Abstract
We perform an effective-field-theory-based coupled-channel analysis of the recent BES III data on the $e^+e^-$ annihilation into the final state $K^+(D_s^-D^{*0}+D_s^{*-}D^0)$ 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 $\bar D_s^* D^*$ threshold in fit 1, while no such state exists in fit 2. We predict the $\bar{D}_s^*D^*$ invariant mass distribution in the $J^{P}=1^+$ channel for the reaction $e^+e^-\to K^+D_s^{*-}D^{*0}$ and argue that this line shape can be used to distinguish between the two scenarios once data in this channel are available.
Highlights
Since 2003 when the famous χc1ð3872Þ, known as Xð3872Þ, was discovered by the Belle Collaboration [1], the number of states in the spectrum of charmonium and bottomonium that do not fit into the simple quark-model classification scheme grows very fast
We predict the D ÃsDÃ invariant mass distribution in the JP 1⁄4 1þ channel for the reaction eþe− → KþDÃs−DÃ0 and argue that this line shape can be used to distinguish between the two scenarios once data in this channel are available
A coupled-channel analysis of the reaction eþe− → KþðD−s DÃ0 þ DÃs−D0Þ is presented for the whole energy range measured by BES III
Summary
Since 2003 when the famous χc1ð3872Þ, known as Xð3872Þ, was discovered by the Belle Collaboration [1], the number of states in the spectrum of charmonium and bottomonium that do not fit into the simple quark-model classification scheme grows very fast. All measurements by BES III were performed in the energy range close to the state ψð4660Þ, known as Yð4660Þ (JPC 1⁄4 1−−), with a width of Γ 1⁄4 62þ−79 MeV This state is by itself quite interesting since it apparently does not fit into the spectrum of vector charmonia predicted by various quark models, some adjustment of the models might improve the situation—see the related discussion in Ref. [38]; see the discussion of a possibly large HQSS breaking in production contained in this reference) This picture is especially intriguing given that the production of the Zcð3900Þ in the decay of Yð4230Þ is claimed to be dominated by triangle diagrams2 [37,40] in the same way as the triangle loops are important for the Zcsð3982Þ production in the scenario put forward in Ref. In this paper we focus on the BES III data and postpone an analysis of the LHCb data to a later, more complete, study
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