Highlights About the J∕ J∕ peak of LHCb: fully-charmed tetraquark?

Jean-Marc Richard

• Exotic hadrons • LHCb experiment

• Constituent quark model arXiv:2008.01962v1 [hep-ph] 5 Aug 2020 About the J∕ J∕ peak of LHCb: fully-charmed tetraquark? ∗ Jean-Marc Richard ,1 aInstitut de Physique des 2 Infinis, IN2P3 & Université Claude Bernard, 4 rue Enrico Fermi, 69622 Villeurbanne, France

ARTICLEINFO ABSTRACT

Keywords: We discuss the interpretation of the J∕ J∕ peak recently seen by the LHCb collaboration at CERN, exotic hadrons and take the opportunity to review the experimental and theoretical state of the art for exotic hadrons. LHCb It is stressed that in constituent models, the states in the continuum require a dedicated treatment to quark model single out resonances atop the continuum.

Since several decades, a particular attention has been old, and a width of about 80 MeV, and this revitalized the devoted to hadrons with anomalous properties [1–5]. On studies about multiquark resonances made of heavy quarks the experimental side, the search has been very difficult and and antiquarks. This is a very important step in the explo- disappointing. For instance, in the early 60s, there has been ration of the heavy hadrons, after the charmonium c ̄c in 1974, some claims for baryons resonances with strangeness S = +1, the charmed hadrons c ̄q and cqq in the following years (here ̄ the so-called Z baryons, while the established baryons have q denotes a light quark), the bottomonium bb in 1977, and either S = 0 or S < 0. But the Z spectrum was based on then the mesons and baryons carrying beauty, the Bc = b ̄c + somewhat hazardous analyses of K -nucleon scattering data in 1996 at Fermilab, and the double-charm baryons ccq in without spin observables, and it faded away. It reappeared 2017 by LHCb. For a review of the salient contributions to under the name of  pentaquark, but it was never firmly the early part of this history, see, e.g., Ref. [8]. established. So far, J∕ J∕ is just the discovery channel. Obviously, Another example is the set of “baryonium” mesons [1], the measurement of other properties is desirable. In particular, preferentially coupled to baryon-antibaryon channels, and the decay into other pairs of charmonia, cc, c J , ...would seen as peaks in antinucleon-induced reactions. A low-energy be crucial for identifying the quantum numbers and screening antiproton facility was built at CERN in the 80s to study the the internal dynamics. The literature will very probably privi- baryonium, as a side product of the search for W and Z lege either a four-quark state, or a “molecular” system of two bosons in high-energy antiproton-proton collisions, but none charmonia with, perhaps, higher Fock components. There of the baryonium candidates was confirmed. is an abondant literature on molecular hadrons, as reviewed, From the above examples, and others, it became clear that e.g., in Ref. [5]. Its extension for a system of two charmo- the search for exotic hadrons requires intense beams, pow- nia is in order, with an interaction which is probably very erful detectors and sophisticated programs for the analysis. short-ranged. Heavier molecules with double hidden-charm With the advent of charm and beauty factories, i.e., high- can be envisaged, made of excited charmonium states or a ̄ intensity electron-positron colliders and the newest hadronic baryon-antibayron pair with double-charm, ΞccΞcc [9]. colliders, more reliable data have been acquired, and, indeed, On the theory side, a peak in such a hadron-hadron mass remarkable hadronic states have been discovered. distribution stimulates new debates on an old problem: are The first and most emblematic state of this “new gener- there hadrons beyond the quark-antiquark mesons and the ation” is the X(3872), a meson with hidden charm, but not baryons made of three quarks? The molecular picture is fitting any radial and/or orbital excitation of charmonium, supported by effective field theories: an effective Lagrangian i.e., having a structure more complicated than a mere charm is designed, inspired by QCD, and adapted to a specific sector quark-antiquark pair c ̄c. The X(3872), first discovered with of the hadron spectrum. At the quark-gluon level, the most an electron-positron machine, has been confirmed in a variety advanced method is lattice QCD, in which the space-time of experiments. For a review, see, Ref. [5], with a critical is discretized [5].We shall restrict here to simple constituent discussion of other hidden-charm or hidden-beauty mesons. models that already give a good insight on the problem of New pentaquark states have also been discovered by LHCb, the existence of multiquarks. again with hidden-charm content. The name “pentaquark” The simplest multiquark configuration consists of two refers to baryons with a minimal content of four quarks and quarks and two antiquarks. The light sector is somewhat one antiquark. The LHCb pentaquarks have been described the realm of chromomagnetism, and, in particular, the qq ̄q̄q in Ref. [6]. states have been categorized according to the eigenvalues ∑ ̃ ̃ Recently, the same LHCb collaboration has found a peak of the color-spin operator ilead to

J.-M. Richard: Preprint submitted to Elsevier Page 1 of 2 J∕ -J∕ resonance stable multiquarks in the dibaryon sector such as uuddss, or attraction, a chromoelectric effect, and if qq = ud, a favor- the sector of anticharmed baryons such as ̄cuuds, as reviewed, able chromomagnetic attraction. This will perhaps be the e.g., in Ref. [3]. first stable multiquark, besides the deuteron. Amazingly, the As the mass of the constituent quarks increases, the chro- chromo-electric effect is similar to the observation that the hy- − − momagnetic term vanishes, as it contains for each pair a drogen molecule ppe e is more stable than the positronium + + − − 1∕(mi mj) factor, like in the Breit-Fermi interaction in atomic molecule e e e e , due to a favorable symmetry breaking. physics. Hence the spectroscopy becomes dominated by the chromoelectric interaction, and in the simplest model, the Conflict of interest Hamiltonian reads The author declares that he has no conflict of interest. 2 É p 3 É H = i − ̃ .̃ v(r ) , Acknowlegments m i j ij (1) i 2 i 16 itetraquarks, Phys. Rev. C 97 (3) (2018) the Hamiltonian of Eq. (1) can be modified to include a non- 035211. pairwise interaction for the confining part, which turns out [11] Q. Meng, E. Hiyama, K. U. Can, P. Gubler, M. Oka, A. Hosaka, H. Zong, Compact sssc ̄c pentaquark states predicted by a quark model, more attractive; see, e.g., [3, 10]. Phys. Lett. B 798 (2019) 135028. A rather popular model, nowadays, describes the baryons [12] M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, D. B. Lichten- and the multiquarks in terms of diquarks. This is a rather berg, Diquarks, Rev. Mod. Phys. 65 (1993) 1199–1234. old idea, though the contributions of the pioneers [12] are not always acknowledged. If the diquark D is taken as an DD̄ Jean-Marc Richard received his doctorate in physics effective degree of freedom, the difficulty is to relate the at the University of Paris in 1975. He started his spectrum to the quarkonium masses that enter the threshold. carreer as Assistant-Professor in Orsay, and he is Now, the diquark sometimes appears as a short-cut to avoid now Emeritus Professor at the University of Lyon. the complications of the four-body problem, but it turns out During sabbatical leaves, he visited Stony-Brook, Brookhaven, Aarhus, Heidelberg, Bonn, Trento, that this approximation tends to overbind, with the risk of ILL and CERN. His research focuses on nuclear transforming resonances into bound states [10]. physics, hadron physics, and few-body systems in An interesting interplay of light-quark and heavy-quark atomic physics. physics is provided by the QQ ̄q̄q configuration with dou- ble heavy flavor, first discussed decades ago (see Ref. [3]), and now regularly revisited. As compared to its threshold Q ̄q + Q ̄q, it benefits from two advantages: the strong QQ

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