The newly confirmed pentaquark state $P_c(4312)$ has been treated as a weakly bound $(Σ_c\bar{D})$ state by a well-established chiral constituent quark model and by a dynamical calculation on quark degrees of freedom where the quark exchange effect is accounted for. The obtained mass $4308$ MeV agrees with data. In this work, the selected strong decays of the $P_c(4312)$ state are studied with the obtained wave function. It is shown that the width of the $Λ_c\bar{D}^*$ decay is overwhelmed and the branching ratios of the $p\,η_c$ and $p\,J/ψ$ decays are both less than 1 percentage.
The LHCb collaboration reported a fully charmed tetraquark state X(6900) in the invariant mass spectrum of $J/ψ$ pairs in 2020. This discovery inspires us to further study the fully heavy pentaquark system. In this work, we investigate systematically all possible configurations for ground fully heavy pentaquark system via the variational method in the constituent quark model. According to our calculations, we further analyze the relative lengths between quarks and the contributions to the pentaquark masses from different terms of the Hamiltonian. We think no stable states exist in fully heavy …
Some recent developments in the study of light and heavy pentaquarks are reviewed, mainly within constituent quark models. Emphasis is made on results obtained in the flavor-spin model where a nearly ideal octet-antidecuplet mixing is obtained. The charmed antisextet is reviewed in the context of an SU(4) classification.
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 …
We discuss the magnetic moments of the recently discovered exotic baryons Theta(+) and Xi(--) and their multiplet partners in the framework of a naive additive quark model. These baryons are set up as pentaquark states where four quarks and a single antiquark are located in their ground state orbit. The pentaquark states are classified as members of the flavor SU(3) octet and antidecuplet with spin-parity J^P = (1/2)^- and (3/2)^-, where we determine the magnetic moments of these pentaquark states.
We discuss certain general features of the pentaquark picture for the theta, its 10bar_F partner, Xi_{3/2}, and possible heavy quark analogues. Models employing spin-dependent interactions based on either effective Goldstone boson exchange or effective color magnetic exchange are also used to shed light on possible corrections to the Jaffe-Wilczek and Karliner-Lipkin scenarios. Some model-dependent features of the pentaquark picture (splitting patterns and relative decay couplings) are also discussed in the context of these models.
The newly observed $Θ^+$ 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 al…
It is shown that standard constituent quark models produce $(\bar c c qqq)$ hidden-charm pentaquarks, where $c$ denotes the charmed quark and $q$ a light quark, which lie below the lowest threshold for spontaneous dissociation and thus are stable in the limit where the internal $\bar c c$ annihilation is neglected. The binding is a cooperative effect of the chromoelectric and chromomagnetic components of the interaction, and it disappears in the static limit with a pure chromoelectric potential. Their wave function contains color sextet and color octet configurations for the subsystems and can…
Dynamical calculations are performed for all members of the flavor antidecuplet to which the pentaquark $Θ^+$ belongs. The framework is a constituent quark model where the short-range interaction has a flavor-spin structure. From symmetry considerations the lowest state acquires a positive parity. By fitting the mass of $Θ^+$ of minimal content $uudd\bar{s}$, the mass of $Ξ^{--}$, of minimal content $ddss \bar{u}$, is predicted to be approximately 1960 MeV. It is shown that the octet and antidecuplet states with the same quantum numbers mix ideally due to SU(3)$_F$ breaking.
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…
The recently discovered $P_c(4380)^+$ and $P_c(4450)^+$ states at LHCb have masses close to the $\bar DΣ_c^*$ and $\bar D^*Σ_c$ thresholds, respectively, which suggest that they may have significant meson-baryon molecular components. We analyze these states in the framework of a constituent quark model which has been applied to a wide range of hadronic observables, being the model parameters, therefore, completely constrained. The $P_c(4380)^+$ and $P_c(4450)^+$ are studied as molecular states composed by charmed baryons and open charm mesons. Several bound states with the proper binding energ…
We study hidden-flavor pentaquarks, $Q\bar Q qqq$, based on a constituent quark-model with a standard quark-quark interaction that reproduces the low-energy meson and baryon spectra. We make use of dynamical correlations between the heavy quarks arising from the Coulomb-like nature of the short-range interaction. A detailed comparison is made with other results in the literature and with experimental data. Our results show a different pattern for open-flavor and hidden-flavor pentaquarks, as suggested by the data. Further implications about the existence of quarkonia bound to nuclei are discus…
Within the chiral constituent quark model of Glozman and Riska, we discuss the stability of heavy pentaquarks, i.e. hadrons containing four light quarks and a heavy antiquark. The spin-dependent part of the Hamiltonian is dominated by the short-range part of the Goldstone-boson-exchange interaction. We find that these systems are not bound, having an energy above the lowest dissociation threshold into a baryon and a meson.
