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D 102, 094016 (2020)

First exotic with open heavy flavor: csu¯ d¯

† Marek Karliner 1,* and Jonathan L. Rosner 2, 1School of Physics and Astronomy University, Tel Aviv 69978, Israel 2Enrico Fermi Institute and Department of Physics, University of Chicago, 5620 S. Ellis Avenue, Chicago, Illinois 60637, USA

(Received 23 August 2020; accepted 22 October 2020; published 16 November 2020)

The LHCb Collaboration has reported resonant activity in the channel DþK−, identifying two P þ P components: X0ð2900Þ with J ¼ 0 at 2866 7 MeV, Γ0 ¼ 57 13 MeV and X1ð2900Þ with J ¼ − ¯ 1 at 2904 7 MeV, Γ1 ¼ 110 12 MeV. We interpret the X0ð2900Þ component as a csu¯ d isosinglet compact tetraquark, calculating its mass to be 2863 12 MeV. This is the first with open heavy flavor. The analogous bsu¯ d¯ tetraquark is predicted at 6213 12 MeV. We discuss possible interpretations of the heavier and wider X1ð2900Þ state and examine potential implications for other systems with two heavy .

DOI: 10.1103/PhysRevD.102.094016

Very recently, the LHCb Collaboration reported a narrow b results in a significant shift of the tetraquark mass peak in the DþK− (þ charge conjugate) ( c:c:) channel as vs the two- threshold. seen in the decay B → DþD−K. The peak has been We have approached this problem using two different parametrized in terms of two Breit-Wigner resonances: methods, both based on constituent quarks. In the first, we note that different quark masses are needed to describe

X0ð2900Þ∶ and [2], with baryonic quarks approxi- P þ mately 55 MeV heavier than mesonic ones. We used this J ¼ 0 ;M¼ 2866 7 MeV; Γ0 ¼ 57 13 MeV; ð1Þ method to successfully anticipate [3] the mass of the doubly charmed Ξcc discovered by the LHCb experiment bbu¯ d¯ X1ð2900Þ∶ [4,5] and to predict the existence of a tetraquark below threshold for weak or electromagnetic decay [6]. JP ¼ 1−;M¼ 2904 5 ; Γ ¼ 110 12 : ð Þ MeV 1 MeV 2 (See also Ref. [7].) A second method, permitting the use of universal quark The statistical significance is ≫ 5σ. This is the first exotic masses to describe mesons and baryons, is to ascribe a mass hadron with open heavy flavor [1]. An obvious question is contribution S to each QCD string junction [8,9], of which the interpretation of these states and whether their structure a meson has none, a baryon has one, and a tetraquark has and properties can be elucidated with our current under- two, as illustrated in Fig. 1. standing of nonperturbative QCD. This method was used to predict masses of þ We believe that, regarding the lighter and narrower 0 containing only heavy quarks c or b [10,11]. component, the answer is likely affirmative. We interpret In the present article, we compare the predictions of the this state as a csu¯ d¯ compact S-wave tetraquark, with string-junction picture with the baryonic-quark picture for structure completely analogous to the stable, deeply bound the mass of a JP ¼ 0þ tetraquark composed of bbu¯ d¯ tetraquark expected well below BB threshold. csu¯ d¯, finding preference for the former in light of the new The I ¼ 0 and JP ¼ 0þ , , and quantum LHCb result [1]. The preferred string-junction method is numbers are robust consequences of this structure. That also applied to obtain the ground state mass of the exotic said, the c and s quarks being significantly lighter than the tetraquark bsu¯ d¯. The two methods are then compared for ¯ ¯ ¯ bbu¯ d, ccu¯ d, and bcu¯ d ground states and for MðΞccÞ *marek@tauex..ac.il originally calculated using baryonic quark masses [3]. † [email protected] The LHCb Collaboration has reported two resonances in the DþK− (þ c:c:) channel around 2.9 GeV [1]:onewith Published by the American Physical Society under the terms of JP ¼ 0þ and the other broader one with JP ¼1− [see Eqs. (1) the Creative Commons Attribution 4.0 International license. 0þ Further distribution of this work must maintain attribution to and (2).] We can attempt to describe the state in either the author(s) and the published article’s title, journal citation, the baryonic-quark picture or the string-junction (universal and DOI. Funded by SCOAP3. quark mass) picture, treating the as heavy.

