A renormalization scheme for the nucleon-nucleon (NN) interaction based on a subtracted T-matrix equation is proposed and applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. With only one scaling parameter ($\mu$), the results show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. The agreement is qualitative in the $^1S_0$ channel. Between the low-energy NN observables we have examined, the mixing parameter of the $^3S_1-^3D_1$ states is the most sensible to the scale. The scheme is renormalization group invariant for $\mu\to\infty$.Comment: 16 pages, 4 eps figures, to appear in Nuclear Physics

The phenomenon of inverse magnetic catalysis of chiral symmetry in QCD predicted by lattice simulations can be reproduced within the Nambu-Jona-Lasinio model if the coupling G of the model decreases with the strength B of the magnetic field and temperature T . The thermo-magnetic dependence of G(B, T ) is obtained by fitting recent lattice QCD predictions for the chiral transition order parameter. Different thermodynamic quantities of magnetized quark matter evaluated with G(B, T ) are compared with the ones obtained at constant coupling, G. The model with G(B, T ) predicts a more dramatic chiral transition as the field intensity increases. In addition, the pressure and magnetization always increase with B for a given temperature. Being parametrized by four magnetic field dependent coefficients and having a rather simple exponential thermal dependence our accurate ansatz for the coupling constant can be easily implemented to improve typical model applications to magnetized quark matter.

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The subtracted kernel approach is shown to be a powerful method to be implemented recursively in scattering equations with regular plus point-like interactions. The advantages of the method allows one to recursively renormalize the potentials, with higher derivatives of the Dirac-delta, improving previous results. The applicability of the method is verified in the calculation of the 1 S 0 nucleon-nucleon phase-shifts, when considering a potential with one-pion-exchange plus a contact interaction and its derivatives. The 1 S 0 renormalization parameters are fitted to the data. The method can in principle be extended to any derivative order of the contact interaction, to higher partial waves and to coupled channels.

We analyze the role played by Long Distance Symmetries within the context of the Similarity Renormalization Group (SRG) approach, which is based on phase-shift preserving continuous unitary transformations that evolve hamiltonians with a cutoff on energy differences. We find that there is a SRG cutoff for which almost perfect fulfillment of Wigner symmetry is found. We discuss the possible consequences of such finding.

Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the outcoming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei Λ 200MeV. This amounts to a great simplification in the determination of the effective interaction parameters.

We obtain a q-deformed algebra version of the Nambu-Jona-Lasinio model gap equation. In this framework we discuss some hadronic properties such as the dynamical mass generated for the quarks, the pion decay constant and the phase transition present in this model.Comment: 5 pages, 1 eps figure, to appear in Phys. Lett. B 448 (1999) 1-

The well-known correlations of low-energy three and four-nucleon observables with a typical three-nucleon scale (e.g., the Tjon line) is extended to light nuclei and nuclear matter. Evidence for the scaling between light nuclei binding energies and the triton one are pointed out. We argue that the saturation energy and density of nuclear matter are correlated to the triton binding energy. The available systematic nuclear matter calculations indicate a possible band structure representing these correlations