Light tetraquark states with $J^{PC}=1^{--}$ from QCD sum rules

Abstract

We perform a systematic QCD sum rule study of light tetraquark states with $J^{PC}=1^{--}$ in the diquark--antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations ($q=u/d$): the isoscalar $qq\bar{q}\bar{q}$, $qs\bar{q}\bar{s}$, and $ss\bar{s}\bar{s}$ sectors, the isovector $qq\bar{q}\bar{q}$ and $qs\bar{q}\bar{s}$ sectors, and the isotensor $qq\bar{q}\bar{q}$ sector. The lowest masses in these sectors are derived to be $1.64_{-0.14}^{+0.15}$~GeV, $1.86_{-0.14}^{+0.14}$~GeV, $2.34_{-0.30}^{+0.23}$~GeV, $1.53_{-0.19}^{+0.17}$~GeV, $1.86_{-0.14}^{+0.14}$~GeV, and $2.24_{-0.14}^{+0.12}$~GeV, respectively. We further compare the present $1^{--}$ tetraquark spectrum with previous QCD sum rule results for the $1^{-+}$ tetraquark and hybrid states~\cite{Su:2025bhv}, aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor $1^{-+}$ tetraquark entry and obtain its lowest mass to be $M=2.19_{-0.24}^{+0.26}\mathrm{GeV}$, which is included in the spectral comparison.

Comments: 15 pages, 4 figures, 1 table, suggestions and comments are welcome