$S$-wave $KK^*$ interaction in a finite volume and the $f_1(1285)$

TL;DR

This paper investigates the $KK^*$ interaction in a finite volume to understand the nature of the $f_1(1285)$ resonance, using lattice QCD-inspired methods and analyzing energy levels to distinguish between different theoretical interpretations.

Contribution

It introduces a finite volume calculation of the $KK^*$ system using the chiral unitary approach and compares it with the Lüscher method, providing insights into the $f_1(1285)$ resonance structure.

Findings

Energy levels of the $KK^*$ system are computed in finite volume.

The loop function is calculated using dimensional regularization.

The inverse problem of extracting bound state information is analyzed.

Abstract

Lattice QCD simulations provide a promising way to disentangle different interpretations of hadronic resonances, which might be of particular relevance to understand the nature of the so-called $XYZ$ particles. Recent studies have shown that in addition to the well-established naive quark model picture, the axial-vector meson $f_1(1285)$ can also be understood as a dynamically generated state built upon the $KK^*$ interaction. In this work, we calculate the energy levels of the $KK^*$ system in the $f_1(1285)$ channel in finite volume using the chiral unitary approach. We propose to calculate the loop function in the dimensional regularization scheme, which is equivalent to the hybrid approach adopted in previous studies. We also study the inverse problem of extracting the bound state information from synthetic lattice QCD data and comment on the difference between our approach and the L{\" u}scher method.