Two regularizations - two different models of Nambu-Jona-Lasinio

Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional cutoff and the model with dimensionally-analytical regularization -- are systematically compared. It is shown that they are, in essence, two different models of light-quark interaction. In the mean-field approximation the distinction becomes apparent in a behavior of scalar amplitude near the threshold. For 4-dimensional cutoff the pole term can be extracted, which corresponds to sigma-meson. For dimensionally-analytical regularization the singularity of the scalar amplitude is not pole, and this singularity is quite disappeared at some value of the regularization parameter. Still more essential distinction of these models exists in the next-to-leading order of mean-field expansion. The calculations of meson contributions in the quark chiral condensate and in the dynamical quark mass demonstrate, that these contributions though their relatively smallness can destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical regularization is stabilized with the next-to-leading order, i.e. the value of the regularization parameter shifts to the stability region, where these contributions decrease.Comment: 14 pages; Journal version; parameter fixing procedure is modifie

Modelling marine emissions and atmospheric distributions of halocarbons and dimethyl sulfide: the influence of prescribed water concentration vs. prescribed emissions

Marine-produced short-lived trace gases such as dibromomethane (CH2Br2), bromoform (CHBr3), methyliodide (CH3I) and dimethyl sulfide (DMS) significantly impact tropospheric and stratospheric chemistry. Describing their marine emissions in atmospheric chemistry models as accurately as possible is necessary to quantify their impact on ozone depletion and Earth's radiative budget. So far, marine emissions of trace gases have mainly been prescribed from emission climatologies, thus lacking the interaction between the actual state of the atmosphere and the ocean. Here we present simulations with the chemistry climate model EMAC (ECHAM5/MESSy Atmospheric Chemistry) with online calculation of emissions based on surface water concentrations, in contrast to directly prescribed emissions. Considering the actual state of the model atmosphere results in a concentration gradient consistent with model real-time conditions at the ocean surface and in the atmosphere, which determine the direction and magnitude of the computed flux. This method has a number of conceptual and practical benefits, as the modelled emission can respond consistently to changes in sea surface temperature, surface wind speed, sea ice cover and especially atmospheric mixing ratio. This online calculation could enhance, dampen or even invert the fluxes (i.e. deposition instead of emissions) of very short-lived substances (VSLS). We show that differences between prescribing emissions and prescribing concentrations (−28 % for CH2Br2 to +11 % for CHBr3) result mainly from consideration of the actual, time-varying state of the atmosphere. The absolute magnitude of the differences depends mainly on the surface ocean saturation of each particular gas. Comparison to observations from aircraft, ships and ground stations reveals that computing the air–sea flux interactively leads in most of the cases to more accurate atmospheric mixing ratios in the model compared to the computation from prescribed emissions. Calculating emissions online also enables effective testing of different air–sea transfer velocity (k) parameterizations, which was performed here for eight different parameterizations. The testing of these different k values is of special interest for DMS, as recently published parameterizations derived by direct flux measurements using eddy covariance measurements suggest decreasing k values at high wind speeds or a linear relationship with wind speed. Implementing these parameterizations reduces discrepancies in modelled DMS atmospheric mixing ratios and observations by a factor of 1.5 compared to parameterizations with a quadratic or cubic relationship to wind spee

The cryogenic system for the SLAC E158 experiment

E158 is a fixed target experiment at SLAC in which high energy (up to 48 GeV) polarized electrons are scattered off the unpolarized electrons in a 1.5 m long liquid hydrogen target. The total volume of liquid hydrogen in the system is 47.1. The beam can deposit as much as 700 W into the liquid hydrogen. Among the requirements for the system are: that density fluctuations in the liquid hydrogen be kept to a minimum, that the target can be moved out of the beam line while cold and replaced to within 2 mm and that the target survive lifetime radiation doses of up to 1×106 Gy. The cryogenic system for the experiment consists of the target itself, the cryostat containing the target, a refurbished CTI 4000 refrigerator providing more than 1 kW of cooling at 20 K and associated transfer lines and valve boxes. This paper discusses the requirements, design, construction, testing and operation of the cryogenic system. The unique features of the design associated with hydrogen safety and the high radiation field in which the target resides are also covered

