A study of the pion effective mass at finite temperature using the linear sigma model

We have used the Cornwall--Jackiw--Tomboulis method of composite operators and its formulation at finite temperature by Amelino-Camelia and Pi, in order to calculate the effective potential of the O(4) linear sigma model beyond the Hartree approximation. We have obtained a system of gap equations for the effective mass of sigma and the pions as well as for the condensate, the order parameter of the chiral phase transition. We find that the thermal effective mass of the pions at low temperatures remains lower than in the Hartree case, nevertheless deviates from the chiral limit. Our observation is consistent with other results which have been published previously.Comment: Typos in address and references corrected. Latex2e, 5 pages, 2 .eps figures. Contribution to the proceedings of the conference: X Hadron Physics and VII Relativistic Aspects of Nuclear Physics: A joint meeting on QCD and QGP, (HADRON-RANP 2004), 28 March--3 April 2004, Angra dos Reis, Rio de Janeiro, Brazi

Linear sigma model at finite temperature

The chiral phase transition is investigated within the framework of thermal field theory using the O(N) linear sigma model as an effective theory. We calculate the thermal effective potential by using the Cornwall-Jackiw-Tomboulis formalism of composite operators. The thermal effective potential is calculated for N=4 involving as usual the sigma and the three pions, and in the large-N approximation involving N-1 pion fields. In both cases, the system of the resulting gap equations for the thermal effective masses of the particles has been solved numerically, and we have investigated the evolution of the effective potential. In the N=4 case, there is indication of a first-order phase transition, while in the large N approximation the phase transition appears as second-order. In this analysis, we have ignored quantum fluctuations and have used the imaginary time formalism for calculations. We have extended our calculation in order to include the full effect of two loops in the calculation of the effective potential. In this case, the effective masses are momentum dependent. In order to perform the calculations, we found the real time formalism to be convenient. We have calculated the effective masses of pions at the low-temperature phase and we found a quadratic dependence on temperature, in contrast to the Hartree case, where the mass is proportional to temperature. The sigma mass was investigated in the presence of massive pions, and we found a small deviation compared to the Hartree case. In all cases, the system approaches the behaviour of the ideal gas at the high temperature limit.Comment: 33 pages, 40 eps figures, based on PhD thesis submitted to Manchester University in Oct 200

Baryogenesis at the electroweak phase transition

A possible solution to the observed baryon asymmetry in the universe is described, based on the physics of the standard model of electroweak interactions. At temperatures high enough electroweak physics provides violation of baryon number, while C and CP symmetries are not exactly conserved, although in the context of the minimal electroweak model with one Higgs doublet the rate of CP violation is not sufficient enough to generate the observed asymmetry. The condition that the universe must be out of thermal equilibrium requires the electroweak phase transition (EWPT) to be first order. The dynamics of the phase transition in the minimal model is investigated through the effective potential, which is calculated at the one loop order. Finite temperature effects on the effective potential are treated numerically and within the high temperature approximation, which is found to be in good agreement with the exact calculation. At the one loop level the phase transition was found to be of the first order, while the strength of the transition depends on the unknown parameters of the theory which are the Higgs boson and top quark masses.Comment: 30 pages, 15 eps figures, revtex4, based on MSc thesis report submitted to Manchester Universit

Thermal effective potential of the linear sigma model

We have attempted an approach to the chiral phase transition of QCD using the linear sigma model as an effective theory. In order to get some insight into how the phase transition could proceed, we have calculated the finite temperature effective potential of this model in the Hartree and large N approximations using the Cornwall-Jackiw-Tomboulis formalism of composite operators.Comment: 4 pages revtex, 5 eps figures, axodraw.sty, poster presented in the 5th International Workshop on Thermal Field Theories, Regensburg, German

