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Strange Hadrocharmonium ∗ M.B Physics Letters B 798 (2019) 135022 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Strange hadrocharmonium ∗ M.B. Voloshin a,b,c, a William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA b School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA c Institute of Theoretical and Experimental Physics, Moscow, 117218, Russia a r t i c l e i n f o a b s t r a c t Article history: It has been recently suggested that the charged charmoniumlike resonances Zc (4100) and Zc (4200) Received 23 May 2019 are two states of hadrocharmonium, related by the charm quark spin symmetry in the same way Received in revised form 12 August 2019 as the lowest charmonium states ηc and J/ψ. It is pointed out here that in this picture one might Accepted 16 September 2019 expect existence of their somewhat heavier strange counterparts, Zcs, decaying to ηc K and J/ψ K . Some Available online 11 October 2019 expected properties of such charmoniumlike strange resonances are discussed that set benchmarks for Editor: B. Grinstein their search in the decays of the strange Bs mesons. © 2019 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license 3 (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP . Numerous new resonances recently uncovered near the open down to about 4220 MeV), has been recently invoked [11]for de- charm and open bottom thresholds, the so-called XYZ states, ap- scription of the charged charmoniumlike resonances Zc(4100) and parently do not fit in the standard quark-antiquark template and Zc(4200) observed respectively in the decay channels ηcπ [12] 1 contain light constituents in addition to a heavy quark-antiquark and J/ψπ [13]. pair. (Recent reviews of the data and of the theoretical approaches It can be noted that some of the observed XYZ resonances have can be found in Refs. [1–3].) It becomes clear that the internal dy- a nontrivial light flavor structure and come in isotopic triplets with namics of these essentially multi-body systems is likely very much charged components as well the neutral ones. However as of yet different in different states [4]. In particular, some of these exotic no states of this type with open strangeness have been observed. resonances, with mass very near a threshold for a heavy meson The (non)existence of molecular strange threshold systems could pair appear to display properties characteristic for loosely corre- be closely related to the problem of the forces between heavy lated threshold state, a molecule [5], made of the meson pair, with mesons that give rise to the threshold singularities, in particular such picture likely applicable to the Zb(10610) and Zb(10650) bot- the significance of the pion exchange. The long-range interaction tomoniumlike resonances [6], and to the X(3872) [9], Zc(3900) [7] mediated by the pions has been much discussed in connection and Zc(4020) [8]in the charmoniumlike sector. Another type of with the molecular states (see e.g. in Refs. [18–21]). This inter- states is apparently presented by those that are not especially action however is impossible between a non-strange and strange close to any heavy meson pair threshold and tend to decay into heavy meson, and the lightest exchanged meson is η, generally re- a particular state of quarkonium and one or more light mesons. sulting in a somewhat different dynamics [22]. Thus it is not likely Combined with the observation that the latter resonances do not that a straightforward application of the flavor SU(3) symmetry to overwhelmingly decay into pairs of heavy mesons, this has led to the threshold states can be justified. the ‘hadroquarkonium’ picture [4,10]of such resonances, where The situation looks quite different for the hadrocharmonium a compact state of quarkonium is embedded into excited light type systems where the flavor SU(3) may be applicable. Indeed, in mesons by a QCD analog of the van der Waals force. The ob- these systems the compact heavy quarkonium interacts with the served decays into quarkonium and light meson(s) are then due to ‘hosting’ light-quark resonance by exchange of gluons, rather than the de-excitation of the light degrees of freedom. The hadrochar- of quarks. Thus an application of the SU(3) symmetry is the stan- monium picture, originally suggested for explaining the proper- dard one for the light-quark excited states. As is well known the ties of the J/ψππ resonance Y (4260) (lately “shifted” in mass symmetry works reasonably well for such objects with the main 1 * Correspondence to: William I. Fine Theoretical Physics Institute, University of Some alternative models of the Zc (4100) resonance can be found in Refs. Minnesota, Minneapolis, MN 55455, USA. [14–17]. Here however we use only the hadrocharmonium interpretation [11]of E-mail address: [email protected]. this state as well as of Zc (4200). https://doi.org/10.1016/j.physletb.2019.135022 0370-2693/© 2019 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 2 M.B. Voloshin / Physics Letters B 798 (2019) 135022 0 → − + 0 → + − Fig. 1. The quark graphs for the decays B Zc K (a) and B Zc π (b). → − + → + − Fig. 2. The quark graphs for the decays of strange Bs meson, Bs Zcs K (a) and Bs Zcs K (b). effect being that the strange states are heavier than their non- in Fig. 1 and for the strange Bs mesons the relevant types of pro- ≈ − strange partners by (150 200) MeV due to larger mass of cesses are shown in Fig. 2. (We use generic notation Zc and Zcs in the strange quark. Based on this argument one can expect that the figures and in the text, where the discussion is the same for P + + non-strange light-flavor non-singlet hadrocharmonium resonances the J = 0 and 1 resonances.) The graph in Fig. 1a is described should have strange analogs that are heavier by about the same in Ref. [12], and it is clear from it that the Zc resonance gets the amount and have similar large widths in the ballpark of (100 - spectator quark from the parent B meson. For this reason the de- 400) MeV. + cay of a non-strange B meson into a final state with a strange Zcs In the model where the Zc(4100) and Zc(4200) are states of 0 → + − ¯ resonance, B Zcsπ would require absorption of the s anti- hadrocharmonium with respectively η and J/ψ bound in S wave c quark emerging from the decay and would thus not be similar to to the same light quark excitation with the quantum numbers the observed process of Fig. 1a. A similar to the observed produc- of a pion, one thus can expect existence of two similar strange tion of non-strange Zc resonances would rather be the decay of states with the pion excitation being replaced by one with quan- the strange Bs meson that contains spectator s quark as shown in tum numbers of a Kaon. It is known [23] that the observed among Fig. 2a. In the approximation where the OZI suppressed ss¯ anni- light mesons Kaon excitation K (1460) is by ∼ 160 MeV heavier hilation is neglected, the amplitudes of the processes in Fig. 2 are than its non-strange analog π(1300). Thus the strange hadrochar- P + + simply related by the SU(3) flavor symmetry to those in Fig. 1, im- monium resonances with quantum numbers J = 0 and 1 can plying that the processes in Figs. 1a and 2a are described by the be expected with the mass around 4250 MeV and 4350 MeV, and, same amplitude A, while those in the Figs. 1b and 2b are given by for concreteness, these will be referred here as Z (4250) and cs 2 a separate common amplitude B. Neglecting the [SU(3) breaking] Zcs(4350). It should be mentioned however that the specific val- ues of the masses of both the known non-strange broad struc- kinematical differences between the processes, one can write the rates of the discussed decays in terms of the amplitudes A and B tures Zc(4100) and Zc(4200) as well as of the hypothetical strange states are subject to a considerable uncertainty. (For illustration: as the PDG tables quote a ±100 MeV uncertainty for the mass of the − + + − (B0 → Z K ) =|A|2 , (B0 → Z ) =|B|2 (1) π(1300) resonance.) c csπ Clearly, it should be expected that a significant, if not dom- and inant, decay modes of the suggested strange resonances should − + 2 + − 2 (Bs → Z K ) =|A| , (Bs → Z K ) =|B| . (2) be Zcs(4250) → ηc K and Zcs(4350) → J/ψ K , and they can be cs cs sought for in the decays of non-strange and strange B mesons, It should be noted that the latter relations are written for the 0 → + − → + − → − + e.g. in the processes B Zcsπ , Bs Zcs K or Bs Zcs K . flavor-specific state Bs, where the discussed two amplitudes de- Out of these processes only the latter decay is a direct analog of the processes where the Zc(4100) and Zc(4200) resonances 0 + − + 0 2 As is mentioned in the text this relation is valid as long as the s and s¯ quarks were observed [12,13]: B → Zc(4100)K → ηcπ K and B → → − + act as spectators.
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