Thermal modification of $K_1(1270)\to {\pi }^{+}{\pi }^{-}{K}^{+}$ in a hot hadronic medium

Abstract

We study the thermal modification of the exclusive decay $K_1^{+}(1270)\to {\pi }^{+}{\pi }^{-}{K}^{+}$ in a hot hadronic medium. The decay amplitude is constructed from effective hadronic interactions dominated by the $\rho$- and $K^{\ast }$-pole contributions, which enables a Dalitz-level analysis of the three-body decay in medium. Thermal effects associated with partial chiral-symmetry restoration are incorporated through a phenomenological interpolation toward vector--axial-vector degeneracy near the chiral crossover. As the temperature increases, the reduction of the parent $K_1$ mass strongly compresses the available three-body phase space, leading to substantial deformation of the Dalitz distribution and invariant-mass spectra, as well as to a pronounced suppression of ${\Gamma }_{K_1\to {\pi }^{+}{\pi }^{-}{K}^{+}}(T)$. As a further step toward future experimental comparison, we introduce normalized shape observables that quantify the thermal evolution of the $K^{\ast }$-dominated $\pi K$ region, the upper-edge weight of the $\pi \pi$ spectrum, and the compactification of the Dalitz population. The dominant effect identified in the present framework is therefore kinematic: thermal phase-space reduction in the strange axial-vector channel. These results suggest that the exclusive $K_1(1270)$ channel may provide a useful qualitative probe of in-medium strange axial-vector dynamics near the pseudocritical region.

Comments: 13 pages, 7 figures