$a_1(1420)$ resonance as a tetraquark state and its isospin partner

We systematically construct tetraquark currents of $I^G{J}^{PC}=1^{-}{1}^{++}$ 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 tetra quark 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 contents $qs\bar{q}\bar{s}$($q=u$ or $d$) leading to a mass of $1.44\pm 0.08$ 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 $a_1(1420) \rightarrow K^(892)K$and$P$-wave$a_1(1420)\rightarrow f_0(980) \pi$ while the possible decay patterns of $f_1(1420)$ are $S$-wave $f_1(1420) \rightarrow K^(892)K$and$P$-wave$f_1(1420) \rightarrow a_0(980) \pi$\mathrm{.}Wespeculatethat$a_1(1420)$ispartlyresponsibleforthelargeisospinviolationinthe$\eta(1405)\to f_0(980)\pi_0$ decay mode which is reported by BESIII collaboration in the $J\mathrm{/}\psi \to \gamma 3\pi$ process.