In the framework of the chiral quark model, we investigate the hidden strange pentaquark system of the $Nϕ$ state with the quantum numbers of IJ=$\frac{1}{2}$$\frac{3}{2}$. The results show that the $Nϕ$ state can be bound through the interaction of the $σ$ meson exchange plus the effect of the channel coupling, which means that the effect of the channel coupling has an influence on the existence of this bound state.
We use a constituent model to analyze the stability of pentaquark $\bar Q qqqq$ configurations with a heavy antiquark $\bar c$ or $\bar b$, and four light quarks $uuds$, $ddsu$ or $ssud$. The interplay between chromoelectric and chromomagnetic effects is not favorable, and, as a consequence, no bound state is found below the lowest dissociation threshold.
We study the stability of the pentaquarks uuddQbar, uudsQbar and udssQbar (Q = c, b, or t) of positive parity in a constituent quark model based on Goldstone boson exchange interaction between quarks. The pentaquark parity is the antiquark parity times that of a quark excited to a p-shell. We show that the Goldstone boson exchange interaction favors these pentaquarks much more than the negative parity ones of the same flavour content but all quarks in the ground state. We find that the nonstrange pentaquarks are stable against strong decays.
States beyond those expected in the simple constituent quark model are now emerging. I focus on the scalar glueball and its mixing with states in the $q\bar{q}$ nonet, and also on correlations in Strong QCD that may form diquarks and seed $qq\bar{q}\bar{q}$ states. Some models of the pentaquark candidate $Θ(1540)$ are critically discussed.
Studying scattering of heavy flavor hadrons and looking for bound states is shown to give experimental information otherwise unobtainable about effective two-body interactions between constituent $(qq)_6$ and $(\bar qq)_8$ pairs respectively in color sextet and color octet states. All the successes of the constituent quark model in $(uds)$ hadron spectroscopy are shown to depend only on effective two-body interactions in color $3^*$ and singlet states. New directions for bound pentaquark searches are discussed following the availability of vertex detectors which can pinpoint events where a pro…
Is there a theory or good experimental evidence? Bj's question: Pentaquark is created by $e^+e^-$. $2q + q \to$ Baryon $; ~ ~ ~ 2q + \bar q \to $ Triquark$ ; ~ ~ ~ 2q + $Triquark $ \to $Pentaquark Does it live long onough to be observable? Basic physics of constituent quarks and flavor antisymmetry. Report of $Θ^+$ violating flavor antisymmetry indicates need for two-cluster model.. Ball in Experimental Court - Some experiments see $Θ^+$; others don't. Possible production mechanisms present in some experiments, absent in others; e.g. via $N^*(2.3 \rm{GeV}) \to Θ^+ + \bar K$?
The constituent quark model with color-spin hyperfine potential is used to investigate the property of a compact pentaquark configuration with $J^p$=$3/2^-$ and isospin=1/2, which is the most likely quantum number of one of the recently observed exotic baryon states at LHCb. Starting from the characterization of the isospin, color, and spin states for the pentaquark configuration, we construct the total wave function composed of the spatial wave function, which we take to be symmetric and in S-wave, and the four orthogonal isospin $\otimes$ color $\otimes$ spin states that satisfy the Pauli pr…
The exotic baryon $Θ^+$ (1540 MeV)$ is visualised as an expected (iso) rotational excitation in the Chiral Soliton Model. It is also argued as a Pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast the two points of view; the similarities and differences between the two pictures. Collective excitation, characteristic of Chiral Soliton Model points toward small mixing of representations in the wake of SU(3) breaking. In contrast, Constituent quark Models prefer near ``ideal'' mixing, similar to $ω- ϕ$ mixing.
In present work, we investigate the spectrum of several low-lying $sscq\bar{q}$ pentaquark configurations employing the constituent quark model, within which the hyperfine interaction between quarks is taken to be mediated by Goldstone boson exchange. Our numerical results show that four $sscq\bar{q}$ configurations with $J^{P}=1/2^{-}$ or $J^{P}=3/2^{-}$ lie at energies very close to the recently observed five $Ω_{c}^{0}$ states by LHCb collaboration, this indicates that the $sscq\bar{q}$ pentaquark configurations may form sizable components of the observed $Ω_{c}^{0}$ resonances.
