Chiral Evolution and Femtoscopic Signatures of the $K_1(1270)$ Resonance

Abstract

We present a comprehensive study of the axial-vector resonance $K_1(1270)$ within the unitarized chiral perturbation theory, focusing on its two-pole structure and manifestation in femtoscopic observables. By considering the dominant $ρK$ and $K^*π$ coupled channels, we reproduce the well-established double-pole structure and trace the chiral evolution of both poles as functions of the pion mass, using the vector-meson mass trajectories fitted to lattice-QCD data and experimental values. The lower pole, dominantly coupled to $K^*π$, evolves from an above-threshold resonance to a virtual or bound state with increasing pion mass. In comparison, the higher pole, dominantly coupled to $ρK$, moves downward in energy, reflecting the strengthening of the chiral attraction. The influence of the finite vector-meson widths is systematically examined, showing that their inclusion smooths the pole trajectories without altering their qualitative behavior. Furthermore, femtoscopic CFs are calculated for all relevant vector-pseudoscalar channels in both charged sectors. The results exhibit distinct resonance and bound-state features consistent with the two-pole dynamics. The weak impact of higher channels, such as $ω\bar{K}$, $\bar{K}^*η$, and $φ\bar{K}$, confirms that the simplified two-channel treatment captures the essential dynamics of the $K_1(1270)$ resonance. This study demonstrates that combining chiral extrapolation and femtoscopic correlation analyses provides a powerful and complementary framework for connecting lattice-QCD calculations, chiral effective theory, and experimental measurements, offering new insights into the molecular nature and chiral origin of the $K_1(1270)$ resonance.

Figures (5)

• Figure 1: (a) Chiral extrapolation of the $K^{*}$ mass and decay width; (b) chiral extrapolation of the $\rho$ mass and decay width. The solid and dashed lines denote the continuum-limit and the discrete lattice QCD fits, respectively, and the shaded regions correspond to the $1\sigma$ uncertainty bands.
• Figure 2: Chiral evolution of the two-pole structure of the $K_{1}(1270)$ resonance in the $\rho K$--$K^{*}\pi$ coupled-channel system. The left and right panels correspond to the lower and higher poles, mainly coupled to $K^{*}\pi$ and $\rho K$, respectively. Solid and dashed lines denote the results without and with finite vector-meson widths, respectively. Markers indicate pole positions at different pion masses, with the critical masses explicitly labeled.
• Figure 3: Femtoscopic correlation functions $C_i(p)$ for the $Q = 0$ sector, corresponding to the coupled-channel system $\{\rho^{+} K^{-},\, \rho^{0}\bar{K}^{0},\, \bar{K}^{*0}\pi^{0},\, K^{*-}\pi^{+},\, \omega \bar{K}^{0},\, \bar{K}^{*0}\eta,\, \phi \bar{K}^{0}\}$. The red and blue curves represent results without and with vector-meson widths, respectively, and different line transparencies correspond to source sizes of $R = 1$, $2$, and $3~\mathrm{fm}$.
• Figure 4: Femtoscopic correlation functions $C_i(p)$ for the $Q = -1$ sector, corresponding to the coupled-channel system $\{\rho^{0} K^{-},\, \rho^{-}\bar{K}^{0},\, K^{*-}\pi^{0},\, \bar{K}^{*0}\pi^{-},\, \omega K^{-},\, K^{*-}\eta,\, \phi K^{-}\}$. The red and blue curves denote calculations without and with the finite vector-meson widths, respectively, and different line transparencies correspond to source sizes of $R = 1$, $2$, and $3~\mathrm{fm}$.
• Figure 5: Femtoscopic correlation functions $C_i(p)$ for the two channels $\rho^-\bar{K}^0$ and $\bar{K}^{*0}\pi^-$ in the $Q=-1$ system. The red and blue lines represent the individual contributions to $C(p)$ from the $\rho\bar{K}$ and $\bar{K}^*\pi$ channels, respectively. Different line transparencies correspond to source radii of $R = 1$, $2$, and $3~\mathrm{fm}$.