PHYSICAL REVIEW D 102, 094016 (2020) First exotic hadron with open heavy flavor: csu¯ d¯ tetraquark † 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 Æ 7 MeV, Γ0 ¼ 57 Æ 13 MeV and X1ð2900Þ with J ¼ − ¯ 1 at 2904 Æ 7 MeV, Γ1 ¼ 110 Æ 12 MeV. We interpret the X0ð2900Þ component as a csu¯ d isosinglet compact tetraquark, calculating its mass to be 2863 Æ 12 MeV. This is the first exotic hadron with open heavy flavor. The analogous bsu¯ d¯ tetraquark is predicted at 6213 Æ 12 MeV. We discuss possible interpretations of the heavier and wider X1ð2900Þ state and examine potential implications for other systems with two heavy quarks. DOI: 10.1103/PhysRevD.102.094016 Very recently, the LHCb Collaboration reported a narrow b quark results in a significant shift of the tetraquark mass peak in the DþK− (þ charge conjugate) ( c:c:) channel as vs the two-meson threshold. seen in the decay BÆ → DþD−KÆ. 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∶ mesons and baryons [2], with baryonic quarks approxi- P þ mately 55 MeV heavier than mesonic ones. We used this J ¼ 0 ;M¼ 2866 Æ 7 MeV; Γ0 ¼ 57 Æ 13 MeV; ð1Þ method to successfully anticipate [3] the mass of the doubly charmed baryon 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 Æ 5 ; Γ ¼ 110 Æ 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 tetraquarks 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 ground state JP ¼ 0þ tetraquark composed of bbu¯ d¯ tetraquark expected well below BBà threshold. csu¯ d¯, finding preference for the former in light of the new The I ¼ 0 and JP ¼ 0þ isospin, spin, and parity 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 *[email protected] 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 strange quark 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 → DÃKà (e.g., via pion 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 Æ 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 BÃKà threshold at notation of Ref. [6] to obtain 6216 MeV, while the 0þ ðcsu¯ d¯Þ state in the charm sector at 2866 MeV is close to the DÃKà 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 diquark 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;barÞ¼2754.1Æ12MeV, 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 kaons. 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 Æ 12Þ MeV: ð5Þ breaking is ignored. where the theoretical error is that encountered in fits to light- Baryonic quarks Universal quarks quark hadrons [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 ÁÁÁ ÁÁÁ 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 Æ 12 Total 10514.9 Æ 12 in the Dalitz plot giving rise to that state must be due to 094016-2 FIRST EXOTIC HADRON WITH OPEN HEAVY FLAVOR: … PHYS. REV. D 102, 094016 (2020) 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.