A chiral quark-soliton model with broken scale invariance for nuclear matter

por Valentina Mantovani Sarti (INFN - Sezione di Ferrara, Italy)

viernes 3 feb. 2012 12:00 → 13:00 Europe/Madrid

Sala Seminarios (Dpto. de Física Teórica (UVEG))

The problem of studying nuclear matter with chiral Lagrangians is not trivial; for instance models based on the linear sigma-model fail to describe nuclear matter already at rho ~ rho_0 because the normal solution in which chiral symmetry is broken becomes unstable respect to the Lee-Wick phase. The failure of the sigma-model is totally due to the restrictions on the scalar field dynamics imposed by the Mexican hat potential. A possible solution to this problem is still to use a linear realization, but with a new potential, which includes terms not present in the Mexican hat potential. A guideline in building such a potential is to include in the Lagrangian another fundemantal symmetry of QCD: the scale invariance. Here we present a model for describing nuclear matter at finite density based on quarks interacting with chiral fields, sigma and pion and with vector mesons introduced as massive gauge fields. The chiral Lagrangian includes a logarithmic potential, associated with the breaking of scale invariance. We provide results for the soliton in vacuum and at finite density, using the Wigner-Seitz approximation. Moreover we present a first attempt to go beyond the Wigner-Seitz approximation and we study the interaction between two B=1 solitons by using the product ansatz to build up the B=2 system. The first aim of our work is to check whether the inclusion of the logarithmic potential allows the soliton crystal to reach higher densities. The second and more important aim is to verify whether the inclusion of vector mesons in the dynamics of the quarks can provide saturation for chiral matter.