We discuss the relatively low mass and narrow width prediction for the exotic baryon Theta+, and refute recent statements of R.L. Jaffe on the subject.

We consider the effect of an exotic S=+1 $\Theta^+$ resonance on the scattering of neutral kaons off protons. Explicit results are presented for the $K^0_L p$ total cross sections.

We compute the spectra of exotic pentaquarks and monopole excitations of the low--lying ${1/2}^+$ and ${3/2}^+$ baryons in a chiral soliton model. Once the low--lying baryon properties are fit, the other states are predicted without any more adjustable parameters. This approach naturally leads to a scenario in which the mass spectrum of the next to lowest--lying $J^\pi={1/2}^+$ states is fairly well approximated by the ideal mixing pattern of the $\mathbf{8}\oplus\bar{\mathbf{10}}$ representation of flavor SU(3). We compare our results to predictions obtained in other pictures for pentaquarks and speculate about the spin--parity assignment for $\Xi(1690)$ and $\Xi(1950)$

In this work we study the Theta(1540) in the framework of QCD sum rules based on (ud)^2\bar{s} diquark clustering as suggested by Jaffe and Wilczek. Within errors, the mass of the pentaquark is compatible with the experimentally measured value. The mass difference between the Theta and the pentaquark with the quantum numbers of the nucleon amounts to 70 MeV, consistent with the interpretation of the N(1440) as a pentaquark.

Starting from the lowest order chiral Lagrangian for the interaction of the baryon decuplet with the octet of pseudoscalar mesons we find an attractive interaction in the $\Delta K$ channel with L=0 and I=1, while the interaction is repulsive for I=2. The attractive interaction leads to a pole in the second Riemann sheet of the complex plane and manifests itself in a large strength of the $\Delta K$ scattering amplitude close to the $\Delta K$ threshold, which is not the case for I=2. The large differences between the I=1 and I=2 channels should be clearly visible in different reactions and we suggest some of them to observe this exotic dynamically generated resonance, which in the quark language would stand as a pentaquark.

We analyze the existence of the exotic $\Theta^+$ from the perspective of instanton induced quark dynamics. The 't Hooft interaction gives strong attraction in specific channels of the triquark $ud\bar s$ and diquark $ud$ configurations. In particular it leads to a light $ud\bar s$ triquark cluster, with the mass around $750 {\rm MeV}$, in the I=0, $S=1/2$ and color 3 configuration, and a light $ud$-diquark configuration, with mass $440 {\rm MeV}$, in the I=0, S=0 and color {$\bar{3}$} configuration. If we consider the pentaquark as a bound state of such triquark and diquark configurations in a relative L=1 state we obtain good agreement with the data. The small width of $\Theta^+$ has a natural explanation in this model.

I study the charmed $uudd\bar c$ resonance D*p (3100) very recently discovered by the H1 collaboration at Hera. An anticharmed resonance was already predicted, in a recent publication mostly dedicated to the S=1 resonance Theta+(1540). To confirm these recent predictions, I apply the same standard quark model with a quark-antiquark annihilation constrained by chiral symmetry. I find that repulsion excludes the D*p (3100) as a $uudd\bar c$ s-wave pentaquark. I explore the D*p (3100) as a heptaquark, equivalent to a N-pi-D* linear molecule, with positive parity and total isospin I=0. I find that the N-D repulsion is cancelled by the attraction existing in the N-pi and pi-D channels. In our framework this state is harder to bind than the Theta+ described by a k-pi-N borromean bound-state, a lower binding energy is expected in agreement with the H1 observation. Multiquark molecules N-pi-D, N-pi-B* and N-pi-B are also predicted.

An analysis of the recent results from several experimental groups reported observation of a new $\Theta$ baryon has been presented from a view point of the unified picture for hadron spectra developed early \cite{12}. It is shown that, in fact, two different $\Theta$ baryons have been discovered. We have also established that both $\Theta$ baryons are excellently incorporated in the unified picture for hadron spectra. It is argued that the presented experimental material revealed an existence of the positive srangeness $\Theta$ partners for the observed $\Lambda$ and $\Sigma$ states with negative strangeness as we predicted.

We discuss a realisation of the pentaquark structure proposed by Jaffe and Wilczek within a simple quark model with colour-spin contact interactions and coloured harmonic confinement, which accurately describes the $\Delta-N$ splitting. In this model spatially compact diquarks are formed in the pentaquark but no such compact object exists in the nucleon. The colour-spin attraction brings the Jaffe-Wilczek-like state down to a low mass, compatible with the experimental observation and below that of the naive ground state with all $S$-waves. We find, however, that although these trends are maintained, the extreme effects observed do not survive the required ``smearing'' of the delta function contact interaction. We also demonstrate the weakness of the ``schematic'' approximation when applied to a system containing a $P$-wave. An estimate of the anti-charmed pentaquark mass is made which is in line with the Jaffe-Wilczek prediction and significantly less than the value reported by the H1 collaboration.

We point out that meson spectrum indicates the existence of a degenerate chiral nonet in the energy region around 1.4 GeV with a slightly inverted spectrum with respect to a qq nonet. Based on this observation, the approximately linear rising of the mass of a hadron with the number of constituent quarks, and the existence of a cuasidegenerate pseudoscalar nonet, we conjecture the existence of a tetraquark chiral nonet in this energy region with chiral symmetry implemented directly. We realize this idea in a chiral model and take into account the mixing of the tetraquark chiral nonet with a conventional qq nonet. We find that the mass spectrum of mesons below 1.5 GeV is consistent with this picture. In general, pseudoscalar states arise as mainly qq states but scalar states turn out to be strong admixtures of qq and tetraquark states.

