One Loop Integrals at Finite Temperature and Density

The technique of decomposing Feynman diagrams at the one loop level into elementary integrals is generalized to the imaginary time Matsubara formalism. The three lowest integrals, containing one, two and three fermion lines, are provided in a form that separates out the real and imaginary parts of these complex functions, according to the input arguments, in a fashion that is suitable for numerical evaluation. The forms given can be evaluated for arbitrary values of temperature, particle mass, particle momenta and chemical potential.Comment: 32 Pages REVTeX, 9 Figures available as separate fil

Families of particles with different masses in PT-symmetric quantum field theory

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green's functions of the quantum field theory converges in different pairs of Stokes' wedges in complex field space, and the solutions are physically viable if the pairs of Stokes' wedges are PT symmetric.Comment: 4 pages, 3 figure

Amplitude determination for MM -> MM, M= pi, K and cross-sections for gamma gamma -> pi^+pi^-, pi^0 pi^0 in a chiral model

Recently Dai and Pennington have performed a comprehensive analysis of essentially all pion and kaon pair production data from two-photon collisions below 1.5 GeV, including all high statistics results from Belle, as well as the older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. Imposing the basic constraints required by analyticity, unitarity, and crossing symmetry and making use of Low's low energy theorem for QED, they are able to extract the final-state strong-interaction scattering amplitudes for the intermediate pi pi->pi pi and pi pi-> K\bar K reactions in a model-independent fashion. In addition, they provide good fits to the respective gamma gamma-> pi pi cross-sections that are known in the low-energy sector in the restricted angular range, | cos theta|< 0.6-0.8. Using the parameters obtained in this fashion, these authors contruct the \gamma\gamma->pi pi cross-sections integrated over the full angular range. In this work, we use a version of chiral perturbation theory developed by Oller and Oset to evaluate the final-state strong-interaction amplitudes directly theoretically and we compare our thus obtained low-energy QCD-based results directly with the amplitudes extracted by Dai and Pennington. We also calculate the gamma gamma -> pi pi cross-sections (integrated over the full angular range) and compare these with those obtained by Dai and Pennington. This calculation thus gives a more detailed insight into the fit of chiral perturbation theory, not just to the measured gamma gamma-> pi pi cross-sections, as is usually presented, but rather to a higher level of detail through the available analysis of the experimental data for the underlying final-state strong-interaction meson-meson scattering amplitudes pi pi-> pi pi and pi pi-> K\bar K themselves. The fits appear to be reasonable over the energy range considered.Comment: 17 pages, 5 figure