The pentaquarks are exotic baryons formed of four quarks and an antiquarks. Their existence has been discussed in the literature over the last 30 years or more, first in connection with kaon nucleon scattering data. The subject has been revived by the end of 2002 when experimental evidence of a narrow baryon of strangeness $S$ = + 1, and mass $M \simeq$ 1530 MeV has been found. This is interpreted as the lightest member of an SU(3)-flavor antidecuplet. Here we shall mainly review the predictions of pentaquark properties as e.g. mass, spin and parity, within constituent quark models. Both light…
The pentaquark is studied in a simple model of confinement where the quarks and the antiquark are linked by flux tubes of minimal cumulated length, and the Coulomb-like interaction, the spin-dependent terms and the antisymmetrization constraints are neglected.. The ground-state is found to be stable against spontaneous dissociation into a meson and a baryon, both in the case of five equal-mass constituents and for a static quark or antiquark surrounded by four equal masses.
We analyse the decay $Θ_s(1/2^+)\to NK$ in a non-relativistic Fock space description using three and five constituent quarks for the nucleon and the pentaquark, respectively. Following Jaffe and Wilczek \cite{jw}, we assume that quark-quark correlations in spin-zero state play an important role for the pentaquark internal structure. Within this scenario, a strong dynamical suppression of the decay width is shown to be possible only if the pentaquark has an asymmetric "peanut" structure with the strange antiquark in the center and the two extended composite diquarks rotating around. In this cas…
We consider the $Θ^+(1540)$ pentaquark in the string model that correctly reproduces the linear Regge trajectories for the case of orbital excitations of light $q\bar q$ mesons and $qqq$ baryons. Assuming (and arguing in favour of) the diquark-antiquark-diquark ($[ud]\bar s [ud]$) clustering of this orbitally excited object we found its mass about $290 \rm {MeV}$ above the experimental value $1540 \rm {MeV}$. In the model considered this discrepancy could be attributed to the change of the constituent mass of $\bar s$ antiquark as compared to that of $s$ quark localized at the string end.
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 ef…
We systematically analyze the flavor color spin structure of the pentaquark $q^4\bar{Q}$ system in a constituent quark model based on the chromomagnetic interaction in both the SU(3) flavor symmetric and SU(3) flavor broken case with and without charm quarks. We show that the originally proposed pentaquark state $\bar{Q}s qqq$ by Gignoux et al and by Lipkin indeed belongs to the most stable pentaquark configuration, but that when charm quark mass correction based on recent experiments are taken into account, a doubly charmed antistrange pentaquark configuration ($udc c \bar{s}$) is perhaps the…
With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some insights on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the gaussian expansion method, has been employed systematically in the real- and complex-range investigations. We review herein the double- and full-heavy tetraquarks, but also the hidden-charm, -bottom and doubly charmed pentaquarks. Several experimentally observed exotic hadrons are well reproduced within our approach; moreover, their p…
QCD instantons are known to produce deeply bound diquarks which may be used as building blocks in the formation of multiquark states, in particular pentaquarks and dibaryons. We suggest a simple model in which the lowest scalar diquark (and possibly the tensor one) can be treated as an independent ``body'', with the same color and (approximately) the mass as a constituent (anti)quark. In this model a new symmetry between states with the same number of ``bodies'' but different number of quarks appear, in particular the 3-``body'' pentaquarks can be naturally related to decuplet baryons. We esti…
Dynamical calculations are performed for all isomultiplets of the flavour antidecuplet to which the newly discovered pentaquark $Θ^+$ belongs. The framework is a constituent quark model where the short-range interaction has a flavour-spin structure. In this model the lowest pentaquarks have positive parity. Each antidecuplet member is described by a variational solution with the Pauli principle properly taken into account. By fitting the mass of $Θ^+$ of minimal content $uudd\bar{s}$, the mass of $Ξ^{--}$, of minimal content $ddss \bar{u}$, is predicted at approximately 1960 MeV. The influence…
We study a few of the lowest states of the pentaquark $uudc\overline{c}$, of positive and negative parity, in a constituent quark model with an SU(4) flavor-spin hyperfine interaction. For positive parity we introduce space wave functions of appropriate permutation symmetry with one unit of orbital angular momentum in the internal motion of the four-quark subsystem or an orbital excitation between the antiquark and the four quark subsystem which remains in the ground state. We show that the lowest positive parity states $1/2^+, 3/2^+$ are provided by the first alternative and are located below…
