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

Abstract

We study the thermal modification of the exclusive decay $K_1^+(1270)\to π^+π^-K^+$ in a hot hadronic medium. The decay amplitude is constructed from effective hadronic interactions dominated by the $ρ$- and $K^*$-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 $Γ_{K_1\toπ^+π^-K^+}(T)$. As a further step toward future experimental comparison, we introduce normalized shape observables that quantify the thermal evolution of the $K^*$-dominated $πK$ region, the upper-edge weight of the $ππ$ 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.

Figures (7)

• Figure 1: Relevant Feynman diagrams for the decay $K_1^+\to \pi^+\pi^-K^+$, namely, the $\rho$- and $K^*$-pole contributions. The four-momentum assignments are also indicated.
• Figure 2: Invariant-mass distribution $d\Gamma/dM(\pi^-K^+)$ for $K_1(1270)^+\to\pi^+\pi^-K^+$ with $\mathcal{M}_{\rm BKG}=25$, 30, and 35 at $T=0$. The background mainly changes the overall strength, while the spectral shape remains nearly unchanged.
• Figure 3: Temperature dependence of the meson properties used in the present calculation: (a) masses of the $\rho$, $K^*$, and $K_1(1270)$ mesons, and (b) their corresponding decay widths. The more rapid variation in the range $T =(120$--$160)~\mathrm{MeV}$ reflects the approach to the pseudocritical region, where approximate vector--axial-vector degeneracy sets in, and the $K_1$ channel begins to show strong suppression.
• Figure 4: Dalitz plots for $K_1^+(1270)\to \pi^+\pi^-K^+$ as functions of the invariant masses $M_{\pi^+\pi^-}$ and $M_{\pi^-K^+}$, shown with a common color normalization for $T=(0$--$160$) MeV.
• Figure 5: Invariant-mass distributions for $K_1^+\to \pi^+\pi^-K^+$ at several temperatures: (a) $d\Gamma/dM_{\pi^+\pi^-}$ and (b) $d\Gamma/dM_{\pi^-K^+}$. The vertical thick lines stand for the mass of $\rho^0(770)$ and $K^{*0}(892)$.