A1(1420)resonance as a tetraquark state and its isospin partner

Abstract

We systematically construct tetraquark currents of ${I}^{\mathrm{G}}{J}^{\mathrm{PC}}={1}^{\ensuremath{-}}{1}^{++}$ and classify them into types $\mathbf{A}$ (antisymmetric), $\mathbf{S}$ (symmetric) and $\mathbf{M}$ (mixed), based on flavor symmetries of diquarks and antidiquarks composing the tetraquark currents. We use tetraquark currents of type $\mathbf{M}$ to perform QCD sum rule analyses, and find a tetraquark current ${\ensuremath{\eta}}_{5\ensuremath{\mu}}^{M}$ with quark content $qs\overline{q}\overline{s}$ ($q=u$ or $d$) leading to a mass of $1.44\ifmmode\pm\else\textpm\fi{}0.08\text{ }\text{ }\mathrm{GeV}$ consistent with the ${a}_{1}(1420)$ state recently observed by the COMPASS Collaboration. Our results support tetraquark explanations for both ${a}_{1}(1420)$ and ${f}_{1}(1420)$, assuming that they are isospin partners. We also study their possible decay patterns. As tetraquark candidates, the possible decay modes of ${a}_{1}(1420)$ are $S$-wave ${a}_{1}(1420)\ensuremath{\rightarrow}{K}^{*}(892)K$ and $P$-wave ${a}_{1}(1420)\ensuremath{\rightarrow}{f}_{0}(980)\ensuremath{\pi}$, while the possible decay patterns of ${f}_{1}(1420)$ are $S$-wave ${f}_{1}(1420)\ensuremath{\rightarrow}{K}^{*}(892)K$ and $P$-wave ${f}_{1}(1420)\ensuremath{\rightarrow}{a}_{0}(980)\ensuremath{\pi}$. We speculate that ${a}_{1}(1420)$ is partly responsible for the large isospin violation in the $\ensuremath{\eta}(1405)\ensuremath{\rightarrow}{f}_{0}(980){\ensuremath{\pi}}_{0}$ decay mode, which is reported by BESIII Collaboration in the $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}3\ensuremath{\pi}$ process.