The newly discovered exotic $\Theta$ baryon of mass 1540 MeV (and very small width) truly has a very low mass, if it is a pentaquark system of even parity. A schematic model in which the coherent interaction of $u\bar s$ and $d\bar s$ pairs leads to a very large residual (non-confining) attractive interaction is introduced. This collective vibrational model accounts for the mass and small decay width to the $KN$ channel, but yields a significant coupling to the virtual $K^*N$ channel. The schematic model predicts an attractive $\Theta$-nucleon interaction strong enough to bind a $\Theta$ particle to a nucleus in a state that is stable against decay via strong interactions. The discovery of $\Theta$-nuclei could be a definitive proof that the $\Theta$ parity is even.

We illustrate the exotic SU(3) baryon sub-multiplets in the SU(4) baryon multiplets predicted from the flavor SU(4) collective-coordinate quantization, and investigate the exotic states with charm number $C=\pm1$ up to leading order of $1/N_c$ under chiral $SU(3)_L\times SU(3)_R$ symmetry and the heavy quark limit from bound state approach. We find that there exist the $\bar{15}$-plets and 24-plets with C=1 and the $\bar{6}$-plets, 15-plets and $15^{\prime}$-plets with $C=-1$ bounded in this approach, qualitatively consistent with predictions from the flavor SU(4) collective-coordinate quantization. In the case of two light flavors, we also calculate the average mass of the $\Theta^0_c(uudd\bar{c})$ states, which belong to the $\bar{6}$-plets with $S_l=1$ and, accordingly, $S=(1/2,~3/2)$ due to the heavy quark spin symmetry. By fitting one unique parameter with the $\Lambda_c$ mass, the average mass $\bar{m}_{\Theta^0_c}$ is estimated to be 2704 MeV.

We discuss the $10_F$-plet relative to the ${\bar {10}}_F$-plet of pentaquarks for both the flavour-spin and the colour-spin hyperfine interactions, for both parities of the pentaquark ground states. We show that the colour-spin interaction leads to degenerate $10_F$- and ${\bar {10}}_F$-plets when the parity is positive, and a mass splitting of 75 MeV for negative parity. The flavour-spin interaction leads to $10_{F}-{\bar {10}}_F$ mass splittings of 200 MeV and 40 MeV, for positive and negative parities, respectively. We analyze the presently known baryon resonances in this light.

If the Theta^+(1540) is interpreted as a bound state of a $\bar s$ quark and two (ud) diquarks in a relative P-wave, then it is very likely that there exist pentaquark states with a heavy antiquark, $\bar b$ or $\bar c$, and two ``light'' diquarks in a relative S-wave which are stable against strong decays. We make a mass estimate for exotic states of this type and discuss their weak decays. Isospin relations are constructed which test their flavor quantum numbers.

Dynamical calculations are performed for all isomultiplets of the flavour antidecuplet to which the newly discovered pentaquark $\Theta^+$ belongs. The framework is a constituent quark model where the short-range interaction has a flavour-spin structure. In this model the lightest pentaquarks are parity even states. They are described by variational solutions where the Pauli principle is properly taken into account. By fitting the mass of $\Theta^+$ of minimal content $uudd\bar{s}$ the mass of $\Xi^{--}$ of minimal content $ddss \bar{u}$ is predicted at approximately 1960 MeV.

The octet, decuplet and antidecuplet baryon mass spectrum as a function of the Skyrme charge e and the SU(3)_f symmetry breaking parameters is given in tabular form. We also estimate the decuplet-octet and the antidecuplet-octet mass difference. Comparison with existing literature is given.

The 1/N expansion for exotic baryons is developed, and applied to the masses, meson couplings, and decay widths. Masses and widths of the 27 and 35 states in the same tower as the Theta are related by spin-flavor symmetry. The 27 and 35 states can decay within the pentaquark tower, as well as to normal baryons.

We re-analyze the predictions of chiral-soliton models for the masses and decay widths of baryons in the exotic antidecuplet of flavour SU(3). The calculated ranges of the chiral-soliton moment of inertia and the \pi-nucleon scattering \Sigma term are used together with the observed baryon octet and decuplet mass splittings to estimate 1430 MeV < m_{\Theta^+} < 1660 MeV} and 1790 MeV < m_{\Xi^{--}} < 1970 MeV. These are consistent with the masses reported recently, but more precise predictions rely on ambiguous identifications of non-exotic baryon resonances. The overall decay rates of antidecuplet states are sensitive to the singlet axial-current matrix element in the nucleon. Taking this from polarized deep-inelastic scattering experiments, we find a suppression of the total \Theta^+ and \Xi^{--} decay widths that may not be sufficient by itself to reproduce the narrow widths required by experiments. We calculate SU(3) breaking effects due to representation mixing and find that they tend to suppress the \Theta^+ decay width, while enhancing that of the \Xi^{--}. We predict light masses for some exotic 27 baryons, including the I=1, J^P={3/2}^+ \Theta^+ and I=3/2, J^P={3/2}^+ \Xi multiplets, and calculate their decay widths.

The relativistic five-quark equations are found in the framework of the dispersion relation technique. The solutions of these equations using the method based on the extraction of the leading singularities of the amplitudes are obtained. The five-quark amplitudes for the low-lying pentaquarks including the u, d, s- quarks are calculated. The poles of these amplitudes determine the masses of Theta-pentaquarks. The mass spectra of the isotensor Theta-pentaquarks are calculated.

We present a consistent color-flavor-spin-orbital wave function for a positive parity Theta^+ that naturally explains the observed narrowness of the state. The wave function is totally symmetric in its flavor-spin part and totally antisymmetric in its color-orbital part. If flavor-spin interactions dominate, this wave function renders the positive parity Theta^+ lighter than its negative parity counterpart. We consider decays of the Theta^+ and compute the overlap of this state with the kinematically allowed final states. Our results are numerically small. We note that dynamical correlations between quarks are not necessary to obtain narrow pentaquark widths.

