The effective ω-meson mass with a vector field self-interaction

We calculate the effective mass m∗ω of the ω-meson in nuclear medium by the σ-ω model with a vector field self-interaction (VFSI). We found that the direct and the indirect effects of the VFSI almost cancel each other and the result is changed only slightly at the normal density. The VFSI makes m∗ω smaller at lower density and makes m ∗ ω larger at higher density. However, both effects are not large. The effective meson mass in nuclear medium is one of the most interesting issues in intermediate energy physics. Much attention has been paid to predicting the meson masses in nuclear medium from various approaches such as quantum hadrodynamics (QHD) [1]-[7], the QCD sum rules [8, 9] and the quark meson coupling model [10]. It is widely accepted that the effective mass of the vector meson (ω and ρ ) decreases as density increases. However, quantitatively, the result is considerably variable in each model. In QHD, there are some versions of the Lagrangian to reproduce the properties of the nuclear matter and finite nuclei. One interesting version of them is the σ-ω model with the vector field self-interaction (VFSI). [11] From phenomenological analyses, the VFSI is needed for a better fit of equation of state at high density. (See, e.g., reference [12].) As usual, this VFSI is regarded as an effective interaction caused by the quantum corrections. This means that the effective potential of the VFSI is added to the effective potential of the total system. On the other hand, the effective meson mass can be defined as a second derivative of the effective potential with respect to the meson-field expectation value. Therefore, the VFSI just shifts the effective ω-meson mass. Naively the VFSI is expected to make the effective ω-meson mass larger, since the potential of the VFSI has a plus sign. Is it true or not? In this brief report,