Multiquark resonances
Introduction
Yet another review on tetraquarks, pentaquarks, and all that?
Indeed this paper comes after a number of encyclopædic reviews on the theme appeared since the discovery of the — see [1], [2], [3], [4], [5] and the latest, very comprehensive [6].
Despite the considerable amount of information provided by these articles, what presented here is a further attempt to report more specifically on those efforts made to find simple theoretical descriptions, even though incomplete, which include and explain, in a unitary picture, most of the exotic resonances observed at the time of this writing. Along these lines, some new arguments and work in progress will also be presented.
We assume that there is a common theoretical description of the , , , , , , and the pentaquarks, and we collect those ideas which appear to us to be functional to formulate such a comprehensive picture, even if it cannot yet be considered as complete and satisfactory.
The non-observation of , the isospin violating decay pattern of , the absence of partners in the beauty sector, which challenge the compact tetraquark interpretation [7], [8], are taken as starting points of our analysis.1 On the other hand, an obvious merit of compact tetraquark models was that of strongly motivating the research on charged resonances, which were eventually copiously observed, contrary to most expectations.
The evident proximity of meson–meson thresholds to the observed states, which appears as an impressive fine-tuning in the case of the , is also taken as a serious indication which, in the light of available data, seems unlikely to be accidental.
Meson molecule models have the same problem with the proliferation of states, despite of the attempts made to solve it. Moreover they have definitive problems at explaining prompt production at hadron colliders, especially in the case of the . Bona fide molecules like the deuteron are observed at hadron colliders, but only at very low transverse momenta, contrary to the , which is detected at extremely large transverse momenta (). These are very serious features, often forgotten, which should not be ignored.
Because of these and other reasons, explained with more details in the text, we might conclude that none of these two models reaches a fully satisfactory or definitive description of what observed in experiment, even though we must recognize a certain degree of success of both of them at explaining the features of some specific resonances.
On the other hand, we are convinced that diquark degrees of freedom are essential for the construction of a theory of multiquark resonances and that most of the work done in refining the predictions of the diquarkonium picture must be part of it.
What has been missing in the diquarkonium model are sort of ‘selection rules’ explaining the paucity of states which have been observed over the years. Same for the hadron molecules. Together with the presentation of hadron molecule and diquark–antidiquark models, we collect here some ideas we have been working on, which never appeared in an extensive discussion, to show one possible way to describe and resonances as the result of an effective interaction in meson–meson channels leading to the formation of resonant metastable states. This effective interaction is due to the presence of the discrete spectrum of diquarkonia immersed in the continuum spectrum of would-be molecules.
Special conditions are needed to switch on this interaction, but once they are met, sharp resonances are expected to be produced. These conditions strongly restrict the number of possible states and we have used the best experimentally assessed tetraquark resonance to test the picture. This discussion is presented in Section 6 and the arguments there formulated are admittedly not yet fully satisfactory, although showing rather suggestive aspects.
The paper is organized as follows.
We first analyze the core of ideas and methods at the basis of meson molecule models, starting from those textbook results on low energy scattering which we found useful to set the frame for the arguments to be developed. We criticize the limits of the hadron molecule approach, and discuss just some of the various technical solutions employed. This is done in Sections 2 Scattering in presence of shallow bound states, 3 Loosely bound molecules.
In Section 4 we present the diquarkonium model and the methods developed to obtain a spectrum of states which remarkably reproduces the mass pattern. The limitation of this model resides in the number of states predicted which, at the time of this writing, have not been observed. If in some future the experimental picture will be revolutionized by the appearance of the large number of expected resonances, together with states (which mysteriously evaded observation until now) etc., the diquarkonium model alone will certainly be, in our view, the strongest and most grounded option to describe this physics.
A more theoretical discussion of tetraquarks in the expansion [9] adds confidence on the specific role of diquarks as the right degrees of freedom to treat the emergence of tetraquark poles in meson–meson amplitudes. This is discussed in Section 5, which reproduces some results recently obtained.
This review might be read as a standalone research paper by skipping the first five sections. Section 6 stems from some work initiated in [10] and especially in [11]. However incomplete it might appear, the approach presented appears to us as one of the possible routes which should be explored to overcome the phenomenological problems of resonances.
In addition to this, in Section 7 we have presented known results on some interesting approaches, which are needed to offer a coherent picture of the work done in the field, going beyond the molecule picture of hadrons held together by nuclear forces. This is also done with the purpose of underscoring the efforts towards a ‘unified’ approach to the description of the observed phenomenology.