From the interpretation of the $\Theta^+(1540)$ and $\Xi_{3/2}(1862)$ baryons as an excitation of the ``skyrmion liquid'' with SU(3) flavour symmetry $\bar{10}$ we deduce a new series of baryons, $\Theta_1^{++}$, $\Theta_1^{+}$ and $\Theta_1^0$, situated at the top of the 27-plet of SU(3) flavour, with hypercharge Y=2, isospin I=1 and spin $J=\frac32$. The $\Theta_1$ mass and width are estimated from the chiral quark soliton model. We demonstrate that the predicted mass, $m_{\Theta_1}=1599 \mathrm{MeV/c^2}$, and broad width are in qualitative conflict with experiment which shows no structure in the total $K^+p$ cross section near $P_\mathrm{lab}=585$ MeV/c. We also discuss properties of other exotic baryons from the 27- and 35-plets.

A light collective $\theta^+$ baryon state (with strangeness +1) was predicted via rigid-rotor collective quantization of SU(3) chiral soliton models. This paper explores the validity of this treatment. It is shown that predictions of exotic baryon properties based on this approximation do not follow from large $N_c$ QCD. A number of rather general analyses lead to this conclusion. These include an analysis of the baryon's width, a comparison of the predictions with general large $N_c$ consistency conditions of the Gervais-Sakita-Dashen-Manohar type; an application of the technique to QCD in the limit where the quarks are heavy; a comparison of this method with the vibration approach of Callan and Klebanov; and the $1/N_c$ scaling of the excitation energy. The origin of the problem lies in a flaw in the original rigid-rotor collective quantization treatment which implicitly assumes that the collective motion is orthogonal to vibrational motion. This is untrue for chiral soliton models: the Wess-Zumino term induces mixing at leading order between collective and vibrational motion with exotic quantum numbers. This suggests that successful phenomenological predictions of $\theta^+$ properties based on rigid-rotor quantization were accidental.

Recently the so-called $\Theta^+$ resonance has been reported first from SPring8\cite{nakano} and many following experiments showed clear evidence of the state. The existence of $\Theta^+$ is now confirmed. Since $\Theta^+$ exclusively decays into either $K^+ n$ or $K^0 p$, it is explained to be the long waited penta-quark state which includes $ u u d d \bar{s}$ quarks. However, one yet has to obtain consistent picture of $\Theta^+$. We try to explain $\Theta^+$ in a conventional picture and show that such picture leads to new prediction on kaon and pion system.

In the chiral quark soliton model the smallness of $\Theta^+$ width is due to the cancellation of the coupling constants which are of different order in $N_c$. We show that taking properly into account the flavor structure of relevant SU(3) representations for arbitrary number of colors enahnces the nonleading term by an additional factor of $N_c$, making the cancellation consistent with the $N_c$ counting. Moreover, we show that, for the same reason, $\Theta^+$ width is suppressed by a group-theoretical factor ${\cal O}(1/N_c)$ with respect to $\Delta$ and discuss the $N_c$ dependence of the phase space factors for these two decays.

We investigate four-body states with only charm quarks. Working in a large but finite oscillator basis, we present a net binding analysis to determine if the resulting states are stable against breakup into a pair of c-cbar mesons. We find several close-lying bound states in the two models we examine.

We have calculated the magnetic moment of the recently observed $\Theta^+$ pentaquark state in the framework of the light cone QCD sum rules using the photon distribution amplitudes. We find that $\mu_{\Theta^+}=(0.12\pm 0.06) \mu_N$, which is quite small. We also compare our result with predictions of other groups.

We explore molecular states of two open heavy-quark mesons (Q qbar)-(qbar Q) in a quark-based model in terms of a four-body non-relativistic Hamiltonian with pairwise effective interactions. Molecular states are found in the combinations of {D, D*, B, B*} with {Dbar, Dbar*, Bbar, Bbar*}, including a weakly-bound D-Dbar* state near the threshold which may be qualitatively identified as the 3872 state observed recently by the Belle Collaboration.

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, singlets, octets, 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 scheme is general and model independent and is useful both for model builders and experimentalists. The mass spectrum is obtained from a Gursey-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 Theta(1540) 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. Independent from the parity of the Theta(1540), we predict excited exotic baryons at 1659 and 1774 MeV.

QCD instantons are known to produce deeply bound diquarks. We speculate that they may be used as building blocks in the formation of multiquark states, in particular pentaquarks. We suggest a simple constituent ``diquark'' model in which the lowest pentaquark states are made of a scalar plus a tensor diquark and an antiquark. In such a model there is the analogy between baryon and pentaquark states, allowing to estimate both the masses and widths of those states.

The relativistic five-quark equations are found in the framework of the dispersion relation technique. The five-quark amplitudes for the low-lying pentaquarks including u, d quarks are calculated. The poles of the five-quark amplitudes determine the masses of the lowest pentaquarks. The calculation of pentaquark amplitudes estimates the contributions of four subamplitudes. The main contributions to the pentaquark amplitude are determined by the subamplitudes, which include the meson states M.

The status of the exotic baryons is analyzed in the context of the 1/Nc-expansion. An exactly solvable toy model reproducing the main symmetries of QCD is studied in order to clarify the recent controversy concerning the consistency of various approaches to the 1/Nc-expansion for exotic baryons. In particular, in the context of the toy model it is explicitly demonstrated that the naive rigid-rotator approach agrees with the exact solution for nonexotic baryons but fails in the exotic sector.

Further consequences of the 1540 MeV Theta+ resonance as an isotensor pentaquark beyond Capstick et al. are explored. It is argued that the SAPHIR data may not currently exclude the existence of the charged partner Theta++. The usual prediction of the dominance of non-resonant Theta+ K, and Theta+ K*, final states in photoproduction on the proton is argued not to obtain for an isotensor Theta+. This enhances the importance of excited baryon final states, where the excited baryon decays to Theta+ K or Theta+ K*; as well as the non-resonant Theta+ K pi final state. The small width of the recently discovered Xi-- cascade resonance to Xi- pi- is easier to explain if Theta+ is an isotensor pentaquark than if it is in the 10bar representation, due to both an isospin and U-spin selection rule. A new production diagram for Theta+ in the photoproduction on the deuteron is suggested.

