Pion properties at finite nuclear density based on in-medium chiral perturbation theory

Abstract

The in-medium pion properties, {\it i.e.} the temporal pion decay constant $f_t$, the pion mass $m_{\pi }^{\ast }$ 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 the experimental observables. We carefully define the in-medium state of the pion and find that the pion wave function plays an essential role for the in-medium pion properties. We show that the linear density correction is dominated and the next-leading corrections is not so large at the saturation density, while their contributions can be significant in higher densities. The main contribution of the next-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 nuclear medium beyond the linear density approximation. We find also that the wave function renormalization is enhanced as largely as $50\%$ at the saturation density including the next-leading contribution and the wave function renormalization could be measured in the in-medium ${\pi }^0\to \gamma \gamma$ decay.

26 pages, 5 figures

References in corpus (5)

• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• In-medium chiral condensate beyond linear density approximation
• In-medium Pion and Partial Restoration of Chiral Symmetry
• The chiral quark condensate and pion decay constant in nuclear matter at next-to-leading order
• The s-wave pion-nucleus optical potential

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• Metastable pions in dense media
• Spectral function of the ${\eta }^{\prime }$ meson in nuclear medium based on phenomenological models
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Pion in the Medium with a Light-Front Model
• $K^{+}$-nucleus elastic scattering revisited from perspective of partial restoration of chiral symmetry
• Generalized Nambu-Goldstone pion in dense matter: a schematic NJL model
• The ${\eta }^{\prime }N$ interaction from the ${\eta }^{\prime }p$ correlation function
• Mesons in Nuclei and Partial Restoration of Chiral Symmetry
• Direct measurement of the in-medium ${\eta }^{\prime }$ mass spectrum through the $\gamma \gamma$ decay channel