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Register a new userEvaluation of pion-nucleon sigma term in Dyson-Schwinger equation approach of QCD
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We calculate the variation of the chiral condensate in medium with respect to the quark chemical potential and evaluate the pion-nucleon sigma term via the Hellmann-Feynman theorem. The variation of chiral condensate in medium are obtained by solving the truncated Dyson-Schwinger equation for quark propagator at finite chemical potential, with different models for the quark-gluon vertex and gluon propagator. We obtain the value of the sigma term $sigma_{pi N}$ = 62(1)(2) MeV, where the first represents the systematic error due to our different model for the quark-gluon vertex and gluon propagator and the second represents a statistical error in our linear fitting procedure.
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We have reanalyzed the $pi ^{pm} p$ scattering data at low energy in the Coulomb-nuclear interference region as measured by the CHAOS group at TRIUMF with the aim to determine the pion-nucleon $sigma$ term. The resulting value $sigma=(44pm 12)$ MeV, while in agreement with lattice QCD calculations and compatible with other recent analyses, is significantly lower than that from the GWU-TRIUMF analysis of 2002.
We present a simple description of pion-nucleon ($pi N$) scattering taking into account the full complexity of pion absorption and creation on the nucleon. To do this we solve Dyson-Schwinger equations within the framework of Time-Ordered Perturbation Theory. This enables us to construct partial wave separable $ pi N$ t matrices that can be useful in models of nuclear processes involving fully dressed nucleons. At the same time, our approach demonstrates features of Quantum Field Theory, like particle dressing, renormalisation, and the use of Dyson-Schwinger equations, in a non-relativistic context that is maximally close to that of Quantum Mechanics. For this reason, this article may also be of pedagogical interest.
Any practical application of the Schwinger-Dyson equations to the study of $n$-point Greens functions of a field theory requires truncations, the best known being finite order perturbation theory. Strong coupling studies require a different approach. In the case of QED, gauge covariance is a powerful constraint. By using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the Landau-Khalatnikov-Fradkin transformations are linear operations on the spectral densities. Here we formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gauge covariance of any viable truncation of the Schwinger-Dyson equation for the fermion 2-point function.
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.
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.
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