The masses of $uudd\bar s $ and $uudd\bar d$ pentaquarks are evaluated in a framework of the Effective Hamiltonian approach to QCD using the Jaffe-Wilczek $[ud]^2\bar q$ approximation. The mass of the $[ud]^2\bar s$ state is found to be $\sim 300-500$ MeV higher than the observed $\Theta^+(1540)$ mass.

We study the group structure of baryon anti-decuplet. Assuming that the recently discovered $\Theta^+$ is a member of the anti-decuplet, we derive mass sum rules among the baryons within the anti-decuplet and other multiplets. The estimated mass of the nucleon resonance in the anti-decuplet is around 1780 MeV. We also derive SU(3) symmetric Lagrangian for the interactions of the anti-decuplet with the meson octet and the baryon octet. As there is no direct coupling between the baryon anti-decuplet, the meson octet, and the baryon decuplet, the fact that the N(1710) decays strongly into $\pi \Delta$ rules out the possibility that it a member of the baryon anti-decuplet unless it is strongly mixed with other multiplets.

The structure of the pentaquark state uudd-sbar is studied in the chiral SU(3) quark model as well as in the extended chiral SU(3) quark model, in which the vector meson exchanges are included. Four configurations of JP=1/2- and four of JP=1/2+ are considered. The results show that the isospin T=0 state is always the lowest one for both JP=1/2- and JP=1/2+ cases in various models. But the theoretical value of the lowest one is still about 200-300 MeV higher than the experimental mass of $\Theta$. It seems that a dynamical calculation should be done for the further study.

We consider the possibility that the lightest pentaquark is a parity even state, with one unit of orbital angular momentum. Working within the framework of a constituent quark model, we show that dominant spin-flavor interactions render certain parity-even states lighter than any pentaquark with all quarks in the spatial ground state. For such states, we focus on predicting the mass and decays of other members of the same SU(3) flavor multiplet. Specifically, we consider the strangeness -2 cascade pentaquarks, which are relatively immune to mixing. We take into account flavor SU(3) breaking effects originating from the strange quark mass as well as from the structure of the spin-flavor exchange interactions themselves. We predict the lightest cascade pentaquarks at approximately 1906 MeV, with a full width about 3 times larger than that of the Theta^+.

Several recent experiments have reported evidence for a narrow feature in the K(+)-neutron system, an apparent resonant state ~ 100 MeV above threshold and with a width < 25 MeV. This state has been labelled as Theta(+) (previously as Z(*)), and because of the implied inclusion of a anti-strange quark, is referred to as a pentaquark, that is, five quarks within a single bag. We present an alternative explanation for such a structure, as a higher angular momentum resonance in the isospin zero K(+) -N system. One might call this an exit channel or a molecular resonance. In a non-relativistic potential model we find a possible candidate for the kaon-nucleon system with relative angular momentum L=3, while L=1 and 2 states possess centrifugal barriers too low to confine the kaon and nucleon in a narrow state at an energy so high above threshold. A rather strong state-dependence in the potential is essential, however, for eliminating an observable L=2 resonance at lower energies.

Systematic treatment of the collective rotation of the nonrigid chiral soliton is developed in the SU(3) chiral quark soliton model and applied to the octet and decuplet baryons. The strangeness degrees of freedom are treated by a simplified bound-state approach which omits the locality of the kaon wave function. Then, the flavor rotation is divided into the isospin rotation and the emission and absorption of the kaon. The kaon Hamiltonian is diagonalized by the Hartree approximation. The soliton changes the shape according to the strangeness. The baryons appear as the rotational bands of the combined system of the soliton and the kaon.

We analyze the possibility of heavy-light tetraquark bound states by means of a chiral constituent quark model. The study is done in a variational approach. Special attention is paid to the contribution given by the different terms of the interacting potential and also to the role played by the different color channels. We find a stable state for both $qq\bar{c}\bar{c}$ and $qq\bar{b}\bar{b}$ configurations. Possible decay modes of these structures are analyzed.

We generalize the usual octet, decuplet and exotic antidecuplet and higher baryon multiplets to any number of colours Nc. We show that the multiplets fall into a sequence of bands with O(1/Nc) splittings inside the band and O(1) splittings between the bands characterized by "exoticness", that is the number of extra quark-antiquark pairs needed to compose the multiplet. Unless exoticness becomes very large, all multiplets can be reliably described at large Nc as collective rotational excitations of a chiral soliton.

A strangeness +1 exotic baryon Theta^+ has recently been seen in a number of experiments. We demonstrate that in large N_c QCD the existence of such a state implies the existence of S = +1 partner states with various spins and isospins but comparable masses. We discuss the spectroscopy of such states and possible channels in which they can be observed, based on the simple assumption that those states with pentaquark quantum numbers are unlikely to be large N_c artifacts.

Exotic penta-quark baryon with strangeness +1, \Theta^+, is studied in the QCD sum rule approach. We derive sum rules for the positive and negative parity baryon states with J=1/2 and I=0. It is found that the standard values of the QCD condensates predict a negative parity \Theta^+ of mass \simeq 1.5 GeV, while no positive parity state is found. We stress the roles of chiral-odd condensates in determining the parity and mass of \Theta^+.

Predictions for a light collective $\Theta^+$ baryon state (with strangeness +1) based on the collective quantization of chiral soliton models are shown to be inconsistent with large $N_c$ QCD. The lightest strangeness +1 state to emerge from the analysis has an excitation energy which at large $N_c$ scales as $N_c^0$ while collective quantization is legitimate only for excitations which go to zero as $N_c \to \infty$. This inconsistency strongly suggests that predictions for $\Theta^+$ properties based on collective quantization of chiral solitons are not valid.