2470-0010=2020=102(9)=094016(4) 094016-1 Published by the American Physical Society MAREK KARLINER and JONATHAN L. ROSNER PHYS. REV. D 102, 094016 (2020)

another source. One possibility is a consequence of rescattering DK → DK (e.g., via exchange), whose threshold is at 2.9 GeV [1]. The string-junction picture may also be applied to the exotic configuration bsu¯ d¯. The terms contributing to its ¯ mass are mb plus an I ¼ J ¼ 0 u¯ d “good quark” mass m½ud lumped into MðΛbÞ¼5619.5 MeV; a strange quark mass FIG. 1. QCD strings connecting quarks (open circles) and ms ¼ 482.2 MeV; a string junction term S ¼ 165.1 MeV; antiquarks (filled circles). (a) Quark-antiquark meson with one and a binding energy BðbsÞ¼−41.8 MeV and bs hyper- string and no junctions, (b) three-quark baryon with three strings −12 and one junction, and (c) baryonium (tetraquark) with five strings fine term of MeV, both taken from [3]. The result is the and two junctions. prediction M½Tðbsu¯ d;¯ 0þÞ ¼ ð6213 12Þ MeV: ð6Þ In a scheme with baryonic quarks, whose masses are labeled by superscripts b, we follow the approach and the It is interesting that this is very close to the BK threshold at notation of Ref. [6] to obtain 6216 MeV, while the 0þ ðcsu¯ d¯Þ state in the sector at 2866 MeV is close to the DK threshold at 2902 MeV. M½Tðcsu¯ d;¯ Þ bar Tðbsu¯ d¯Þ is approximately 440 MeV above the BK thresh- b b b ¼ mc þ ms þ m½ud þ BðcsÞþΔEHFðcsÞ; ð3Þ old. It should be seen in ¯ ¯ 0 − b b Tðbsu¯ dÞ → B K ð7Þ where mc ¼ 1710.5 MeV, ms ¼ 538 MeV, the mass of the I ¼ J ¼ 0 is mb ¼ 576 MeV, the binding ½ud and energy of a cs pair is BðcsÞ¼−35.0 MeV, and the cs ΔE ðcsÞ¼−35 4 − 0 hyperfine interaction accounts for HF . MeV Tðbsu¯ d¯Þ → B K : ð8Þ (the last being taken from the footnote of Table IV of ¯ Ref. [3]). The result is M½Tðcsu¯ d;barÞ¼2754.112MeV, The first mode is preferable because it avoids the s vs s¯ where the theoretical error is that encountered in Ref. [3]. ambiguity associated with neutral . In principle, it In the string-junction picture, with universal-mass should be possible to observe this state in LHCb and perhaps quarks, the relevant parameters are S ¼ 165.1 MeV, in other LHC experiments. ms ¼ 482.2 MeV, and mc ¼ 1655.6 MeV. One can com- The contributions to the mass of the lightest tetraquark ðbÞ ðbÞ Tðbbu¯ d¯Þ JP ¼ 1þ bine mc þ m½ud ¼ MðΛcÞ in either calculation, so the only with two bottom quarks and are listed in difference between the two calculations is one string- Table I. The notation and the numerical values of the parameters are the same as in Tables VI and IX of Ref. [3]. junction term [a second is contained in MðΛcÞ] and the difference in strange quark masses, Theoretical errors reflect deviations from experiment of fits to light-quark states. bbu¯ dJ¯ P ¼ 1þ M½Tðcsu¯ d;¯ strÞ − M½Tðcsu¯ d;¯ barÞ The mass of the ground state is 125.5 higher for universal quarks with two string junctions but is b ¼ S þ ms − ms

¼ð165.1 þ 482.2 − 538Þ MeV ¼ 109.3 MeV; ð4Þ TABLE I. Contributions to the mass of the lightest tetraquark Tðbbu¯ d¯Þ with two bottom quarks and JP ¼ 1þ. Baryonic quarks or as used in Ref. [6] (with superscript b); universal quarks as used in Ref. [10] (no superscript). q denotes u or d quark; isospin M½Tðcsu¯ d;¯ strÞ ¼ ð2863.4 12Þ MeV: ð5Þ breaking is ignored. where the theoretical error is that encountered in fits to light- Baryonic quarks Universal quarks quark [10]. This is within 3 MeVof the experimental Contribution Value (MeV) Contribution Value (MeV) þ central value of the 0 mass (1). A clear preference for the 2S 330.2 b 2m string-junction (universal quark mass) picture emerges. 2mb 10087.0 b 9977.2 0þ JP ¼ 1þ b The state state in Eq. (5) has a hyperfine 2mq 726.0 2mq 617.0 þ þ cs 0 1 b 2 2 partner in which the pair is replaced by a , abb=ðmbÞ 7.8 abb=ðmbÞ 7.8 ΔE ðcsÞ¼þ17 7 b 2 2 with HF . MeV. The mass of the state is −3a=ðmqÞ −150.0 −3a=ðmqÞ −151.2 2916.5 MeV. As it is of unnatural parity, it cannot decay bb binding −281.4 bb binding −266.1 into DK and so cannot account for the state (2). The activity Total 10389.4 12 Total 10514.9 12 in the Dalitz plot giving rise to that state must be due to

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TABLE II. Contributions to the mass of the lightest tetraquark TABLE IV. Contributions to the mass of Ξcc, the spin-1=2 Tðccu¯ d¯Þ with two charmed quarks and JP ¼ 1þ. ground state of ccq (q ¼ u, d); isospin breaking is ignored.

