, in all the rates. At small mass ($m_i(T)<2T$), the production is largely dominated by the thermal gluon decay channel. We obtain numerical and analytic solutions of one-dimensional hydrodynamic expansion of an initially pure glue plasma. Our results show that even in a quite optimistic scenario, all quarks are far from chemical equilibrium throughout the expansion. Thermal production of light quarks (u, d and s) is nearly independent of species. Heavy quark (c and b) production is quite independent of the transition temperature and could serve as a very good probe of the initial temperature. Thermal quark production measurements could also be used to determine the gluon damping rate, or equivalently the magnetic mass.Comment: 14 pages (latex) plus 6 figures (uuencoded postscript files); CERN-TH.7038/9

Gap equation in scalar field theory at finite temperature

We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde

Structure Functions of the Nucleon in a Statistical Model

Deep inelastic scattering is considered in a statistical model of the nucleon. This incorporates certain features which are absent in the standard parton model such as quantum statistical correlations which play a role in the propagation of particles when considering Feynman diagrams containing internal lines. The inclusion of the ${\cal O}(\alpha_{s})$ corrections in our numerical calculations allows a good fit to the data for $x\geq 0.25$. The fit corresponds to values of temperature and chemical potential of approximately $T=0.067$ GeV and $\mu=0.133$ GeV. The latter values of parameters, however, give rise, for all $x$, to a large value for $R=\sigma_{L}/\sigma_{T}$.Comment: 16 pages TeX, 11 figures available as Postscript files, University of Bielefeld preprint BI-TP 93/3

Two Loop Low Temperature Corrections to Electron Self Energy

We recalculate the two loop corrections in the background heat bath using real time formalism. The procedure of the integrations of loop momenta with dependence on finite temperature before the momenta without it, has been followed. We determine the mass and wavefunction renormalization constants in the low temperature limit of QED, for the first time with this preferred order of integrations. The correction to electron mass and spinors in this limit is important in the early universe at the time of primordial nucleosynthesis as well as in astrophysics.Comment: 8 pages and 1 figure to appear in Chinese Physics

Two mechanisms for the elimination of pinch singularities in out of equilibrium thermal field theories

We analyze ill-defined pinch singularities characteristic of out of equilibrium thermal field theories. We identify two mechanisms that eliminate pinching even at the single self-energy insertion approximation to the propagator: the first is based on the vanishing of phase space at the singular point (threshold effect). It is effective in QED with a massive electron and a massless photon. In massless QCD, this mechanism fails, but the pinches cancel owing to the second mechanism, i.e., owing to the spinor/tensor structure of the single self-energy insertion contribution to the propagator. The constraints imposed on distribution functions are very reasonable.Comment: 24 pages, Latex, no figures, revised version, many minor changes and correction

The heavy fermion damping rate puzzle

: We examine again the problem of the damping rate of a moving heavy fermion in a hot plasma within the resummed perturbative theory of Pisarski and Braaten. The ansatz for its evaluation which relates it to the imaginary part of the fermion propagator pole in the framework of a self-consistent approach is critically analyzed. As already pointed out by various authors, the only way to define the rate is through additional implementation of magnetic screening. We show in detail how the ansatz works in this case and where we disagree with other authors. We conclude that the self-consistent approach is not satisfactory.Comment: 17 page

Comments on two papers by Kapusta and Wong

We critically examine recently published results on the thermal production of massive vector bosons in a quark-gluon plasma. We claim the production rate is a collinear safe observable.Comment: 6 pages LATEX documen

Syros Metasomatic Tourmaline: Evidence for Very High-δ11B Fluids in Subduction Zones

High-pressure (HP) metamorphic blocks enclosed in a mafic to ultramafic matrix from a mélange on the island of Syros are rimmed by tourmaline-bearing reaction zones (blackwalls). The B isotopic composition of dravitic tourmaline within these blackwalls was investigated in situ by secondary ion mass spectrometry. Boron in these tourmalines is unusually heavy, with δ11B values exceeding +18‰ in all investigated samples and reaching an extreme value of +28·4‰ in one sample. Blackwalls formed during exhumation of the HP mélange at a depth of 20-25 km at temperatures of 400-430°C, by influx of external hydrous fluids. The compositions of the fluids are estimated to be in the range of 100-300 μg/g B with δ11B values of +18 to +28‰. The high δ11B values cannot be explained by tourmaline formation from unmodified slab-derived fluids. However, such fluids could interact with the material in the exhumation channel on their way from the dehydrating slab to the site of tourmaline formation in the blackwalls. This could produce exceptionally high δ11B values in the fluids, a case that is modelled in this study. The model demonstrates that subduction fluids may be effectively modified in both trace element and isotopic composition during their migration through the material overlying the subducting slab. Blackwall tourmaline from Syros has a large grain size (several centimetres), high abundance, and an exceptionally high δ11B value. The formation of tourmaline at the contact between mafic or felsic HP blocks and their ultramafic matrix involved fluids released during dehydration reactions in the subducting slab. It forms a heavy-boron reservoir in hybrid rocks overlying the subducting slab, and may, thus, have a significant impact on the geochemical cycle of B and its isotopes in subduction zone

Non-Invariant Ground States, Thermal Average, and generalized Fermionic Statistics

We present an approach to generalised fermionic statistics which relates the existence of a generalised statistical behaviour to non-invariant ground states. Considering the thermal average of an operatorial generalization of the Heisenberg algebra, we get an occupation number which depends on the degree of mixing between symmetric and antisymmetric sectors of the ground state. A natural prescription is given for the construction of a supersymmetric statistics. We also show that the structure of the vacuum, and therefore the statistical behaviour of the system, can be accounted for in terms of a second order phase transition.Comment: 11 pages, accepted in Physics Letters

On the imaginary parts and infrared divergences of two-loop vector boson self-energies in thermal QCD

We calculate the imaginary part of the retarded two-loop self-energy of a static vector boson in a plasma of quarks and gluons of temperature T, using the imaginary time formalism. We recombine various cuts of the self-energy to generate physical processes. We demonstrate how cuts containing loops may be reinterpreted in terms of interference between Order $\alpha$ tree diagrams and the Born term along with spectators from the medium. We apply our results to the rate of dilepton production in the limit of dilepton invariant mass E>>T. We find that all infrared and collinear singularities cancel in the final result obtained in this limit.Comment: references added, typos corrected, slightly abridged, version accepted for publication in Phys. Rev.