We consider a $[ud]^2\bar{s}$ current in the QCD sum rule framework to study the mass of the recently observed pentaquark state $\Theta^+(1540)$, obtaining good agreement with the experimental value. We also study the mass of the pentaquark $[ud]^2\bar{d}$. Our results are compatible with the interpretation of the $[ud]^2\bar{d}$ state as being the Roper resonance N(1440), as suggested by Jaffe and Wilczek.

The recently discovered pentaquark $\Theta^+$ is described within the chiral constituent quark model. Within this picture the flavor-spin interaction between valence quarks inverts the $(1s)^4$ and $(1s)^3(1p)$ levels of the four-quark subsystem and consequently the lowest-lying pentaquark is a positive parity, I=0, J=1/2 state of the flavor antidecuplet, similar to the soliton model prediction. Contrary to the soliton model, however, the quark picture predicts its spin-orbit partner with $J=3/2$. Different interpolating fields intended for lattice calculations of $\Theta^+$ are constructed, which have a maximal overlap with this baryon if it is indeed a quark excitation in the 5Q system.

We present a non-relativistic quark molecular model (QMM) of the strange crypto-exotic pentaquark baryon spectrum motivated by the recent data showing narrow, resonance enhancements in electromagnetic and hadronic production of kaons. Our model assumes color octet bonded quark molecular clusters forming exotic color singlet pentaquark baryons. We develop explicit molecular pentaquark wavefunctions that exhibit color interchange and cluster fermion antisymmetry. Our color electro-dynamics (CED) inspired Hamiltonian, which includes confinement, one gluon exchange and color magnetic interactions, is a natural generalization of the Isgur and Karl quark model Hamiltonian that reproduces the conventional meson (q-qbar) and baryon (qqq) spectrumWe introduce the idea of Color Magnetic Confinement (CMC) which is employed to restrict the physical pentaquark spectrum and constrain the fundamental constants (color gyromagnetic ratios) of the QMM-CED Hamiltonian. Comparing our QMM spectrum predictions with the recent experimental data in associated strangeness photo- and electro-production reactions, we identify 4 candidate states that have masses and total widths consistent with exotic pentaquark structure.

The newly observed $\Theta^+$ resonance is believed to be a pentaquark with the constituent quarks $uudd\bar s$. There are a few options for the constituent quark structure. Some advocate diquark-diquark-antiquark $(ud)$-$(ud)$-$\bar s$ while others favor diquark-triquark $(ud)$-$(ud\bar s)$. We use the color-spin hyperfine interaction to examine the energy levels of these structures, and we find that the diquark-diquark-antiquark structure is slight favored. We proceed to write down the flavor triplet and antisextet of the charmed or bottomed exotic baryons with internal $qqqq\bar Q$ quarks. We also estimate the mass of $\Theta_c^0$ and $\Theta_b^+$.

The mass of the newly discovered pentaquark is calculated within the framework of the SU(3) Skyrme Model. Various estimates based on the \emph{model independent} approach are compared with the model results and with the Chiral Quark Model. Our discussion shows that $\Theta^{+}$ is light with the mass of the order 1.5 GeV.

We consider the mass splittings and strong decays of members of the lowest-lying pentaquark multiplet, which we take to be a parity-odd antidecuplet. We derive useful decompositions of the quark model wave functions that allow for easy computation of color-flavor-spin matrix elements. We compute mass splittings within the antidecuplet including spin-color and spin-isospin interactions between constituents and point out the importance of hidden strangeness in rendering the nucleon-like states heavier than the S=1 state. Using recent experimental data on a possible S=1 pentaquark state, we make decay predictions for other members of the antidecuplet.

From the interpretation of the $\Theta^+$ baryon resonance as an excitation of the ``skyrmion liquid'' with SU(3) flavor symmetry $\bar{10}$ we deduce a new series of baryons, $\Theta_1^{++}$, $\Theta_1^{+}$ and $\Theta_1^0$, situated at the top of the 27-plet of SU(3) flavor, with hypercharge Y=2, isospin T=1 and spin $J=\frac32$. The mass of $\Theta_1$ is estimated 55 MeV/c^2 higher then the mass of $\Theta^+$ and its width at 80 MeV. We also discuss the other baryons from the 27-plet.

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 $(1.55\pm 0.15)$ GeV. The experimentally observed baryon resonance $\Theta^+ (1540)$ with $S=+1$ can be consistently identified as a pentaquark state if its $J^P={1\over 2}^-$. Such a state is expected in QCD. If its parity is positive, this pentaquark state is really exotic. Now the outstanding issue is to determine its quantum numbers experimentally.

We propose that the recently discovered \Th(1540)baryon is a bound state of four quarks and an antiquark, containing two highly correlated $ud$-pairs. If so, the \Th(1540) has positive parity, and it lies in an near-ideally mixed SU(3)_{f}\mathbf{\bar{10}}_{f}\oplus \mathbf{8}_{f}.The Roper resonance and the P_{11}(1710) fit naturally into this classification. We predict an isospin 3/2 multiplet of \Xi$'(S=-2) with J^{\Pi}=\half^{+} around 1750 MeV. A search for manifestly exotic \Xi^{+} and \Xi^{--} in this mass range could provide a sharp test of our proposal.

Motivated by the recent discovery of the exotic S=+1 narrow baryon resonance Theta^+ at 1540 MeV, with quark content {uudd sbar}, we conjecture the existence of its anti-charmed analogue Theta_c, with quark content {uudd cbar}, and compute its likely properties. We rely on the recently constructed model of a novel kind of a pentaquark with an unusual color structure which provides a good approximation to the Theta^+ mass. We expect that Theta_c is an isosinglet with J^P=1/2^- and estimate its mass at 2985 \pm 50 MeV. We also discuss another possible exotic baryon resonance containing heavy quarks, the Theta_b^+, a {uudd bbar} state, and estimate m_{Theta_b^+}=6398 \pm 50 MeV. These states should appear as unexpectedly narrow peaks in D^-p, Dbar^0 n, B^0 p and B^+ n mass distributions.

