We systematically construct tetraquark currents of $I^{\mathrm{G}}{J}^{\mathrm{PC}}=1^{-}{1}^{++}$ 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 ${\eta }_{5\mu }^M$ with quark content $qs\overline{q}\overline{s}$ ($q=u$ or $d$) leading to a mass of $1.44\pm 0.08\mathrm{GeV}$ 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 $a_1(1420)\to K^{*}(892)K$ and $P$-wave $a_1(1420)\to f_0(980)\pi$, while the possible decay patterns of $f_1(1420)$ are $S$-wave $f_1(1420)\to K^{*}(892)K$ and $P$-wave $f_1(1420)\to a_0(980)\pi$. We speculate that $a_1(1420)$ is partly responsible for the large isospin violation in the $\eta (1405)\to f_0(980){\pi }_0$ decay mode, which is reported by BESIII Collaboration in the $J/\psi \to \gamma 3\pi$ process.

• Received 15 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.094022