Pion Mass Dependence of Nucleon Magnetic Moments

The relevance of the pion mass, provenient from a term which explicitely breaks chiral symmetry in the Lagrangian, for nucleon magnetic moment in the frame of the Skyrmion model in two different versions: the usual Skyrme model and a modified one which includes a coupling to a light scalar meson field, the sigma $\sigma (\simeq 500-600$ MeV). The results are compared to other calculations. Our main motivation comes from usual extrapolations for values of low energy QCD observables obtained in lattices with large values of pion/quark masses toward realistic value of $m_{\pi}$. which do not allow it. We do a comparison with results from the Cloudy Bag Model and a chiral hadronic model from chiral perturbation theory. There are several resulting extrapolations from the region of large pion mass to the realistic value depending on the considered model for low energy QCD.Comment: five pages, Contribution for the Proceedings of the Meeting on Hadronic Interactions, Mackenzie University, S\~ao Paulo, SP, Brazil, May 200

Linear Sigma Model at finite baryonic density and symmetry breakings

The linear sigma model at finite baryonic density with a massive vector field is investigated considering that all the bosonic fields develop non zero expected classical values, eventually associated to condensates and corresponding to dynamical symmetry breakings which might occur in the QCD phase diagram. A modified equation for the classical vector field is proposed with its respective solution. Some in medium properties of the model (mainly masses) are investigated within reasonable prescriptions. In particular the behavior of the {\it in medium} pion and sigma masses and a particular way of calculating {\it in medium} coupling to baryons is investigated. A symmetry radius for finite baryonic densities is proposed and calculated in different ways in terms of the other variables of the model and these different ways of calculating it agree quite well. However, assuming that the pion and sigma masses go to zero close to the restoration of chiral symmetry a too high value for the critical density is obtained $\rho_c \simeq 4.3 \rho_0$.Comment: Work presented at the 18th Workshop on Hadronic Interactions, Sao Paulo, SP, Brazil, May 2006. Accepted to be publishe