Prompted by the recent surprising results in QCD spectroscopy, we extend to heavy flavors the hadron mass relations showing that the constituent quark mass differences and ratios have the same values when obtained from mesons and baryons. We obtain several new successful relations involving heavy quarks and provide some related predictions. We discuss in detail the apparent sharp decrease in m_s and m_c, when a light partner quark in a meson is replaced by a heavy one and construct a potential model which qualitatively reproduces this pattern through wave function effects. We apply these ideas to the recently discovered theta^+ exotic KN resonance and propose its interpretation as a novel kind of a pentaquark with an unusual color structure, J^P=1/2^+, I=0 and an antidecuplet of SU(3)_f. A rough mass estimate of this pentaquark is close to experiment.

The mass formulae for the supernarrow dibaryons and the exotic baryons with small masses are consructed. With this aim their self energies are calculated in one loop approximation using the dispersion relations with two subtractions. The values of the masses obtained in this approach are in a good agreement with the experimental data. The mass formula for the baryons is also used to calculate the mass of the $\Delta(1232)$ resonance.

We discuss a possible interpretation for the pentaquark baryon $\Theta^+$ which has an exotic quantum number of strangeness $S = +1$. The role of the pion which modifies the structure of single-particle levels of quarks is examined. When the pion field is sufficiently strong, the ground state of five quarks for $\Theta^+$ acquires positive parity. If this is the case, an excited state may appear slightly above the ground state with negative parity.

The group classification of exotic pentaquarks involving four standard quarks and a single antiquark to produce pentaquarks of strangeness +1 is outlined.

The stability of strange pentaquarks $uudd\bar s$ is studied in a constituent quark model based on a flavor-spin hyperfine interaction between quarks. With this interaction model, which schematically represents the Goldstone boson exchange interaction between constituent quarks, the lowest lying strange pentaquark is a $p-$shell state with positive parity. The flavor-spin interaction lowers the energy of the lowest $p-$shell state below that of the lowest $s-$shell state, which has negative parity because of the negative parity of the strange antiquark. It is found that the strange pentaquark is stable against strong decay provided that the strange antiquark interacts by a fairly strong spin-spin interaction with $u$ and $d$ quarks. This interaction has a form that corresponds to $\eta$ meson exchange. Its strength may be inferred from the $\pi^0$ decay width of $D_s^*$ mesons.

The recent reported charmed-strange resonance at 2.32 GeV/c suggests a possible multiquark state. Three types of multiquark bound states are reviewed. A previous model-independent variational approach considers a tetraquark with two heavy antiquarks and two light quarks as a heavy antidiquark with the color field of a quark bound to the two light quarks with a wave function like that of a heavy baryon. Results indicate that a charmed-strange tetraquark $\bar c \bar s u d$ or a bottom-strange tetraquark $\bar b \bar s u d$ with this "diquark-heavy-baryion" wave function is not bound, in contrast to "molecular-type" $D-K$ and $B-K$ wave functions. However, a charmed-bottom tetraquark $\bar c \bar b u d$ might be bound with a very narrow weak decay mode. A "molecular-type" $D-B$ state can have an interesting $B_c \pi$ decay with a high energy pion,

We discuss the new state $D_{sJ}(2317)$ discovered by BaBar and demonstrate using QCD inequalities that if indeed the $f_0(980)$ and the new $D_{sJ}(2317)$ ($0^+$) are primarilly made of four quarks that a new I=0 ``$\bar DD$ bound state'' at a mass smaller than 3660 MeV must exist. Observation of such a state will constitute definitive evidence for four-quark states.

Dibaryon candidates with strangeness S=-2,-3,-4,-5,-6 are studied in terms of the extended quark delocalization and color screening model. The results show that there are only few promising low lying dibaryon states: The H and di-Omega may be marginally strong interaction stable but model uncertainties are too large to allow any definitive statement; the SIJ=-3,1/2,2 N-Omega state is 62 MeV lower than the N-Omega threshold and 24 MeV lower than the Lambda-Xi-pion threshold. In addition, we study the mechanisms of effective intermediate range attraction, sigma-meson exchange and the kinetic energy reduction due to quark delocalization.

Using the quark mass density- and temperature-dependent model, we have studied the properties of the dibaryon systems. The binding energy, radius and mean lifetime of Omega-Omega and Omega-Xi are given. We find the dibaryons Omega-Omega, Omega-Xi are metastable at zero temperature, but the strong decay channel for Omega-Omega opens when temperature arrives at 129.3MeV. It is shown that our results are in good agreement with those given by the chiral S(3) quark model.

The novel observation of an exotic strangeness S=+1 baryon state at 1.54 GeV will 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 non-exotic quantum numbers.

The dibaryon states as six-quark clusters of exotic QCD states are investigated in this paper. With the inherent nodal surface structure analysis, the wave functions of the six-quark clusters (in another word, the dibaryons) are classified. The contribution of the hidden color channels are discussed. The quantum numbers of the low-lying dibaryon states are obtained. The States $[\Omega\Omega]_{(0,0^{+})}$, $[\Omega\Omega]_{(0,2^{-})}$, $[\Xi^{*}\Omega]_{(1/2,0^{+})}$, $[\Sigma^{*}\Sigma^{*}]_{(0,4^{-})}$ and the hidden color channel states with the same quantum numbers are proposed to be the candidates of dibaryons, which may be observed in experiments.

The relativistic five-quark equations are found in the framework of the dispersion relation technique. The solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The five-quark amplitudes for the low-lying pentaquarks are calculated under the condition that flavor SU(3) symmetry holds. The poles of five-quark amplitudes determine the masses of the lowest pentaquarks. The mass spectra of pentaquarks which contain only light quarks are calculated. The calculation of pentaquark amplitudes estimates the contributions of three subamplitudes. The main contributions to the pentaquark amplitude are determined by the subamplitudes, which include the meson states.

