Mixing angle of $K_1(1270/1400)$ and the $K{\bar{K}}_1(1400)$ molecular interpretation of ${\eta }_1(1855)$

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.

Comments: 11 pages, 9 figures. Accepted by Physical Review D