Exotic baryon states in topological soliton models

The novel observation of an exotic strangeness S=+1 baryon state at 1.54 GeV is to trigger an intensified search for this and other baryons with exotic quantum numbers. This state was predicted long ago in topological soliton models. We use this approach together with the new datum in order to investigate its implications for the baryon spectrum. In particular, we estimate the positions of other pentaquark and septuquark states with exotic and with nonexotic quantum numbers.     

A new hadron spectroscopy

QCD-motivated models for hadrons predict an assortment of “exotic” hadrons that have structures that are more complex than the quark-antiquark mesons and three-quark baryons of the original quark-parton model. These include pentaquark baryons, the six-quark H-dibaryon, and tetraquark, hybrid and glueball mesons. Despite extensive experimental searches, no unambiguous candidates for any of these exotic configurations have been identified. On the other hand, a number of meson states, one that seems to be a proton-antiproton bound state, and others that contain either charmed-anticharmed quark pairs or bottom-antibottom quark pairs, have been recently discovered that neither fit into the quark-antiquark meson picture nor match the expected properties of the QCD-inspired exotics. Here I briefly review results from a recent search for the H-dibaryon, and discuss some properties of the newly discovered states -the proton-antiproton state and the so-called XY Z mesons- and compare them with expectations for conventional quark-antiquark mesons and the predicted QCD-exotic states.     

Searches for exotic baryons of isospin 5/2 that consist of light quarks

The status of isospin-5/2 exotic baryons consisting of light-quarks is considered. A brief survey of theoretical studies devoted to them is given. Experimental searches for exotic baryons are traced from the first publication on the subject to the present day. Among possible candidates for an exotic baryon, the pentaquark baryon E _{5/2 5/2} of mass M ≈ 1.44 GeV/c ² and width Γ < 0.05 GeV/c ² is the most probable. This state was recorded in six studies at five different facilities. Among these, there are two studies where the excess of the signal above the background is more than five standard deviations. The possibility of further searches for exotic baryons in various reactions is discussed.     

Pentaquarks in the Jaffe-Wilczek approximation

The masses of \(uudd\bar s,{\text{ }}uudd\bar d\), and \(uuss\bar d\) pentaquarks are evaluated in a framework of both the effective Hamiltonian approach to QCD and the spinless Salpeter equation using the Jaffe-Wilczek diquark approximation and the string interaction for the diquark-diquark-antiquark system. The pentaquark masses are found to be in the region above 2 GeV. That indicates that the Goldstone boson exchange effects may play an important role in the light pentaquarks. The same calculations yield the mass of \([ud]^2 \bar c\) pentaquark ～3250 MeV and \([ud]^2 \bar b\) pentaquark ～6509 MeV.     

Mixing of pentaquark and molecular states

There are experimental evidences for the existence of narrow states Θ ⁺ and Θ _c with the same quantum numbers of and pentaquarks and also NK ^(*) and ND ^(*) molecular states. Their masses deviate from many theoretical estimates of the pure pentaquark and molecular states. In this work we study the possibility that the observed Θ ⁺ and Θ _c are mixtures of pure pentaquark and molecular states. The mixing parameters are in general related to non-perturbative QCD which are not calculable at present. We determine them by fitting data from known states and then generalize the mechanism to Θ _b to predict its mass and width. The mixing mechanism can also naturally explain the narrow width for Θ ⁺ and Θ _c through destructive interferences, even if the pure pentaquark and molecular states have much larger decay widths. We also briefly discuss the properties of the partner eigenstates of Θ ⁺ and Θ _c and the possibility of experimentally observe them. Moreover, probable consequences of multi-state mixing are also addressed. Received: 6 March 2005, Revised: 29 July 2005, Published online: 27 September 2005 An erratum to this article is available at .     

Solitons bound to heavy mesons

We improve the bound state approach of the Skyrme model applied to the heavy baryons by adopting a static heavy meson picture where the soliton moves around the fixed heavy meson. This allows to take into account the center of mass corrections in a more consistent way. The bound state masses so obtained are comparable to the experimentally observed Λ _c and Λ _c ^* masses. A loosely bound state of a soliton with an antiflavored heavy meson is found, which leaves a possibility of the nonstrange pentaquark baryon(s).     

Understanding pentaquark States in QCD

We estimate the mass of the pentaquark state with QCD sum rules and find that pentaquark states with isospin I=0,1,2 lie close to each other around (1.55+/-0.15) GeV. The experimentally observed baryon resonance Theta(+)(1540) with S=+1 can be consistently identified as a pentaquark state if its J(P)=1 / 2(-). Such a state is expected in QCD. If its parity is positive, this pentaquark state is really exotic. The outstanding issue now is to determine its quantum numbers experimentally.     

