Multiquark Hadrons Research Articles

Search for Θ+ in KLp→K+n reaction in KLF at JLab

The possibility of the existence of multiquark hadrons made of 4-quarks for mesons and 5-quarks for baryons was predicted by Gell-Mann [Phys. Lett. 8, 214 (1964)]. The renewed interest for the search for exotic pentaquark states was initiated by the paper by Diakonov, Petrov, and Polyakov [Z. Phys. A 359, 305 (1997)]. The 2003 experimental reports on the observation of [Formula: see text] pentaquark with [Formula: see text] quark content created a great excitement and many following experiments have reported its observation [K. H. Hicks, Eur. Phys. J. H 37, 1 (2012)]. After high-statistics experiments at JLab, which did not confirm previous claims by the CLAS collaboration, the community concluded that the [Formula: see text] pentaquark either does not exist at all or has an extremely small cross-section, making it currently unobserved. There were different review papers on this subject, questioning the existence of [Formula: see text] or trying to explain the reasons why reaching a conclusion based on production experiments is challenging [M. Amaryan, Eur. Phys. J. Plus 137, 684 (2022)]. To address the challenge of minimal 3-body final states, a formation experiment with a projectile-kaon beam is proposed. In the following, we discuss how the [Formula: see text] could be observed in the [Formula: see text] reaction in the KLF experiment at JLab [M. Amaryan et al. [KLF Collaboration], arXiv:2008.08215 [nucl-ex]].

Mission Target: Tetraquark Mesons of Flavour-Cryptoexotic Type

Currently, flavour-cryptoexotic tetraquarks form the most common sort of all experimentally established exotic multiquark hadrons. This note points out a few promising concepts that should help improve theoretical (but, for several reasons, not quite straightforward) analyses of this kind of states; among others, their scope of application encompasses the strong interactions in the limit of (arbitrarily) large numbers of colours, and equally analytical and nonperturbative approaches to multiquark states.

Axial-vector and pseudoscalar tetraquarks [ud][{overline{c}}{overline{s}}

Spectroscopic parameters and widths of the fully open-flavor axial-vector and pseudoscalar tetraquarks X_{textrm{AV}} and X_{textrm{PS}} with content [ud][{overline{c}}{overline{s}}] are calculated by means of the QCD sum rule methods. Masses and current couplings of X_{textrm{AV}} and X_{textrm{PS}} are found using two-point sum rule computations performed by taking into account various vacuum condensates up to dimension 10. The full width of the axial-vector state X_{textrm{AV}} is evaluated by including into analysis S-wave decay modes X_{textrm{AV}}rightarrow D^{*}(2010)^{-}K^{+}, {overline{D}}^{*}(2007)^{0}K^{0}, D^{-}K^{*}(892)^{+}, and {overline{D}}^{0}K^{*}(892)^{0}. In the case of X_{textrm{PS}}, we consider S-wave decay X_{textrm{PS}}rightarrow {overline{D}} _{0}^{*}(2300)^{0}K^{0}, and P-wave processes X_{textrm{PS}}rightarrow D^{-}K^{*}(892)^{+} and X_{textrm{PS}}rightarrow {overline{D}} ^{0}K^{*}(892)^{0}. To determine partial widths of these decay modes, we employ the QCD light-cone sum rule method and soft-meson approximation, which are necessary to estimate strong couplings at tetraquark–meson–meson vertices X_{textrm{AV}}D^{-}D^{*}(2010)^{-}K^{+} , etc. Our predictions for the mass m_{textrm{AV}}=(2800 pm 75)~text {MeV} and width Gamma _{textrm{AV}}=(58 pm 10)~text {MeV} of the tetraquark X_{ textrm{AV}}, as well as results m_{textrm{PS}}=(3000 pm 60)~text {MeV} and Gamma _{textrm{PS}}=(65 pm 12)~text {MeV} for the same parameters of X_{textrm{PS}} may be useful in future experimental studies of multiquark hadrons.

