On the Isovector Channels in Relativistic Point Coupling Models within the Hartree and Hartree-Fock Approximations

We investigate the consequences of Fierz transformations acting upon the contact interactions for nucleon fields occurring in relativistic point coupling models in Hartree approximation, which yield the same models but in Hartree-Fock approximation instead. We find for four-fermion interactions occurring in two existing relativistic point coupling phenomenologies that whereas in Hartree the isovector-scalar strength, corresponding to delta-meson exchange, is unnaturally small, indicating a possible new symmetry, in Hartree-Fock it is instead comparable to the isovector-vector strength corresponding to rho-meson exchange, but the sum of the two isovector coupling constants appears to be preserved in both approaches. Furthermore, in Hartree-Fock approximation, both QCD-scaled isovector coupling constants are natural (dimensionless and of order 1) whereas in Hartree approximation only that of the isovector-vector channel is natural. This indicates that it is not necessary to search for a new symmetry and, moreover, that the role of the delta-meson should be reexamined.