Structure and reactions of pentaquark baryons

We review the current status of the exotic pentaquark baryons. After a brief look at experiments of both positive and negative results, we discuss theoretical methods to study the structure and reactions for the pentaquarks. First we introduce the quark model and the chiral soliton model, where we discuss the relation of mass spectrum and parity with some emphasis on the role of chiral symmetry. It is always useful to picture the structure of the pentaquarks in terms of quarks. As for other methods, we discuss a model-independent method, and briefly mention the results from the lattice and QCD sum rule. Decay properties are then studied in some detail, which is one of the important properties of ⊝⁺. We investigate the relation between the decay width and the quark structure having certain spin-parity quantum numbers. Through these analyses, we consider as plausible quantum numbers of ⊝⁺,J ^P = 3/2⁻. In the last part of this note, we discuss production reactions of ⊝⁺ which provide links between the theoretical models and experimental information. We discuss photoproductions and hadron-induced reactions which are useful to explore the nature of ⊝⁺     

Analysis of Ω<Subscript>c</Subscript><Superscript>*</Superscript>(css) and Ω<Subscript>b</Subscript><Superscript>*</Superscript>(bss) with QCD sum rules

In this article, we calculate the masses and residues of the heavy baryons Ω_c ^*(css) and Ω_b ^*(bss) with spin–parity with the QCD sum rules. The numerical values are compatible with the experimental data and other theoretical estimations. PACS 14.20.Lq, 14.20.Mr     

Are there S = -2 pentaquarks?

Recent evidence for pentaquark baryons in the channels , and their anti-particles claimed by the NA49 collaboration is critically confronted with the vast amount of existing data on spectroscopy which was accumulated over the past decades. It is shown that the claim is inconsistent with these data. In addition two further exotic channels of the pentaquark type available in the NA49 data are investigated. It is argued that this study leads to internal inconsistency with the purported signals.Received: 16 January 2004, Published online: 24 August 2004 Correspondence to: S. Wenig     

Phenomenology of Large N c QCD

These lectures are designed to introduce the methods and results of large N _c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, we demonstrate that all quark and gluon Feynman diagrams are organized into classes based on powers of 1/N _c. We then show that this result can be translated into definite statements about mesons and baryons containing arbitrary numbers of constituents. In the mesons, numerous well-known phenomenological properties follow as immediate consequences of simply counting powers of N _c, while for the baryons, quantitative large N _c analyses of masses and other properties are seen to agree with experiment, even when large N _c is set equal to its observed value of 3. Large N _c reasoning is also used to explain some simple features of nuclear interactions.     

Parity doubling among the baryons

We study the evidence for and possible origins of parity doubling among the baryons. First we explore the experimental evidence, finding a significant signal for parity doubling in the non-strange baryons, but little evidence among strange baryons. Next we discuss potential explanations for this phenomenon. Possibilities include suppression of the violation of the flavor singlet axial symmetry (U(1_)A$U(1{)}_A$) of QCD, which is broken by the triangle anomaly and by quark masses. A conventional Wigner–Weyl realization of the SU(2_)L×SU(2_)R$\mathit{SU}(2{)}_L\times \mathit{SU}(2{)}_R$ chiral symmetry would also result in parity doubling. However this requires the suppression of families of chirally invariant   operators by some other dynamical mechanism. In this scenario the parity doubled states should decouple from pions. We discuss other explanations including connections to chiral invariant short distance physics motivated by large _Nc$N_c$ arguments as suggested by Shifman and others, and intrinsic deformation of relatively rigid highly excited hadrons, leading to parity doubling on the leading Regge trajectory. Finally we review the spectroscopic consequences of chiral symmetry using a formalism introduced by Weinberg, and use it to describe two baryons of opposite parity.     

Spectrum of heavy-light mesons in the QCD string picture

We describe in detail predictions of the QCD string approach for the masses of the heavy—light D, D _s , B, and B _s mesons, including orbitally and radially excited states. We discuss the role of the proper dynamics of the QCD string in the formation of the spectrum of the heavy—light mesons, with quark self-energy corrections calculated self-consistently in the same picture. We give our predictions in terms of the current quark masses; the string tension—the only dimensional parameter describing the interquark interaction; and the strong coupling constant, which differs for the fine and the hyperfine interactions. The results are compared with the predictions of other models and with the experimental and lattice results.     