Diabatic representation of exotic hadrons in the dynamical diquark model

We apply the diabatic formalism, an extension of the adiabatic approximation inherent to the Born-Oppenheimer (BO) approach of atomic physics, to the problem of mixing between exotic multiquark hadrons and their nearby di-hadron thresholds. The unperturbed BO eigenstates are obtained using the dynamical diquark model, while the diabatic calculation introduces a mixing potential between these states and the threshold states. We solve the resulting coupled Schr\"odinger equations numerically for hidden-charm tetraquarks of both open and closed strangeness to obtain physical mass eigenvalues, and we explore the di-hadron state content and spatial extent of the eigenstates. As an explicit example, $X(3872)$ emerges with a dominant ${D}^{0}{\overline{D}}^{*0}$ component, but also contains a considerable diquark-antidiquark component that can contribute significantly to its radiative decay widths, and this component also generates a full multiplet of other diquark-based exotic hadrons to be compared with experiment.

Zooming in on Multiquark Hadrons within QCD Sum-Rule Approaches

Aiming at self-consistent descriptions of multiquark hadrons (such as tetraquarks, pentaquarks, hexaquarks) by means of QCD sum rules, we note that the totality of contributions to two-point or three-point correlation functions that involve, respectively, either two or just a single operator capable of interpolating the particular multiquark under study can be straightforwardly disentangled into two disjoint classes defined by unambiguously identifiable members. The first is formed by so-called multiquark-phile contributions which indeed might support multiquarks. In the case of flavour-exotic tetraquarks, by definition composed of four (anti–) quarks of mutually different flavours, a tetraquark-phile contribution has to exhibit two or more gluon exchanges of appropriate topology. The second consists of contributions evidently not bearing any relation to multiquarks; these must be discarded when studying multiquarks by QCD sum rules. The first class only should enter the “multiquark-adequate” QCD sum rules for exotic hadrons.

Multiquark-Oriented QCD Sum Rules

We propose to increase the factual reliability of descriptions of exotic multiquark hadrons utilizing the approach to bound states of strongly interacting constituents known as QCD sum rules, by allowing exclusively all contributions that potentially bear some relevance for multiquark states to enter the correlation functions that form the main ingredient of this framework. The route to this goal is illustrated for the (presumably least involved) special case of tetraquark states.

Search for and Study of Exotic Hadrons in the Fermilab D0 Experiment: Recent Results

Recent results of the studies of exotic multiquark hadrons in the Fermilab D0 experiment are reported. These refer to the search and investigation of the $${{Z}_{c}}(3900)$$ state produced in semi-inclusive beauty-hadron decays and to the search for prompt $${{Z}_{c}}(3900)$$ production in $$p\bar {p}$$ collisions. Results of D0 searches for inclusive production of $${{P}_{c}}(4440)$$ and $${{P}_{c}}(4457)$$ pentaquark states are also presented.

The dynamical diquark model: fine structure and isospin

We incorporate fine-structure corrections into the dynamical diquark model of multiquark exotic hadrons. These improvements include effects due to finite diquark size, spin-spin couplings within the diquarks, and most significantly, isospin-dependent couplings in the form of pionlike exchanges assumed to occur between the light quarks within the diquarks. Using a simplified two-parameter interaction Hamiltonian, we obtain fits in which the isoscalar JPC = 1++ state — identified as the X (3872) — appears naturally as the lightest exotic (including all states that are predicted by the model but have not yet been observed), while the closed-charm decays of Zc(3900) and Zc(4020) prefer J/\U0001d713 and hc modes, respectively, in accord with experiment. We explore implications of this model for the excited tetraquark multiplets and the pentaquarks.

Thermal behaviors of exotic $$Z_{c}$$ (3900) state in tetraquark approach

The discovery of the charged $$Z_{c}$$(3900) exotic resonance with the quantum numbers $$J^{P}$$= $$1^{+}$$ has crucial consequences for comprehending the nature of multi-quark hadrons. In this work, the meson-current coupling constant and mass of $$Z_{c}$$ state are calculated using the Thermal QCD Sum Rules method. We suppose that the positively charged state $$Z_{c}$$ has a quark content $${\bar{c}}cu{\bar{d}}$$ and use tetraquark current with the corresponding quantum numbers. We evaluate the two-point correlation function taking into account the non-perturbative condensates up to six-dimension. We found the hot medium contributions to hadronic parameters of the $$Z_{c}$$ state and exhibit that its meson-current coupling constant and mass are unsusceptible to the change of temperature in low temperature region, but these parameters significantly change in the vicinity of phase transition region. At critical temperature, the meson current-coupling constant reaches approximately to 10% of its vacuum value, while the mass decreases about 28%.

