Mixing angle of $K_1(1270/1400)$ and the $K\bar K_1(1400)$ molecular interpretation of $\eta_1(1855)$

TL;DR

This paper determines the mixing angle of axial-vector kaons using QCD sum rules and explores the potential molecular nature of the $ ext{eta}_1(1855)$, finding negative spectral functions that challenge the molecular interpretation.

Contribution

It introduces a new construction of $K_1$ currents in QCD sum rules and investigates the molecular interpretation of $ ext{eta}_1(1855)$, providing insights into their structures.

Findings

Mixing angle of $K_1(1270)$ and $K_1(1400)$ determined as approximately 47 degrees.

Spectral functions for $Kar K_1$ molecular states are negative, indicating unreliable sum rule analysis.

The molecular interpretation of $ ext{eta}_1(1855)$ is not supported by the sum rule calculations.

Abstract

Due to the SU(3) symmetry breaking effect, the axial-vector kaons $K_1(1270)$ and $K_1(1400)$ are established to be mixtures of two P-wave $K_{1A}\left( {^3{P_1}} \right)$ and $K_{1B}\left( {^1{P_1}} \right)$ states. In QCD sum rules, we propose a new construction of the $K_1$ current operators and calculate the two-point correlation functions by including the next-to-leading order four-quark condensates. The mixing angle is determined as $\theta = \left( {46.95_{ - 0.23}^{ + 0.25}} \right)^\circ$ by reproducing the masses of $K_1(1270)$ and $K_1(1400)$. We further compose the $K\bar K_1\left( {1270} \right)$ and $K\bar K_1\left( {1400} \right)$ interpolating currents with exotic quantum numbers $J^{PC}=1^{-+}$ to investigate the possible molecular interpretation of the recently observed ${\eta _1}(1855)$ state. We calculate the correlation functions and perform the QCD sum rule analyses for these two molecular systems. However, the spectral functions are found to be negative in physical regions so that they are not able to provide reliable investigations of the $K\bar K_1$ molecular states.