Is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>3982</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> a molecular partner of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>3900</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4020</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> states?
V. Baru, E. Epelbaum, A. A. Filin, C. Hanhart, A. V. Nefediev
Abstract
We perform an effective field theory-based coupled-channel analysis of the recent BES III data on the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into the final state ${K}^{+}({D}_{s}^{\ensuremath{-}}{D}^{*0}+{D}_{s}^{*\ensuremath{-}}{D}^{0})$ in a wide energy range and extract the poles responsible for the formation of the ${Z}_{cs}(3982)$. We identify two scenarios which provide a similar description of the experimental mass distributions but result in utterly different predictions for the spin partners of the ${Z}_{cs}(3982)$: although both scenarios are consistent with the ${Z}_{cs}$ as a $SU(3)$ partner of the ${Z}_{c}(3900)$, the ${Z}_{c}(4020)$ appears naturally as a spin partner of these states only in one of them (fit 1) while in the other (fit 2) its nature has to be different. Also, the ${Z}_{cs}(3982)$ has a ${J}^{P}={1}^{+}$ spin partner near the ${\overline{D}}_{s}^{*}{D}^{*}$ threshold in fit 1, while no such state exists in fit 2. We predict the ${\overline{D}}_{s}^{*}{D}^{*}$ invariant mass distribution in the ${J}^{P}={1}^{+}$ channel for the reaction ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{D}_{s}^{*\ensuremath{-}}{D}^{*0}$ and argue that this line shape can be used to distinguish between the two scenarios once data in this channel are available.