Hadron spectroscopy has received revitalised interest due to the discovery of states with unexpected properties. Discussed are the recent findings at BABAR, CLEO, BELLE and BES. A detailed report is given on the many experiments reporting evidence (or counter--evidence) for the $Θ^+(1540)$ and other pentaquarks. In conventional meson and in baryon spectroscopy, evidence is emerging that one--gluon--exchange does not provide the appropiate means to understand low--energy QCD; instanton--induced interactions yield much more insight. In particular the rich spectrum of baryon resonances is very we…
We study pentaquark states of both light $q^4\bar q$ and hidden heavy $q^3 Q\bar Q$ (q = u,d,s quark in SU(3) flavor symmetry; Q = c, b quark) systems with a general group theory approach in the constituent quark model, and the spectrum of light baryon resonances in the ansatz that the $l=1$ baryon states may consist of the $q^3$ as well as $q^4\bar q$ pentaquark component. The model is fitted to ground state baryons and light baryon resonances which are believed to be normal three-quark states. The work reveals that the $N(1535)1/2^{-}$ and $N(1520)3/2^-$ may consist of a large $q^4\bar q$ co…
Basic 1966 physics of Sakharov, Zeldovich and Nambu updated by QCD with constituent-quark quasiparticles having effective masses fits all masses and magnetic moments of ground state meson and baryons having no more than one strange or heavy quark Flavor antisymmetry explains absence of low-lying exotics and suggests diquark-triquark model and two-state model for $Θ^+$ pentaquark. Variational approach gives mass bounds for other pentaquarks.
We investigate light meson bound state contributions to six quark Green's functions and establish that the latter has poles corresponding to baryon bound states. We estimate light baryon masses including the Roper resonance. Constituent quark model and the Parton model are natural consequences of this quantum field theoretic picture. We elaborate this analysis to pentaquarks and heptaquarks. An almost model independent prediction for the mass of $θ$ pentaquark is $1.57Gev$.
In some models, exotic baryons with strangeness and anticharm or antibeauty should exist and even be stable against strong decay. We consider the stability of such possible exotic baryons, which in the constituent quark picture are called pentaquarks (each is composed of four quarks and an antiquark). Our model is based on diquark clustering and supersymmetry in hadrons, and assumes that the spin-dependent force between quarks arises from one-gluon exchange. In the model, a pentaquark with strangeness and anticharm can decay strongly, but an analogous pentaquark with an antibeauty quark is sta…
We explore further the idea that the lattice QCD data for hadron properties in the region m_π^2 > 0.2 GeV^2 can be described by the constituent quark model. This leads to a natural explanation of the fact that nucleon excited states are generally stable for pion masses greater than their physical excitation energies. Finally we apply these same ideas to the problem of how pentaquarks might behave in lattice QCD, with interesting conclusions.
QCD instantons are known to produce deeply bound diquarks. We study whether it may be used as building blocks in the formation of multiquark states, in particular pentaquarks and dibaryons. A simple model is presented in which the lowest scalar diquark (and possibly the tensor one) can be treated as an independent ``body'', with the same color and (approximately) the same mass as a constituent (anti)quark. In it a new symmetry exists between states with the same number of ``bodies'' but different number of quarks appear, in particular the 3-``body'' pentaquarks can be naturally related to some…
We study the spectrum of the isoscalar pentaquark $udsc\overline{c}$, of either positive or negative parity, in a constituent quark model with linear confinement and a flavor-spin hyperfine interaction previously extended to SU(4) and used to describe the spectrum of the $uudc\overline{c}$ pentaquarks observed at LHCb in 2019. For positive parity we make a distinction between the case where one unit of angular momentum is located in the subsystem of four quarks and the case where the angular momentum is located in the relative motion between a ground state four-quark subsystem and the antiquar…
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 …
The recently discovered pentaquark $Θ^+$ 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 $Θ^+$ are constructed, which have …