Baryonic quarks Universal quarks Baryonic quarks Universal quarks Contribution Value (MeV) Contribution Value (MeV) Contribution Value (MeV) Contribution Value (MeV) 2S 330.2 S 165.1 b b b 2m þ m 2mc 3421.0 2mc 3311.2 2mc þ mq 3783.9 c q 3619.7 b b 2 2 2mq 726.0 2mq 617.0 acc=ðmcÞ 14.2 acc=ðmcÞ 14.2 b 2 2 b b −42 4 −3a=ðm m Þ −42 4 acc=ðmc Þ 14.2 acc=ðmcÞ 14.2 −3a=ðmqmcÞÞ . q c . b 2 2 −3a=ðmqÞ −150.0 −3a=ðmqÞ −151.2 cc binding −129.0 cc binding −121.3 cc binding −129.0 cc binding −121.3 Total 3627 12 Total 3635 12 Total 3882.2 12 Total 4000.1 12 To summarize, the exotic tetraquark reported by LHCb still 89 MeV below the B−B¯ 0 threshold and 44 MeV below [1] weighs in favor of the string-junction picture with threshold for decay to B−B¯ 0γ. universal quark masses for mesons and baryons. The þ The calculation of the masses of the lightest ccu¯ d¯ observed 0 mass is 2866 5 MeV, while we predict tetraquark masses proceeds analogously to bbu¯ d¯.In 2754 12 MeV in the baryonic-quark scheme and 2863 Table II, we provide the corresponding contributions to 12 MeV in the string-junction (universal quark mass) the ccu¯ d¯ mass. picture. The mass of Tðccu¯ d¯Þ with universal quarks and two The compact tetraquark picture makes a clear prediction X ð2900Þ string junctions is 117.8 MeV higher than that with that 0 is an isoscalar. This prediction can be tested, D0K− baryonic quarks, well above threshold for decay to a e.g., by looking for its charged partner in the − ¯ 0 0 − DD pair. invariant mass in B → D D K . In Table III, we provide the corresponding contributions The bottom analog of X0ð2900Þ, with quark content ¯ to the bcu¯ d¯ tetraquark mass. The mass of Tðbcu¯ d¯Þ with ðbsu¯ dÞ, is predicted at 6213 12 MeV. universal quarks and two string junctions is 121.6 MeV There remains the question of how to interpret the − higher than that with baryonic quarks. Whereas in the broader 1 peak (2). One possibility, as mentioned, is an baryonic-quark picture this value was just below BD¯ artifact due to rescattering at and above the D K threshold. − threshold, the value in the universal-quark picture is well While the current LHCb analysis [1] prefers a 1 assign- above threshold. ment, it is worth mentioning that if this peak is really due to JP ¼ 2þ We compare in Table IV the predictions for MðΞccÞ in a resonance, it would also populate the Dalitz plot the baryonic and universal quark mass schemes. The band at 2.9 GeV nonuniformly along its length. Such a state predictions of the two schemes are almost the same and could be a D K , very close to the threshold at both compatible with the observed value of ð3621.55 2902 MeV, with pion exchange providing a major part of 0.23 0.30Þ MeV [12]. The shift of three quark masses the attraction. On the other hand, the lighter and narrower þ each by about 55 MeV is compensated by the S term, and 0 state is 36 MeV below the D K threshold, which is the only remaining difference is about 8 MeV in the cc much too large for binding energy in a hadronic molecule. ¯ ¯ binding term. Hence, it is really only when one gets to The predictions for masses of the bbu¯ d; ccu¯ d, and ¯ configurations with two or more string junctions that a bcu¯ d masses are shifted upward in the string-junction distinction emerges. picture by 126, 118, and 122 MeV, respectively. The bbu¯ d¯ state is still stable with respect to strong and EM inter- TABLE III. Contributions to the mass of the lightest tetraquark actions, as its mass is predicted to lie 89 MeV below Tðbcu¯ d¯Þ with one bottom and one charmed quark and JP ¼ 0þ. threshold for strong decay and 44 MeV below that for radiative decay, while the ccu¯ d¯ and bcu¯ d¯ masses lie well Baryonic quarks Universal quarks above strong decay thresholds. Contribution Value (MeV) Contribution Value (MeV) The prediction of the doubly mass [3] 2S 330.2 based on baryonic quarks, MðΞccÞ¼3627 12 MeV, is b b m þ m mb þ mc 6754.0 b c 6644.2 only raised by 8 MeV in the string-junction picture with b 2mq 726.0 2mq 617.0 universal quark masses, still compatible with the exper- b b −25 5 −3a =ðm m Þ −25 5 ð3621 55 0 23 0 30Þ −3abc=ðmbmcÞ . bc b c . imental value of . . . MeV. b 2 2 −3a=ðmqÞ −150.0 −3a=ðmqÞ −151.2 Further tests of the physical picture discussed here will bc binding −170.8 bc binding −159.4 become possible when additional tetraquark states are observed experimentally. We hope that this will be possible Total 7133.7 13 Total 7255.3 13 in the foreseeable future.