Four-body Faddeev-Yakubovsky calculations for Lambda-Lambda-p-n do not produce a bound state for Lambda-Lambda hydrogen 4, although suitably defined three-body Faddeev calculations for Lambda-Lambda-d produce a 1+ bound state for Lambda-Lambda interactions fitted to the Lambda-Lambda helium 6 emulsion event from KEK E373. This is opposite to the normal situation where a four-body Faddeev-Yakubovsky calculation yields stronger binding than that due to a suitably defined three-body Faddeev calculation. For stranger systems, Faddeev calculations using Lambda-Xi interactions which simulate the Nijmegen soft-core model NSC97 (which is close to reproducing the KEK event) suggest that Lambda-Xi helium 6 marks the onset of nuclear stability for Xi hyperons.

Changes in properties of heavy hadrons with a charm or a bottom quark are studied in nuclear matter. Effective masses (scalar potentials) for the hadrons are calculated using quark-meson coupling model. Our results also suggest that the heavy baryons containing a charm or a bottom quark will form charmed or bottom hypernuclei, which was first predicted in mid 70's. In addition a possibility of $B^-$-nuclear bound (atomic) states is briefly discussed.

In this work we study tetraquark bound states in the framework of the constituent quark model of Ref. [2], which has been used for the description of non-strange two- and three-baryon systems and later on applied to the hadron spectra.

The Omega-Omega (SIJ=-6,0,0) dibaryon state is studied with the extended quark-delocalization color-screening model including a pi meson exchange tail, which reproduces the properties of the deuteron quantitatively. We find the mass of the di-Omega to be about 45 MeV lower than the Omega-Omega threshold. The effect of channel coupling due to the tensor force has been calculated and found to be small in this case. We have also studied the effect of other pseudoscalar meson exchanges and sensitivity to the short-range cutoff radius, r_0, for the meson exchanges.

We study the possible existence of nonstrange dibaryons and tribaryons by solving the bound-state problem of the two- and three-body systems composed of nucleons and deltas. The two-body systems are $NN$, $N\Delta$, and $\Delta\Delta$, while the three-body systems are $NNN$, $NN\Delta$, $N\Delta\Delta$, and $\Delta\Delta\Delta$. We use as input the nonlocal $NN$, $N\Delta$, and $\Delta\Delta$ potentials derived from the chiral quark cluster model by means of the resonating group method. We compare with previous results obtained from the local version based on the Born-Oppenheimer approximation.

The relativistic four-quark equations are found in the framework of the dispersion relation technique. The calculations of non-qq meson amplitudes estimate the contributions of three subamplitudes: four-quark amplitude, glueball amplitude and hadronic molecule amplitudes.

The coupling to light mesons leads to large widths and shifts of the energy of the excited states in the baryon spectrum from the predictions of the constituent quark model with three valence quarks. This coupling may be modelled by admixtures of sea-quark $qqq(q\bar q)^n$ configurations in the resonances. Using the same schematic flavor and spin dependent interaction model, which reproduces the low lying part of the experimental baryon spectrum in the valence quark model, the lowest $qqqq\bar q$ states are shown to form nearly degenerate bands of positive and negative parity states, which overlap strongly with the low lying excited $qqq$ states in the P and SD shell.

The characteristic feature of the ground state configuration of the Skyrme model description of nuclei is the absence of recognizable individual nucleons. The ground state of the skyrmion with baryon number 2 is axially symmetric, and is well approximated by a simple rational map, which represents a direct generalization of Skyrme's hedgehog ansatz for the nucleon. If the Lagrangian density is canonically quantized this configuration may support excitations that lie close and possible below the threshold for pion decay, and therefore describe dibaryons. The quantum corrections stabilize these solutions, the mass density of which have the correct exponential fall off at large distances.

In the framework of the SU(3) chiral quark model, the $S-$wave baryon-baryon bound states are investigated. It is found that according to the symmetry character of the system and the contributions from chiral fields, there are three types of bound states. The states of the first type, such as $[\Omega\Omega]_{(0,0)}$ and $[\Xi^{*}\Omega]_{(0,1/2)}$ are deeply bound dibaryon with narrow widths. The second type states, $[\Sigma^{*} \Delta]_{(0,5/2)}$,$[\Sigma^{*} \Delta]_{(3,1/2)}$, $[\Delta\Delta]_{(0,3)}$ and $[\Delta\Delta]_{(3,0)}$ are also bound states, but with broad widths. $[\Xi\Omega - \Xi^{*}\Omega]_{(1,1/2)}$, $[\Xi\Xi]_{(0,1)}$, and $[N \Omega]_{(2,1/2)}$ are third type states. They, like {\em d}, are weakly bound only if the chiral fields can provide attraction between baryons.

The possible candidates of $S-$wave dibaryons with various strange numbers are studied under the chiral SU(3) quark model. It is shown that there are three types of baryon-baryon bound states. The states of the first type are called deuteron-like states. If chiral fields can provide enough attraction between interacting baryons, these systems, such as $[\Xi\Omega - \Xi^{*}\Omega]_{(1,1/2)}$, $[\Xi\Xi]_{(0,1)}$, $[N \Omega]_{(2,1/2)}$ would be weakly bound. The states of the second type such as $[\Sigma^{*} \Delta]_{(0,5/2)}$, $[\Sigma^{*} \Delta]_{(3,1/2)}$, $[\Delta\Delta]_{(0,3)}$ and $[\Delta\Delta]_{(3,0)}$ are named as $\Delta\Delta$-like states. Due to the highly symmetric character in orbital space, these systems could be relatively deeply bound, but the strong decay modes of composed baryons cause the widths of the states much broader. The states of the third type are entitled as $\Omega\Omega$-like states. Due to the same symmetry character shown in the systems of the second type and the only weak decay mode of composed baryons, for instance in $[\Omega\Omega]_{(0,0)}$, or at most one strong decay mode of composed baryons, for example in $[\Xi^{*}\Omega]_{(0,1/2)}$, these states are deeply bound states with narrow widths. The states of latter two types are most interesting new dibaryon states and should be carefully investigated both theoretically and experimentally.