Spectroscopy of pentaquark states

We construct a complete classification of pentaquark states in terms of the spin-flavour SU(6) representations. We find that only some definite SU(3) representations are allowed, that is singlets, octects, decuplets, anti-decuplets, 27-plets and 35-plets. The latter three contain exotic states, which cannot be constructed from three quarks only. This complete classification is general and model independent and is useful both for model builders and experimentalists. The mass spectrum is obtained from a Gürsey-Radicati type mass formula, whose coefficients have been determined previously by a study of qqq-baryons. The ground-state pentaquark, which is identified with the recently observed state, is predicted to be an isosinglet anti-decuplet state. Its parity depends on the interplay between the spin-flavour and orbital contributions to the mass operator.PACS: 14.20.-c Baryons (including antiparticles) - 12.39.-x Phenomenological quark models - 02.20.-a Group theory     

Weak decays of doubly heavy baryons: “decay constants”

Inspired by the recent observation of the Ξ_c~+_c~+)by the LHCb Collaboration, we explore the "decay constants" of doubly heavy baryons in the framework of QCD sum rules. With the Ξ_cc),Ξ_(bc),Ξ_(bb), and ?_(cc),?_(bc),?_(bb) baryons interpolated by three-quark operators, we calculate the correlation functions using the operator product expansion and include the contributions from operators up to dimension six. On the hadron side, we consider both contributions from the lowest-lying states with JP=1/2~+ and from negative parity baryons with JP=1/2~-. We find that the results are stable and the contaminations from negative parity baryons are not severe. These results are ingredients for the QCD study of weak decays and other properties of doubly-heavy baryons.     

1/<Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> countings in baryons

The 1/N _c -power countings for baryon decays and configuration mixings are determined by means of a nonrelativistic quark picture. Such countings are expected to be robust under changes in the quark masses and, therefore, valid as these become light. It is shown that excited baryons have natural widths of \(\mathcal{O}(N_c^0 )\). These dominant widths are due to the decays that proceed directly to the ground-state baryons, with cascade decays being suppressed to \(\mathcal{O}(1/N_c )\). Configuration mixings, defined as mixings between states belonging to different O(3) × SU(2N _f ) multiplets, are shown to be subleading in an expansion in \(1/\sqrt {N_c }\) when they involve the ground-state baryons, while the mixings between excited states can be \(\mathcal{O}(N_c^0 )\).     

Pentaquark search in the NA49 experiment

The NA49 experiment has found narrow peaks in the Ξ^? π ^?, Ξ^? π ⁺ (and antiparticle) spectra at 1862 MeV/c ². These states were identified with the predicted pentaquark cascades. We have searched for other decay channels of the pentaquark cascades. No signal was observed in the ΛK ^? and ΛK _S ⁰ spectra. Based on systematic inconsistencies in the experimental values of the reported Θ⁺, we tried to look for other possible pentaquark states, but observed no signal beyond statistical fluctuations.     

Analysis of the excited Ωc states as the $\tfrac{1}{2}$± pentaquark states with QCD sum rules

We construct both the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type interpolating currents to study the charmed pentaquark states ${susc}\bar{u}$ with ${J}^{P}={\tfrac{1}{2}}^{\pm }$. We employ the QCD sum rules to investigate the masses and pole residues of the charmed pentaquark states by taking into account the vacuum condensates up to dimension 13 in the operator product expansion. Our calculation results indicate that the scalar-diquark-scalar-diquark-antiquark type and axialvector-diquark-axialvector-diquark-antiquark type charmed pentaquark states ${susc}\bar{u}$ with ${J}^{P}={\tfrac{1}{2}}^{-}$ can be possible candidates of the excited Ω_c states observed in the LHCb collaboration.     

Heavy baryon decay widths in the large $$N_c$$ limit in chiral theory

We propose large \(N_c\) generalizations for the “diquark” representations of \(\hbox {SU}(3)_\mathrm{flav}\) relevant for positive parity heavy baryons, including putative exotic states. Next, within the framework of the Chiral Quark Soliton Model, we calculate heavy baryon masses and decay widths. We show that in the limit of \(N_c \rightarrow \infty \) all decay widths vanish, including the widths of exotica. This result is in fact more general than the model itself, as it relies only on the underlying symmetries: i.e. \(\hbox {SU}(3)_\mathrm{flav}\) and hedgehog symmetry. Furthermore, using explicit model formulae for the decay constants in the non-realtivistic limit, we show that there is a hierarchy of the decay couplings, which may explain observed pattern of experimental widths.