The $\eta$ decay into 3$\pi$ in asymmetric nuclear medium

Abstract

We explore how the $\eta$-${\pi }^0$ mixing angle and the $\eta$ meson decay into ${\pi }^{+}{\pi }^{-}{\pi }^0$ and 3${\pi }^0$ are modified in the nuclear medium on the basis of the in-medium chiral effective theory with the isospin asymmetry $\alpha$ varied, where $\alpha \equiv \delta \rho /\rho$ with $\delta \rho ={\rho }_n-{\rho }_p$ and $\rho ={\rho }_n+{\rho }_p$. We find that the larger the isospin asymmetry $\delta \rho$ and smaller the total density $\rho$, the more enhanced the mixing angle. We show that the decay width in the nuclear medium has an additional density dependence which cannot be renormalized into that of the mixing angle: The additional term originates from the vertex proportional to a low energy constant $c_1$, which only comes into play in the nuclear medium but not in the free space. It turns out that the resultant density effect on the decay widths overwhelms that coming from the isospin asymmetry, and the higher the $\rho$, the more enhanced the decay widths; the width for the ${\pi }^{+}{\pi }^{-}{\pi }^0$ decay is enhanced with a factor two to three at the normal density ${\rho }_0$ with a minor increase due to $\delta \rho$, while that for the 3${\pi }^0$ decay shows only a small increase of around 10 percent even at ${\rho }_0$. We mention the possible relevance of the partial restoration of chiral symmetry to the unexpected density effect on the decay widths in the nuclear medium.

arXiv comment22 pages, 10 figures. v2:Numerical errors contaminated in Fig's. 1 to 8 are corrected. Two figures are added to show uncertainties of the results on the decay width due to those of the low energy constants. A misleading statement on Fig. 3 are corrected. Some references are added. v3:Typos and the labels of the legends in Figs. 2, 5, and 6 are corrected

References in corpus (20)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• In-medium nuclear interactions of low-energy hadrons
• Chiral Restoration in Hot and/or Dense Matter
• Aspects of chiral pion-nucleon physics
• Hadron properties in the nuclear medium
• Chiral Dynamics and Nuclear Matter
• A Precursor of Chiral Symmetry Restoration in the Nuclear Medium
• Charmonia and Bottomonia in a Magnetic Field
• In-medium chiral perturbation theory beyond the mean-field approximation
• In-medium Pion and Partial Restoration of Chiral Symmetry
• QCD sum rules for magnetically induced mixing between ${\eta }_c$ and $J/\psi$
• QCD phase diagram at finite baryon and isospin chemical potentials in Polyakov loop extended quark meson model with vector interaction
• Interaction of eta mesons with nuclei
• Chiral condensate at finite density using chiral Ward identity
• Nature of the sigma meson as revealed by its softening process
• Effects of light scalar mesons in $\eta \to 3\pi$ decay
• Chiral Symmetry and Scalar Meson in Hadron and Nuclear Physics
• Neutron-proton mass difference in isospin asymmetric nuclear matter