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þþ In particular, since the doubly charmed baryon Ξcc ðccuÞ by LHCb in the seminar [1]; Lance Dixon, Gabriele has been observed by LHCb [4,12], the data accumulated Veneziano, and Jian-Rong Zhang for comments on the so far might make it possible to observe the Tðccu¯ d¯Þ manuscript; and Eulogio Oset for pointing out Ref. [13]. tetraquark decaying into D0Dþ and DþD0. The measured The research of M. K. was supported in part by NSFC-ISF mass will then tell us whether the string-junction descrip- Grant No. 3423/19. tion applies to this state as well or if the physical picture of Ref. [6] is more appropriate for a tetraquark with two truly Note added.—Recently, it was pointed out to us that a heavy quarks. prediction was made [13] using coupled-channel unitarity DþK− C ¼ 1 S ¼ −1 JP ¼ 0þ ACKNOWLEDGMENTS of a with , , , with pole mass of 2848 MeV (i.e., binding energy of We thank Alex Bondar, Tim Gershon, and Tomasz 54 MeV) and width between 23 and 59 MeV, depending on Skwarnicki for useful discussions about the data presented the value of a cutoff parameter.

[1] LHC Seminar, B → DDh¯ Decays: A New (Virtual) Labo- [7] E. J. Eichten and C. Quigg, Heavy-Quark Implies ratory for Exotic Searches at LHCb, edited by Stable Heavy Tetraquark Mesons QiQjq¯ kq¯ l, Phys. Rev. D. Johnson (CERN, Geneva, 2020), https://indico.cern.ch/ Lett. 119, 202002 (2017). event/900975; R. Aaij et al., A model-independent study of [8] G. C. Rossi and G. Veneziano, A possible description of resonant structure in Bþ → DþD−Kþ decays, arXiv: baryon dynamics in dual and gauge theories, Nucl. Phys. 2009.00025; Amplitude analysis of the Bþ → DþD−Kþ B123, 507 (1977). decay, arXiv:2009.00026. [9] G. Rossi and G. Veneziano, The string-junction picture [2] H. J. Lipkin, A unified description of mesons, baryons and of multiquark states: An update, J. High Energy Phys. 06 baryonium, Phys. Lett. B 74B, 399 (1978). (2016) 041. [3] M. Karliner and J. L. Rosner, Baryons with two heavy [10] M. Karliner, S. Nussinov, and J. L. Rosner, QQQ¯ Q¯ states: quarks: Masses, production, decays, and detection, Phys. Masses, production, and decays, Phys. Rev. D 95, 034011 Rev. D 90, 094007 (2014). (2017). [4] R. Aaij et al. (LHCb Collaboration), Observation of the [11] M. Karliner and J. L. Rosner, Interpretation of structure in þþ Doubly Charmed Baryon Ξcc , Phys. Rev. Lett. 119, the di-J=ψ spectrum, arXiv:2009.04429. 112001 (2017); First Observation of the Doubly Charmed [12] R. Aaij et al. (LHCb Collaboration), Precision mea- þþ þ þ þþ Baryon Decay Ξcc → Ξc π , Phys. Rev. Lett. 121, 162002 surement of the Ξcc mass, J. High Energy Phys. 02 (2018). (2020) 049. [5] We refer the reader to Refs. [4,3] for an extensive list of [13] R. Molina, T. Branz, and E. Oset, A new inter- other predictions. pretation for the Ds2ð2573Þ and the prediction of novel [6] M. Karliner and J. L. Rosner, Discovery of Doubly- exotic charmed mesons, Phys. Rev. D 82, 014010 ¯ Charmed Ξcc Baryon Implies a Stable (bbu¯ d) Tetraquark, (2010). Phys. Rev. Lett. 119, 202001 (2017).

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