Constructing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>J</mml:mi><mml:mrow><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>C</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mo>+</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:math> light flavor hybrid nonet with the newly observed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>η</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1855</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
Bing Chen, Si-Qiang Luo, Xiang Liu
Abstract
The recently discovered ${\ensuremath{\eta}}_{1}(1855)$ and the previously observed ${\ensuremath{\pi}}_{1}(1600)$ state present a valuable opportunity for the investigation of the ${J}^{P(C)}={1}^{\ensuremath{-}(+)}$ light hybrid nonet. In this study, we employ a semirelativistic quark potential model to examine the masses of the ${J}^{P(C)}={1}^{\ensuremath{-}(+)}$ light hybrid states. The static potential, which portrays the confinement force between the quark-antiquark pair in a hybrid system, is borrowed from the SU(3) lattice gauge theory. Additionally, we utilize a constituent gluon model to analyze the strong decay characteristics of these light ${1}^{\ensuremath{-}+}$ hybrids. Our findings suggest that the ${\ensuremath{\pi}}_{1}(1600)$ and ${\ensuremath{\eta}}_{1}(1855)$ states could be potential candidates for ${1}^{\ensuremath{-}+}$ $(u\overline{u}\ensuremath{-}d\overline{d})g/\sqrt{2}$ and $s\overline{s}g$ hybrids, respectively. To ensure comprehensiveness, we also investigate the isospin partners of the ${\ensuremath{\pi}}_{1}(1600)$ and ${\ensuremath{\eta}}_{1}(1855)$ states within the ${1}^{\ensuremath{-}(+)}$ nonet---specifically, the $(u\overline{u}+d\overline{d})g/\sqrt{2}$ and $s\overline{q}g$ ($q=u$ and $d$ quarks) states. We propose some potential decay channels which could be explored in experimental settings to detect these undiscovered states.