Extending the truncated Dyson-Schwinger equation to finite temperatures

In view of the properties of mesons in hot strongly interacting matter the properties of the solutions of the truncated Dyson-Schwinger equation for the quark propagator at finite temperatures within the rainbow-ladder approximation are analysed in some detail. In Euclidean space within the Matsubara imaginary time formalism the quark propagator is not longer a O(4) symmetric function and possesses a discrete spectra of the fourth component of the momentum. This makes the treatment of the Dyson-Schwinger and Bethe-Salpeter equations conceptually different from the vacuum and technically much more involved. The question whether the interaction kernel known from vacuum calculations can be applied at finite temperatures remains still open. We find that, at low temperatures, the model interaction with vacuum parameters provides a reasonable description of the quark propagator, while at temperatures higher than a certain critical value $T_c$ the interaction requires stringent modifications. The general properties of the quark propagator at finite temperatures can be inferred from lattice QCD calculations. We argue that, to achieve a reasonable agreement of the model calculations with that from lattice QCD, the kernel is to be modified in such a way as to screen the infra-red part of the interaction at temperatures larger than $T_c$. For this, we analyse the solutions of the truncated Dyson-Schwinger equation with existing interaction kernels in a large temperature range with particular attention on high temperatures in order to find hints to an adequate temperature dependence of the interaction kernel to be further implemented in to the Bethe-Salpeter equation for mesons. This will allow to investigate the possible in medium modifications of the meson properties as well as the conditions of quark deconfinement in hot matter.Comment: 33 pages, 11 figures. New references, two new figures (Fig.4 and Fig.11) and Appendix have been included in the new version. A new T-dependence of the interaction kernel is considere

Exclusive charge exchange reaction pD->n(pp) within the Bethe-Salpeter formalism

The exclusive charge exchange reaction pD->n(pp) at intermediate and high energies is studied within the Bethe-Salpeter formalism. The final state interaction in the detected pp pair at nearly zero excitation energy is described by the 1S0 component of the Bethe-Salpeter amplitude. Results of numerical calculations of polarization observables and differential cross-section persuade that, as in the non-relativistic case, this reaction (i) can be utilized as a ``relativistic deuteron polarimeter'' and (ii) delivers further information about the elementary nucleon-nucleon charge-exchange amplitude.Comment: 38 pages, 10 eps-figure

Charge-Exchange Reaction pD->n(pp) in the Bethe-Salpeter Approach

The deuteron charge - exchange reaction pD->n(pp) for the low values of momentum transfer and small excitation energies of final pp - pair is considered in the framework of Bethe - Salpeter approach. The method of calculation of the observables is developed for the case, when the pp - pair is in $^1S_0$ - state. The methodical numerical calculations of the differetial cross sections and tensor analysing powers are presented. The reaction under consideration is predicted to be a solid base for construction of the deuteron tensor polarimeter at high energies, and also to obtain some additional information about elementary nucleon - nucleon charge - exchange amplitude.Comment: 4 pages, 5 eps-figures. Talk presented by S. S. Semikh at XV International Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", September 25-29, 2000, Dubna; to appear in the proceedings of this conference. Added references, minor changes in the tex

Solving the Bethe-Salpeter Equation in Euclidean Space

Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.Comment: 19 pages, 7 figures; based on materials of the contribution "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-13, 200