Group theoretic method for the systematic study of five-quark states with meson-baryon ($q\bar{q}-q^3$) configuration is developed. The calculation of matrix elements of many body Hamiltonian is simplified by transforming the physical bases (meson-baryon quark cluster bases) to symmetry bases (group chain classified bases), where the fractional parentage expansion method can be used. Three quark models, the naive Glashow-Isgur model, Salamanca chiral quark model and quark delocalization color screening model, are used to show the general applicability of the method and general results of const…
We calculate light-front wave functions of mesons, baryons and pentaquarks in a model including constituent mass (representing chiral symmetry breaking), harmonic confining potential, and 4-quark local interaction of 't Hooft type. The model is a simplified version of that used by Jia and Vary. The method used is numerical diagonalization of the Hamiltonian matrix, with certain functional basis. We found that the nucleon wave function displays strong diquar correlations, unlike that for Delta (decuplet) baryon. We also calculate 3-quark-5-quark admixture to baryons, and the resulting antiquark…
In a previous work we have studied the isospin 1/2 lowest positive and negative parity states of the pentaquark $uudc\overline{c}$, in a constituent quark model with a linear confinement and an SU(4) flavor-spin hyperfine interaction and we compared the results with the $P^+_c(4312)$, $P^+_c(4440)$ and $P^+_c(4457)$ pentaquarks observed at LHCb in 2019. Here we extend the previous work by calculating ratios of decay rates of the $P_c$ pentaquarks to $J/Ψ$ and $η_c$ and similarly the ratio of decay rates to $Λ_c {\bar D}^*$ and $Λ_c \bar D$. Our predictions are based on the SU(4)$\times$SU(2) s…
The hadron production in relativistic heavy ion collisions is well described by the quark combination model. The mixed ratios for various hadrons and the transverse momentum spectra for long-life hadrons are predicted and agree with recent RHIC data. The production rates for the pentaquarks $Θ^+$, $Θ^{*++}$ and the di-baryon $(ΩΩ)_{0^{+}}$ are estimated, neglecting the effect from the transition amplitude for constituent quarks to form an exotic state.
The exclusive processes are considered, where a point-like source of heavy quark-antiquark pairs $Q \bar Q$, e.g. their electromagnetic current, produces a pair consisting of a heavy quarkoniumlike exotic meson (tetraquark) or baryon (pentaquark) and a light meson or an antibaryon. For a sufficiently large mass of the heavy quark $m_Q$ there is a range of the energy $E$ above the $Q \bar Q$ threshold, where $E \ll m_Q$ and still the energy is large compared to the strong interaction scale, $E \gg Λ_{QCD}$. It is shown that in this energy range, where the heavy quarks are nonrelelativistic, a s…
Exotic hadrons are important because their existence or absence can provide important clues to understanding how QCD makes hadrons from quarks and gluons. The first experimentally confirmed exotic will be the first hadron containing both $qq$ and $\bar q q$ pairs and the first hadron containing color sextet and color octet pairs. Theoretical models are not very useful because there is no accepted model for multiquark systems with color-space correlations. The constituent quark model is the only phenomenological model with predictive power that has given experimentally tested universal predicti…
Spectrum of the low-lying $Ω_{cc}$ resonances with negative parity, which are assumed to be dominated by $sccq\bar{q}$ pentaquark components, is investigated using the chiral constituent quark model. Energies of the $Ω_{cc}$ resonances are obtained by considering the hyperfine interaction between quarks by exchanging Goldstone boson. Possible $sccq\bar{q}$ configurations with spin-parity $1/2^{-}$, $3/2^{-}$ and $5/2^{-}$ are taken into account. Numerical results show that the lowest $Ω_{cc}$ resonances with negative parity may lie at $4050 \pm 100$ MeV. In addition, the transitions of the $Ω_…
In this conference summary talk at Hadron03, questions and challenges for Hadron physics of light flavours are outlined. Precision data and recent discoveries are at last exposing the limitations of the naive constituent quark model and also giving hints as to its extension into a more mature description of hadrons. These notes also pay special attention to the positive strangeness baryon $Θ^+(1540)$ and include a pedagogic discussion of wavefunctions in the pentaquark picture, their relation with the Skyrme model and related issues of phenomenology.
Hidden-charm pentaquark-like $P_{ψs}^Λ(4459)^0$ and $P_{ψs}^Λ(4338)$ resonances are studied in a constituent quark model as molecular meson-baryon structures. Such states are found in the $J^P(I)=\frac{1}{2}^-(0)$ channel with masses and widths compatible with the experimental measurements in a coupled-channels calculation with all the parameters constrained from previous studies. Other candidates are explored in the $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$ channels in the charm and bottom sectors, with isospins $0$ ($P_{ψs}^Λ$ and $P_{Υs}^Λ$) and $1$ ($P_{ψs}^Σ$ and $P_{Υs}^Σ$…