Medium Modification of The Pion-Pion Interaction at Finite Density

We discuss medium modifications of the unitarized pion-pion interaction in the nuclear medium. We incorporate both the effects of chiral symmetry restoration and the influence of collective nuclear pionic modes originating from the p-wave coupling of the pion to delta-hole configurations. We show in particular that the dropping of the sigma meson mass significantly enhances the low energy structure created by the in-medium collective pionic modes.Comment: 26 pages, 7 figures included, Latex fil

Thermal and Nonthermal Pion Enhancements with Chiral Symmetry Restoration

The pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated in the framework of the Nambu-Jona-Lasinio model. The decay rate for the process sigma -> 2pion to the lowest order in a 1/N_c expansion is calculated as a function of temperature T and chemical potential mu. The thermal and nonthermal enhancements of pions generated by the decay before and after the freeze-out present only in the crossover region of the chiral symmetry transition. The strongest nonthermal enhancement is located in the vicinity of the endpoint of the first-order transition.Comment: Latex2e, 12 pages, 8 Postscript figures, submitted to Phys. Rev.

Quark exchange model for charmonium dissociation in hot hadronic matter

A diagrammatic approach to quark exchange processes in meson-meson scattering is applied to the case of inelastic reactions of the type (Q\barQ)+(q\barq)\rightarrow (Q\barq) + (q\barQ), where $Q$ and $q$ refer to heavy and light quarks, respectively. This string-flip process is discussed as a microscopic mechanism for charmonium dissociation (absorption) in hadronic matter. The cross section for the reaction $J/\psi + \pi \to D+ \bar D$ is calculated using a potential model, which is fitted to the meson mass spectrum. The temperature dependence of the relaxation time for the \J/Psi distribution in a homogeneous thermal pion gas is obtained. The use of charmonium for the diagnostics of the state of hot hadronic matter produced in ultrarelativistic nucleus-nucleus collisions is discussed.Comment: 24 pages, 3 tables, 7 figure

Effects of mesonic correlations in the QCD phase transition

The finite temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T_c the pressure is well described by the mean-field approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed.Comment: 11 pages, 4 figures; version accepted for publication in Yad. Fiz., text extended, 1 figure adde

Pion damping width from SU(2) x SU(2) NJL model

Within the framework of the NJL model, we investigate the modification of the pion damping width in a hot pion gas for temperatures ranging from 0 to 180 MeV. The pion is found to broaden noticeably at T > 60 MeV. Near the chiral phase transition T ~ 180 MeV, the pion width is saturated and amounts to 70 MeV. The main contribution to the width comes from pion-pion collisions. Other contributions are found negligibly small.Comment: LaTeX2e, 13 pages, 2 figure

1/N_c- expansion of the quark condensate at finite temperature

Previously the quark and meson properties in a many quark system at finite temperature have been studied within effective QCD approaches in the Hartree approximation. In the present paper we consider the influence of the mesonic correlations on the quark self-energy and on the quark propagator within a systematic $1/N_c$- expansion. Using a general separable ansatz for the nonlocal interaction, we derive a selfconsistent equation for the $1/N_c$ correction to the quark propagator. For a separable model with cut-off formfactor, we obtain a decrease of the condensate of the order of 20\% at zero temperature. A lowering the critical temperature for the onset of the chiral restoration transition due to the inclusion of mesonic correlations is obtained what seems to be closer to the results from lattice calculations.Comment: 19 pages, REVTeX, 5 figure

Chiral symmetry breaking in hot matter

This series of three lectures covers (a) a basic introduction to symmetry breaking in general and chiral symmetry breaking in QCD, (b) an overview of the present status of lattice data and the knowlegde that we have at finite temperature from chiral perturbation theory. (c) Results obtained from the Nambu--Jona-Lasinio model describing static mesonic properties are discussed as well as the bulk thermodynamic quantities. Divergences that are observed in the elastic quark-antiquark scattering cross-section, reminiscent of the phenomenon of critical opalescence in light scattering, is also discussed. (d) Finally, we deal with the realm of systems out of equilibrium, and examine the effects of a medium dependent condensate in a system of interacting quarks.Comment: 62 LaTex pages, incorporating 23 figures. Lectures given at the eleventh Chris-Engelbrecht Summer School in Theoretical Physics, 4-13 February, 1998, to be published by Springer Verla