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

TL;DR

This paper investigates the $K_1(1270)$ resonance's two-pole structure using unitarized chiral perturbation theory, examining its evolution with pion mass and its signatures in femtoscopic observables, linking theory with lattice and experimental data.

Contribution

It provides a detailed analysis of the $K_1(1270)$ resonance's two-pole structure and chiral evolution, incorporating femtoscopic observables and finite vector-meson widths, advancing understanding of its molecular nature.

Findings

Reproduces the double-pole structure of $K_1(1270)$

Tracks pole evolution with pion mass and vector-meson widths

Shows femtoscopic correlations reflect two-pole dynamics

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 $K^*\pi$ 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 $K^*\pi$, 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 $\omega \bar{K}$, $\bar{K}^*\eta$, and $\phi\bar{K}$, 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.