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

Abstract

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 $a_1(1420)\to K^{\ast }(892)K$ and $P$-wave $a_1(1420)\to f_0(980)\pi$ while the possible decay patterns of $f_1(1420)$ are $S$-wave $f_1(1420)\to K^{\ast }(892)K$ 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.

arXiv comment15 pages, 8 figures. Accepted by Phys. Rev. D

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