The mass estimate of the $d^* (IJ^P=03^+)$ dibaryon is improved by a dynamical calculation in the quark delocalization, color screening model. The partial decay width of $d^*$ into an $NN$ D-wave state is also obtained. The mass obtained is slightly larger than that obtained in adiabatic calculations, due to the anharmonicity of the effective potential between two $\Delta$'s. The value of the width obtained due to tensor one-gluon-exchange is about 5 MeV, comparable in magnitude to earlier results found using pion exchange.

We study the questions of the existence and mass of the proposed $d' (IJ^P=00^-)$ dibaryon in the quark-delocalization, color-screening model (QDCSM). The transformation between physical and symmetry bases has been extended to the cases beyond the SU(2) orbital symmetry. Using parameters fixed by baryon properties and $NN$ scattering, we find a mild attraction in the $IJ^P=00^-$ channel, but it is not strong enough to form a deeply bound state as proposed for the $d'$ state. Nor does the (isospin) I=2 N$\Delta$ configuration have a deeply bound state. These results show that if a narrow dibaryon $d'$ state does exist, it must have a more complicated structure.

The work of Yuan et al. (Phys. Rev. C 60 (1999) 045203) is being represented as definitive regarding the non-existence of a particular nonstrange, isoscalar, spin three dibaryon which has been proposed. We comment on this paper and its relation to our work and that of others.

The quark cluster model studies concerning the H-dibaryon are reviewed. The covered topics are the H-dibaryon itself, the interaction between a nucleon and an H-dibaryon, and the one between two H-dibaryons. A related study on the H-dibaryon in nuclear matter is also reviewed and its implication to double hypernuclei is discussed.

We give a brief review of developments in the field of exotic hadrons formed of more than three quarks and/or antiquarks. In particular we discuss the stability of multiquark systems containing heavy flavours. We show that the gluon exchange model and the chiral constituent quark model based on Goldstone boson (pseudoscalar meson) exchange give entirely different results.

We investigate the possible existence of multibaryons with heavy flavor quantum numbers using the bound state approach to the topological soliton model and the recently proposed approximation for multiskyrmion fields based on rational maps. We use an effective interaction lagrangian which consistently incorporates both chiral symmetry and the heavy quark symmetry including the corrections up to order 1/m_Q. The model predicts some narrow heavy flavored multibaryon states with baryon number four and seven.

In the framework of $RGM$, the binding energy of the six quark system with strangeness s=-5 is systematically investigated under the SU(3) chiral constituent quark model. The single $\Xi^*\Omega$ channel calculation with spins S=0 and 3 and the coupled $\Xi\Omega$ and $\Xi^*\Omega$ channel calculation with spins S=1 and 2 are considered, respectively. The results show following observations: In the spin=0 case, $\Xi^* \Omega$ is a bound dibaryon with the binding energy being $80.0 \sim 92.4 MeV$. In the S=1 case, $\Xi\Omega$ is also a bound dibaryon. Its binding energy is ranged from $26.2 MeV$ to $32.9 MeV$. In the S=2 and S=3 cases, no evidence of bound dibaryons are found. The phase shifts and scattering lengths in the S=0 and S=1 cases are also given.

In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B*B* channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model I=1 BB potentials. A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.

The four-quark equations are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of cryptoexotic mesons including the quarks of three flavours (u, d, s) are calculated. The mass values of low-lying cryptoexotic mesons are calculated.

We discuss the stability of multiquark systems containing heavy flavours. We show that the Goldstone boson exchange (GBE) model gives results at variance with the one-gluon-exchange (OGE) model, i.e. when the GBE model stabilizes a system the OGE model destabilizes it and vice-versa.

SU(3) symmetry relations on the recently constructed hyperon-nucleon potentials are used to develop potential models for all possible baryon-baryon interaction channels. The main focus is on the interaction channels with total strangeness S=-2, -3, and -4, for which no experimental data exist yet. The potential models for these channels are based on SU(3) extensions of potential models for the S=0 and S=-1 sectors, which are fitted to experimental data. Although the SU(3) symmetry is not taken to be exact, the S=0 and S=-1 sectors still provide the necessary constraints to fix all free parameters. The potentials for the S=-2, -3, and -4 sectors, therefore, do not contain any additional free parameters, which makes them the first models of this kind. Various properties of the potentials are illustrated by giving results for scattering lengths, bound states, and total cross sections.

In the large $N_c$ limit, one can describe normal heavy baryons $Qqq$ and heavy pentaquarks $\bar Qqqqq$ as bound states of heavy mesons to chiral (anti)solitons. In this picture, the strong and electromagnetic decay parameters of these hadrons can be calculated from those of the constituent heavy mesons and light baryons, while the weak decay form factors can be evaluated analytically.

A systematic study of multiquark exotics with one or $N_c-1$ heavy quarks in the large $N_c$ limit is presented. By binding a chiral soliton to a heavy meson, either a normal $N_c$-quark baryon or an exotic $(N_c+2)$-quark baryon is obtained. By replacing the heavy quark with $N_c-1$ heavy antiquarks, exotic $(2N_c-2)$-quark and $2N_c$-quark mesons are obtained. When $N_c = 3$, they are just the normal triquark baryon $Qqq$, the exotic pentaquark baryon $Q\bar q\bar q\bar q\bar q$, tetraquark di-meson $\bar Q \bar Q qq$ and the hexaquark di-baryon $\bar Q \bar Q \bar q \bar q\ bar q \bar q$ respectively. Their stabilities and decays are also discussed. In particular, it is shown that the ``heavy to heavy'' semileptonic decays are described by the Isgur--Wise form factors of the normal baryons.