Pion properties at finite nuclear density based on in-medium chiral perturbation theory
Abstract
The in-medium pion properties, i.e. the temporal pion decay constant f_t, the pion mass m_π ^*, and the wave function renormalization in symmetric nuclear matter are calculated in an in-medium chiral perturbation theory up to the next-to-leading order of the density expansion O(k_F^4). The chiral Lagrangian for the pion-nucleon interaction is determined in vacuum, and the low-energy constants are fixed by experimental observables. We carefully define the in-medium state of the pion and find that the pion wave function renormalization plays an essential role in the in-medium pion properties. We show that the linear density correction is dominant and the next-to-leading corrections are not so large at the saturation density, while their contributions can be significant at higher densities. The main contribution of the next-to-leading order comes from the double scattering term. We also discuss whether the low-energy theorems, the Gell-Mann-Oakes-Renner relation and the Glashow-Weinberg relation, are satisfied in the nuclear medium beyond the linear density approximation. We also find that the wave function renormalization is enhanced as much as 50% at the saturation density including the next-to-leading contribution, and that the wave function renormalization can be measured in the in-medium π ^0to γ γ decay.
- Publication:
-
Progress of Theoretical and Experimental Physics
- Pub Date:
- March 2014
- DOI:
- 10.1093/ptep/ptu023
- arXiv:
- arXiv:1312.0832
- Bibcode:
- 2014PTEP.2014c3D03G
- Keywords:
-
- D33;
- Nuclear Theory;
- High Energy Physics - Phenomenology
- E-Print:
- 26 pages, 5 figures