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 $\rho K$ and $K^{\ast }\pi$ 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 $K^{\ast }\pi$, evolves from an above-threshold resonance to a virtual or bound state with increasing pion mass. In comparison, the higher pole, dominantly coupled to $\rho K$, 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 $\omega \bar{K}$, ${\bar{K}}^{\ast }\eta$, and $\varphi \bar{K}$, 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.

Comments: 10 pages, 5 figures