Configuration mixing in strange tetraquarks <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math>
Marek Karliner, Jonathan L. Rosner
Abstract
The BESIII Collaboration has observed a candidate for a $c\overline{c}s\overline{u}$ tetraquark ${Z}_{cs}$ at $({3982.5}_{\ensuremath{-}2.6}^{+1.8}\ifmmode\pm\else\textpm\fi{}2.1)\text{ }\text{ }\mathrm{MeV}$ and width $({12.8}_{\ensuremath{-}4.4}^{+5.3}\ifmmode\pm\else\textpm\fi{}3.0)\text{ }\text{ }\mathrm{MeV}$, while the LHCb Collaboration has observed a ${Z}_{cs}$ candidate in the $J/\ensuremath{\psi}{K}^{\ensuremath{-}}$ channel with mass of $(4003\ifmmode\pm\else\textpm\fi{}{6}_{\ensuremath{-}14}^{+4})\text{ }\text{ }\mathrm{MeV}$ and width $(131\ifmmode\pm\else\textpm\fi{}15\ifmmode\pm\else\textpm\fi{}26)\text{ }\text{ }\mathrm{MeV}$. In this paper, we examine the possibility that these two states are distinct eigenstates of a mixing process similar to that which gives rise to two axial-vector mesons labeled by the Particle Data Group [P. Zyla et al., Prog. Theor. Exp. Phys. 6, 083C01 (2020)] ${K}_{1}(1270)$ and ${K}_{1}(1400)$. The main point is that on top of a $\overline{c}c$ pair the ${Z}_{cs}$ states have the same light quark content as the ${K}_{1}$-s. In the compact tetraquark picture, this implies several additional states, analogous to members of the ${K}_{1}$ nonet. These states have not yet been observed; nor are they required in the molecular approach. Thus, experimental discovery or exclusion of these extra states will be a critical test for competing models of exotic mesons with hidden charm.