Abstract

The in-medium pion properties, {\it i.e.} the temporal pion decay constant $f_t$, the pion mass $m_\pi^*$ 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.

Highlights

  • Spontaneous breakdown of chiral symmetry (χ SSB) SU (N f ) L × SU (N f ) R → SU (N f )V characterizes the vacuum and low-energy dynamics of quantum chromodynamics (QCD) [1,2]

  • We have provided a general formalism of the in-medium chiral perturbation theory and have discussed an expansion in terms of Fermi momentum

  • We focus on the expansion of the Fermi momentum of the physical quantities, which are calculated by the QCD

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Summary

Introduction

Spontaneous breakdown of chiral symmetry (χ SSB) SU (N f ) L × SU (N f ) R → SU (N f )V characterizes the vacuum and low-energy dynamics of quantum chromodynamics (QCD) [1,2]. CHPT describes quantitatively the S-matrix elements of the QCD currents In this decade, chiral effective theory for nuclear matter has been developed [15,30] and is applied to study nuclear matter properties, such as the nuclear matter energy density [31], and used to study partial restoration of chiral symmetry and the in-medium changes of the pion properties, such as in-medium pion mass, decay constant [7,25], and the 1s and 2p energy levels of deeply bound pionic atoms [12]. Recent calculations based on CHPT give a + = (7.6 ± 3.1) × 10−3 m −1 π at better than 95% confidence level [36] In this way, we take the in-vacuum physical values to determine the LECs and perform systematic calculations for density effects of the pionic observables based on the counting of Fermi momentum orders. Given by the vector and axial vector external fields vμ and aμ counted as O( p), and the χ field

Pion mass and wave function renormalization
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