The η decay into 3π in asymmetric nuclear medium

sakai, shuntaro; kunihiro, teiji;

We explore how the η–π0 mixing angle and the η meson decay into π+π−
π0 and 3π0 are modified n the nuclear medium on the basis of the in-medium chiral effective theory with varying isospin asymmetry α, where α ≡ δρ/ρ with δρ = ρn − ρp and ρ = ρn + ρp. We find that the
larger the isospin asymmetry δρ and the smaller the total density ρ, the more enhanced the mixing angle. We show that the decay width in the nuclear medium has an additional density dependence that cannot be renormalized into that of the mixing angle: The additional term originates from the vertex proportional to a low-energy constant c1, which only comes into play in the nuclear medium but not in 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 ρ, the more enhanced the decay widths; the width for the π+π−
π0 decay is enhanced by a factor of two to three at the normal density ρ0 with a minor increase due to δρ, while that for the 3π0
decay shows only a small increase of around 10% even at ρ0.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.