The dynamical diquark model: first numerical results

We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schrödinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.

Tetraquarks, pentaquarks and dibaryons in the large N QCD

We study the multiquark hadrons in large N QCD under the ’t-Hooft limit, extending Witten’s picture of the baryons. We explore the decay widths of tetraquarks, pentaquarks and dibaryons. Based on the decay behaviors, we point out that in the Nrightarrow infty limit decay widths of tetraquarks stay constant, while those of pentaquarks and dibaryons above certain thresholds can diverge. In the large N limit, we find that the ground states of the three spectroscopic series are stable or narrow and that the excited states of pentaquarks and dibaryons above the indicated thresholds are not observables. We compare our results with those obtained in previous large N generalizations of tetraquarks.

Tetraquark and Pentaquark Systems in Lattice QCD

Motivated by the recent experimental discoveries of multi-quark candidates, e.g., the $\Theta^+(1540)$, we study multi-quark systems in lattice QCD. First, we perform accurate mass measurements of low-lying 5Q states with $J=1/2$ and I=0 in both positive- and negative-parity channels in anisotropic lattice QCD. The lowest positive-parity 5Q state is found to have a large mass of about 2.24GeV after the chiral extrapolation. To single out the compact 5Q state from $NK$ scattering states, we develop a new method with the hybrid-boundary condition (HBC), and find no evidence of the compact 5Q state below 1.75GeV in the negative-parity channel. Second, we perform the first study of the multi-quark potential in lattice QCD to clarify the inter-quark interaction in multi-quark systems. The 5Q potential $V_{\rm 5Q}$ for the QQ-${\rm \bar{Q}}$-QQ system is found to be well described by the ``OGE Coulomb plus multi-Y Ansatz": the sum of the one-gluon-exchange (OGE) Coulomb term and the multi-Y-type linear term based on the flux-tube picture. The 4Q potential $V_{\rm 4Q}$ for the QQ-${\rm \bar{Q}\bar{Q}}$ system is also described by the OGE Coulomb plus multi-Y Ansatz, when QQ and $\rm \bar Q \bar Q$ are well separated. The 4Q system is described as a "two-meson" state with disconnected flux tubes, when the nearest quark and antiquark pair is spatially close. We observe a lattice-QCD evidence for the ``flip-flop'', i.e., the flux-tube recombination between the connected 4Q state and the ``two-meson'' state. On the confinement mechanism, the lattice QCD results indicate the flux-tube-type linear confinement in multi-quark hadrons.

Heavy flavour hadron spectroscopy: An overview

A comprehensive overview and some of the theoretical attempts towards understanding heavy flavour hadron spectroscopy are presented. Apart from the conventional quark structure (quark, antiquarks structure for the mesons and three-quarks structure of baryons) of hadrons, multiquark hadrons the hadron molecular states etc., also will be reviewed. Various issues and challenges in understanding the physics and dynamics of the quarks at the hadronic dimensions are highlighted. Looking into the present and future experimental prospects at different heavy flavour laboratories like BES-III, CLEO-c, BaBar, Belle, LHC etc., the scope for theoretical extensions of the present knowledge of heavy flavour physics would be very demanding. In this context, many relevant contributions from the forthcoming PANDA Facility are expected. Scopes and outlook of the hadron physics at the heavy flavour sector in view of the future experimental facilities are highlighted.