The "white" ethnic racism" thesis: Application to Greek Americans

[Δε διατίθεται περίληψη / no abstract available]The present report used data collected predomin­antly from second-generation Greek-Americans to test the white-ethnic racism thesis. The thesis states that the descendants of «new immigrant» groups— especially their working class descendants, are prejudiced toward minorities, particularly toward blacks. Two approaches were used to evaluate thethesis.In the first approach, a number of ethnic indicators (e.g. demographic, attitudinal, cognitive, andbehavioral) were compared to the respondent’s levelof tolerance toward Jews and blacks. Some associa­tion between «Greekness» and prejudice was noted. There was no uniformity, however, across indicators, with some ethnic indicators (e.g. low assimilationorientation) being correlatedwith intolerance towardthe Jews and other ethnic indicators (e.g. number ofyears in Greek school) being associated with rejec­tion of stereotypes about blacks. In addition, therewere few strong correlations between the various ethnic indicators and prejudice. Finally, some of theassociations between ethnicity and prejudice werenot robust when more.traditional correlates of prej­udice. such as educational level and authori­tarianism, were controlled. Thus, the ethnic factors had a limited predictive capacity. This, however, doesnot mean that the «universal» correlates of prej­udice, such as education and authoritarianism, can­not interact with cultural tradition to produce a highlevel of racism.The white-ethnic racism thesis was also testedunder standardized conditions of economic status. Two indices of economic status, reported annual in­come and the rental value of the respondent’s dwell­ing, were used. Once again there was no uniform support for the thesis. There was more support forthe thesis («Greekness» associated with prejudiceunderlow economic status) when rental value, ratherthan income, was used as the economic variable. Inpart this may be due to the better distribution of therental value than the income factor. It may also be afunction of the differential meaning of the two status indicators to the Greek-American respondents. The rental value status is more interwoven with house ownership which is a more tangible and overt indi­cator of status than income. In addition, housing hasbeen associated with fears about desegregation.There was more support for the white-ethnic ra­cism thesis in the case of stereotypes about blacksthan attitudes toward the blacks (social distance) or attitudes toward the Jews. This may be due to thefactthat the stereotype measure contained content evok­ing the Greek-American’s «bootstrap attitudes».According to this attitude, the descendant of the newimmigrant claims that his ancestors were also the vic­tims ofnordic prejudice, but diligence, individual ef­fort, and patience led to their contemporary success.Thus, they feel they can not be sympathetic with agroup who they think is demanding rewards without commensurate efforts.The «bootstrap» mentality assumes a parallelism of experiences between the white ethnics and racialminorities. This parallelism, however, breaks downwhen other objective factors are taken into account.First, the degree of prejudice against white ethnicscannot match the degree of overt, organized racismagainst blacks. In part, this is the result of the ethnicsbeing a «cultural» rather than a «racial» minority. Inpart, it is due to the fact that the blacks have had the stigma of slavery at the hands of the «dominant» WASP group. Finally, the «white ethnics» came tothe US at a time (1880-1930) when the country wasindustrializing and offered much opportunity for en­trepreneurial success. When the blacks really began «arriving» in the US (i.e. when their genuine libera­tion began in the 1940s and 1950s), the US technol­ogy was exceedingly complex and the business oppor­tunities were more limited. These factors, however, are rarely considered by the descendants of whiteethnics whose relative status is being challenged bythe just demands of the racial minorities.The findings ofthe present study — and the atten­dant interpretations — can only be suggestive. Thereis a need to obtain better variation on the ethnicity variables such as generational status and regionalorigin. Along the same lines, better variation must besought in the prejudice measures. In the presentstudy, two of these measures (attitudes toward theJews and social distance attitudes toward the blacks)were not as well distributed as the black stereotypemeasure. Thus, some of the findings may be due tomethodological rather than theoretical reasons. These problems can be rectified if research is carried out in large Greek communities such as Chicago and New York. The white-ethnic racism thesis can, ofcourse, also be tested on other «white-ethnic» groups from Southern and Eastern Europe, both on themicro- and macrosociological levels of analysis

The light scalar mesons within quark models

Low-energy meson-meson scattering data are a powerful testing ground for quark models. Here, we describe the behaviour at threshold of S-wave scattering-matrix singularities. The majority of the full scattering-matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesons K0*(830), a0(980), f0(400-1200), and f0(980) do not, but instead originate in 3P0-barrier semi-bound states. We show that the behaviour of the corresponding poles is identical at threshold. In passing, the light-meson sector is given a firm basis.Comment: Plain LaTeX, 16 pages Contribution to the Second International Workshop on Hadron Physics, Effective Theories of Low Energy QCD, 25-29 September, 2002 (Coimbra, Portugal

Bose-Einstein condensation and chiral phase transition in linear sigma model

With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A $\mu-T$ phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored phase area. Bose-Einstein condensation can happen either from the chiral symmetry broken phase or from the restored phase. We show that the onset of the chiral phase transition is restricted in the area where there is no Bose-Einstein condensation.Comment: 13 pages, 7 figure

AC and DC conductivity correlation: The coefficient of Barton--Nakajima--Namikawa relation

It has been some time since an empirical relation, which correlates DC with AC conductivity and contains a loosely defined coefficient thought to be of order one, was introduced by Barton, Nakajima and Namikawa. In this work, we derived this relation assuming that the conductive response consists of a superposition of DC conductivity and an AC conductivity term which materialized through a Havriliak--Negami dielectric function. The coefficient was found to depend on the Havriliak--Negami shape parameters as well as on the ratio of two characteristic time scales of ions motion which are related to ionic polarization mechanism and the onset of AC conductivity. The results are discussed in relation to other relevant publications and they also applied to a polymeric material. Both, theoretical predictions and experimental evaluations of the BNN coefficient are in an excellent agreement, while this coefficient shows a gradual reduction as the temperature increases.Comment: 15 pages plain latex2e, 5 eps figures (new figures added). In this revised version the manuscript has been rewritten extensively due to motivational comments and suggestions made by the referee. Accepted for publication by the Journal of Non--Crystalline Solid