A report on the experimental situation can be found in the last part of the review, Section 8. We go through resonance by resonance, referring to the theoretical interpretations presented in the paper and highlighting connections and common features. The aim is always that of finding more or less hidden connections among the observed resonances. This part is intended to be a guide to the existing spectroscopy, especially meant for ‘model-building’ purposes. We omit a number of details which have been presented in other reviews.
The discussion on pentaquarks is limited to a brief report on what has already been done, especially in the diquark model. Pentaquarks were, before their discovery, a highly undesirable option for hadron molecules. If new resonances with tetraquark or exaquark quantum numbers will be discovered, and if the approach described in Section 6 will resist to new forthcoming data on tetraquarks, it might straightforwardly be applied to more complex hadron structures. The rules for doing these steps are explained, as we understand them at the moment.
Most likely to explain the nature of resonances does not require ‘new physics’, in the most common adopted meaning, but likely some conceptual leap in the use of ‘old’ strong interaction dynamics. We also do not think that resonances are sort of nuclear chemistry phenomena as they also occur, as witnessed by the prompt production of the , at very large transverse momentum.
We hope to offer in this paper some perspective on the field and hopefully a support to identify new research directions.
There is some confusion about the naming of the resonances. At the beginning, the letters , and were used with no clear criteria. The PDG decided to call all the exotic quarkoniumlike states, with the exception of the (initially , then promoted to the ordinary charmonium name in the PDG 2014, now assessed). However, a sort of convention is generally followed in the literature, which calls the charged quarkoniumlike states, the vector ones, the pentaquarks, and all the other ones. We will follow this convention, with the addition of the superscripts and subscripts used by Belle and BES III, to wit , as well as for the hidden charm pentaquarks. We call the state seen in (known in the past as ), the state seen in (known in the past as , , or ), the state seen in (sometimes called ).
The charged conjugated modes are always understood, unless specified. The convention for the phases is such that , while . The reader has to pay attention to different conventions used in the literature.
With a little abuse of notation, we will talk of -parity for charged states, meaning “the -parity eigenvalue of the neutral isospin partner”.
We do not discuss the former and the , which are good candidates for the ordinary charmonia and , respectively.
A detailed analysis of the experimental status of multiquark resonances will be presented in the last section of this report, together with their theoretical interpretations and references to experimental analyses.
Here we shall briefly review the basic experimental facts about the most compelling resonances to set the stage for the discussion to follow.
The first clearly exotic multiquark resonance is the , first claimed by Belle in 2007, but confirmed only in 2014 by the LHCb collaboration. It was observed in the channel, i.e. . The quark from the weak transition makes a with a quark from a vacuum pair. The remaining and quarks, together with the pair, constitute the valence of the resonance. How does hadronization work in this process? Is the resonance, otherwise dubbed , a compact four-quark hadron, like a baryon or a meson, but with a different quark skeleton? Or is it just a hadron molecule kept bound for a finite lifetime by long range residual strong interactions?
In 2013 another resonance, the , was observed simultaneously by BES III and Belle, as a decay product of the with being a neutral state, produced in initial state radiation in collisions. is also a multiquark resonance candidate, albeit neutral, with a quark pair in its valence. Therefore the resonance, otherwise dubbed , has again a minimal valence quark content of four, and .
The appears in the three states of charge, and the same occurs for , another, slightly heavier resonance, also found in BES III data and also unequivocally exotic.
The most aged of these resonances is however the neutral , first observed by Belle in 2003 in the decays of the meson, and then confirmed by all collider experiments. This can be also be found in the decay product as well as promptly produced at the vertex of hadronic collisions. The has quantum numbers, as confirmed with a high degree of precision. This resonance encodes some very problematic features
- 1.
It does not have charged partners (so far);
- 2.
Its mass is almost perfectly fine-tuned to the mass of the meson pair;
- 3.
It decays into and with almost the same branching fraction;
- 4.
It is an extremely narrow resonance, its width being ;
- 5.
It is almost degenerate to the resonance.
The absolute neutralities of the and , which seem to be experimentally well assessed at the time of this writing, do not speak loud as a signal of a four-quark structure, as it is instead the case for , and . On the other hand we have to observe that a charmonium cannot decay violating isospin. A more complex quark structure is therefore needed. The spectacular vicinity to the threshold has suggested to many that the is a loosely bound molecule. It is from this latter picture that we will start our discussion on models of resonances, in the next section.
Summarizing, in the charm sector we have and . The latter might not be included among the lowest states — it can be considered as a radial excitation of . In addition we have the , which might be considered as an orbital excitation of .
Therefore, on the basis of some elementary theoretical assumptions, let us stick to the three resonances , , , reminding that the appears only in the neutral state of charge, differently from the other two. Is this pattern repeated in the beauty sector? The answer that we can give to this question, on the basis of present data, is ‘not entirely’.