Charmed exotics in heavy ion collisions

Based on the color–spin interaction in diquarks, we argue that charmed multiquark hadrons are likely to exist. Because of the appreciable number of charm quarks produced in central nucleus–nucleus collisions at ultrarelativistic energies, the production of charmed multiquark hadrons is expected to be enhanced in these collisions. Using both the quark coalescence model and the statistical hadronization model, we estimate the yield of charmed tetraquark mesons, Tcc, and pentaquark baryons, Θcs, in heavy ion collisions at RHIC and LHC. We further discuss the decay modes of these charmed exotic hadrons in order to facilitate their detections in experiments.

Explanation why theΘ+is seen in some experiments and not in others

To understand the whole set of positive and null data on the Theta+(1530)-production, we suggest the hypothesis that multiquark hadrons are mainly generated from many-quark states, which emerge either as short-term hadron fluctuations, or as hadron remnants in hard processes. This approach allows us to describe both non-observation of the Theta+ in current null experiments and peculiar features of its production in positive experiments. Further, we are able to propose new experiments that might be decisive for the problem of the Theta+ existence. Distributions of the Theta+ in such experiments can give important information both on higher Fock components of conventional hadrons and about structure and hadronization properties of hadron remnants produced in hard processes. We also explain that description of multiquark hadrons may require a modified form of the constituent quark model, with quark masses and couplings being intermediate between their values for the familiar constituent quarks and the current ones.

Experimental searches for exotic multiquark particles

Experimental searches for "exotic" multiquark hadrons are reported. In a hyperon beam experiment at the Organisation Européenne pour la Recherche Nucléaire-superproton synchrotron (CERN-SPS), evidence was found for narrow states at 3.1 GeV/c2, with charges + 1,0, and −1, decaying into Λ, [Formula: see text], and pions. Similar signals were also seen in a neutron beam experiment at Serpukhov. These states, called U (3100), are tentatively explained as [Formula: see text] systems, i.e., [Formula: see text]. Such states were proposed more than a decade ago. New hyperon beam experiments in preparation at CERN and Fermilab will study these states, provided they exist. The proposed multiquark systems H = uuddss and [Formula: see text] are also discussed. One candidate for the decay H(2175) → Σ−p was observed in a propane buble chamber exposed to a proton beam. At Brookhaven National Laboratory, a missing-mass experiment in a high-intensity K− beam will search for the H, and the new hyperon beam experiments will search for inclusive production of both H and P.

Flux-tube model for hadrons in QCD.

We extract from the strong-coupling Hamiltonian lattice formulation of QCD a model for hadrons based on the use of quark and flux-tube degrees of freedom. The ordinary quark model of mesons and baryons is recovered as an appropriate limit, but the properties of hybrids, pure glue, and multiquark hadrons are also predicted by the model. The basic tenets of the model can be tested by lattice Monte Carlo simulations.

Hadronization of quark systems

Hadronization in simple models of quark systems is discussed with emphasis on the combinatorial aspects. The numberN of quarks and the numberN c of colours are the relevant variables. In onedimension and in the meson and baryon sector the problem is completely soluble. When multiquark hadrons are included an iterative procedure still allows a complete solution. Higher dimensions are difficult to treat but global hadronization, without dimensionality constraints, is again soluble. As a general result the baryon/meson ratio is, for large quark densities, rather large, ≳1/3 and may grow without limit asN→∞.

Pionic corrections and multi-quark bags

The authors investigate the influence of pionic corrections on multi-quark hadrons. After determining the bag parameters from ordinary baryons and mesons, they discuss the implications for six-quark configurations.

Multi-Quark Hadrons in the Joined-Spring Quark Model

The level structures of typical multi-quark exotic hadrons, (q2 q2 )-meson, (q' q )-baryon and (q6)-di-baryon with only nuclear quarks, are investigated systematically in the joined spring quark model, where hadron masses squared are described in terms of harmonic oscillators with various quanta. This model was proposed by us as a simple idealization of the string-junction model so as to make it possible a quantum mechanical treatment of constituent quarks. An interesting prediction of our model is that there exist orbital Regge trajectories with the steeper slope than the usual one for non-exotic hadrons_ Somewhat strong experimental suggestions for existence of these trajectories are seen for all respective cases of exotic hadrons.