Indeed a pair of resonances have been found in the -sector, , very close to where expected on the basis of simple quark mass considerations–and again very close to the thresholds–and in the three states of charge. But no trace of a neutral or charged has been observed so far.
Strange valence quarks can be found in another resonance, first observed in 2009 by the CDF collaboration in named . The quark content is and very recently the LHCb collaboration has confirmed its existence and discovered similar resonances at higher masses.
In late 2015, two charged pentaquarks were observed in baryon decays the lowest lying with quantum numbers and the next with , with masses at 4380 and 4550 respectively. The exotic nature of pentaquarks, sometimes dubbed as , is very clear, as it is the case for the s and s.
On the basis of what said, we might also observe that low lying four-quark states appear with positive parities whereas five-quark ones with negative.
Table 1 enumerates the properties of the states we briefly discussed here. To our understanding, those listed are the more solid multiquark resonances on experimental grounds. Probably the amount of data available at this time is not yet sufficient to fully understand the nature of resonances, but this is the challenge undertaken by many, which we mean to review in this paper.
Section snippets
Scattering in presence of shallow bound states
In this and in the following Section 3, we will collect some known results from low energy scattering theory and present, especially in Section 3, some arguments on the limitations of the loosely bound hadron molecule approach to the interpretation of the resonance.
The molecule interpretation of the is however very popular, and is functional to explain the isospin violation pattern. Thus we start from our discussion on models of multiquark resonances from this
Loosely bound molecules
This section is devoted to the molecular picture of the , trying to cover most of its implications. We will also discuss how the relation between binding energy and total decay rate constrains the most simple hadron molecule interpretation, with particular reference to the case of the , and we will remark that a deuteron-like interpretation of has to confront with data on the production of light nuclei in and Pb-Pb collisions at the LHC.
Diquark building blocks
Heavy–light diquarks were introduced by Maiani et al. in [7] to discuss the following the suggestion of Jaffe and Wilczek [77] to use light diquarks in exotic spectroscopy, with particular reference to some experimental hints of a light pentaquark.
Evidence that in a tetraquark system the two quarks arrange their color in a diquark before interacting with the antiquarks has also been found on the lattice in the static limit [78]. The same authors also show how the four constituents
Tetraquarks and diquarks in the expansion
This section is especially based on a work by Maiani et al. on tetraquarks in the expansion [9], where is the number of colors, following a stream of papers on the same subject initiated by Weinberg [124]. The contributions to this discussion by Knecht and Peris [125] and Cohen and Lebed [126] were also particularly useful to us.
The reputation of tetraquarks was somehow obscured by a theorem by S. Coleman and E. Witten [127], [128] stating that: tetraquarks correlators for reduce
An alternative picture of resonances
In this section we propose some arguments on an alternative explanation of the exotic hadron spectrum of resonances, following some early discussions appeared in [10], [11], [30]. Differently from other sections, this one contains a higher fraction of material not discussed before and it relies on results discussed in Sections 2 Scattering in presence of shallow bound states, 4 Diquark building blocks, 5 Tetraquarks and diquarks in the. The mechanism we are going to describe, has been
Other models and approaches
In this section we illustrate other options for the description of phenomenology. These were proposed since the early days after the discovery of the and the and might have a somewhat more restricted application since they do not apply ‘systematically’ to all of the observed states. The fact that observed resonances should all be of the same nature contains admittedly some prejudice, which motivated many of the arguments made in this review. Until a widely accepted
A travel guide to experimental results
We present here a short summary of the most important experimental results in the exotic sector. This chapter does not aim to cover entirely the large number of papers published on this topic, but rather to give a synthetic review of the aspects which appear more relevant from the theoretical point of view. In doing so, we will not follow the chronological order. Whenever available, we will calculate averages using the new published measurement, to update the results shown in the PDG 2014.
Conclusions and outlook
A considerable part of the material presented in this review is selected from the vast literature on the resonances, with the scope of preparing the discussion appearing in the core sections in which we have much further elaborated on some new ideas published recently by our group. The main drive of this paper is to present a clear identification of the most striking conflicts of models with data and the indication of one (or more) possible ways to the solution of them. In some few cases
Acknowledgments
Most of the work presented here derives from invaluable collaboration with Luciano Maiani, Fulvio Piccinini and Veronica Riquer. They are all implicitly coauthoring this paper, exception made for what is imprecise or even wrong, which is our full responsibility. Along the years we benefited of the collaboration of Riccardo Faccini, who helped us to find the way in some experimental data analysis intricacies, and of a number of collaborators each of them contributing with their insight and work
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