We study the hidden-charm pentaquark states $udsc\bar{c}$ with spins 1/2, 3/2, and 5/2 within the QCD sum-rule approach. First, we construct the currents for the particular configuration of pentaquark states that consist of the flavor singlet three-quark cluster $uds$ of spins 1/2 and 3/2 and the two-quark cluster $\bar cc$ of spin 1, where both clusters are in a color-octet state. From the QCD sum rules obtained by the operator product expansion up to dimension-10 condensates, the extracted masses for the pentaquark states $uds$-$\bar{c}c$ are about 4.6 GeV (5.6 GeV) for spin 1/2$^\pm$, about 5.1 GeV (6.0 GeV) for spin 3/2$^\pm$, about 6.1 GeV (5.9 GeV) for spin 5/2$^\pm$, where the masses of the positive parity states are given in parentheses. Additionally, based on the flavor singlet pentaquark states, it is also shown that other pentaquark states of clusters like $udc$-$\bar{c}s$ and $usc$-$\bar cd$ lead to masses similar to the $uds$-$\bar cc$ case within error bars. Furthermore, in order to see whether any of the states, observed by the LHCb Collaboration, could be understood as the pentaquark of two clusters in the color-octet state, we study the pentaquark formed by the two clusters $udc$-$\bar cu$, where the three-quark cluster is assumed to have the same flavor structure as the above $uds$ cluster. We come to the conclusion that if the observed pentaquark will be found to have spin 1/2 and negative parity, then it could be described as a state of two color-octet clusters.
We investigate the decay modes of pentaquark baryons for both the antidecuplet and the octet states, which were recently claimed by Close and Dudek to be potentially narrow due to a hidden selection rule. We discuss how ideal mixing between the pentaquark octet and antidecuplet states can be related to the OZI rule, which also naturally leads to certain selection rules in the pentaquark decays. We then introduce a tensor representation for the pentaquark states, and present the possible decay modes for both the unmixed and ideally mixed pentaquark octet and antidecuplet states. The exclusive d…
The $I(J^P)={1\over 2}({1\over 2}^-)$, ${1\over 2}({3\over 2}^-)$, and ${1\over 2}({5\over 2}^-)$ $uudc\overline{c}$ pentaquarks are investigated by the quark cluster model. This model, which reproduces the mass spectra of the color-singlet $S$-wave $q^3$ baryons and $q\overline{q}$ mesons, also enables us to evaluate the quark interaction in the color-octet $uud$ configurations. It is shown that the color-octet isospin-${1\over 2}$ spin-${3\over 2}$ $uud$ configuration gains attraction. The $uudc\overline{c}$ states with this configuration have structures around the $Σ_c{}^{(*)}\overline{D}{}…
Our hadro-charmonium and compact tetraquark model predictions, published before the BESIII and LHCb experimental data for the $Z_{\rm cs}(3985)$ and $Z_{\rm cs}(4003)$ tetraquarks were released, match surprisingly well with them. Here, we extend our results for the $P_{\rm cs}$ states to $Λ$ + charmonium configurations and also our hadro-charmonium predictions for $Z_{\rm c}$ and $X_{\rm c}$ tetraquarks to charmonium + pion/eta. We use them, in combination with our previous findings, to discuss the possible emergence of SU(3)$_{\rm f}$ pentaquark octets and tetraquark nonets in the hidden-char…
Evidence for the existence of exotic, pentaquark baryons was first found in the invariant mass spectrum of a baryon-meson pair, with the baryon in the octet of flavor SU(3). Exotic pentaquarks may also decay into members of the spin-3/2 baryon decuplet. We calculate relations between decay rates of the exotic pentaquark into a baryon decuplet and an octet of pseudoscalar mesons based on SU(3) flavor symmetry, including the leading flavor symmetry breaking term. We consider all possible representations for an exotic pentaquark, namely, that it belongs to either a \bar{10}, 27, or 35 representat…
We study the group structure of baryon anti-decuplet containing the $Θ^+$. We derive the SU(3) mass relations among the pentaquark baryons in the anti-decuplet, when there is either no mixing or ideal mixing with the pentaquark octet, as advocated by Jaffe and Wilczek. This constitutes the Gell-Mann--Okubo mass formula for the pentaquark baryons. We also derive SU(3) symmetric Lagrangian for the interactions of the baryons in the anti-decuplet with the meson octet and the baryon octet. Our analysis for the decay widths of the anti-decuplet states suggests that the N(1710) is ruled out as a pur…
The flavor SU(3) group structure of pentaquark baryons which form $\bm{1}$, $\bm{8}$, $\bm{10}$, $\bar{\bm{10}}$, $\bm{27}$, and $\bm{35}$ multiplets is investigated in quark model. The flavor wave functions of all the pentaquark baryons are constructed in SU(3) quark model and their Yukawa interactions with meson octet are obtained in general and in the special case of the octet-antidecuplet ideal mixing with the OZI rule. The mass sum rules of pentaquark baryons are also discussed.
A new type of charm pentaquark $P_{cs}$ with quark content $c\bar{c}uds$ in light-flavor singlet state is studied in the quark model. This state is analogous to the $P_{c}$ with $c\bar{c}uud$ in light-flavor octet, which was observed in LHC in 2015. Considering various combinations of color, spin and light flavor as internal quantum numbers in $P_{cs}$, we investigate the mass ordering of the $P_{cs}$'s by adopting both the one-gluon exchange interaction and the instanton-induced interaction in the quark model. The most stable configuration of $P_{cs}$ is identified to be total spin $1/2$ in w…
We consider hidden charm pentaquarks as hadroquarkonium states in a QCD inspired approach. Pentaquarks arise naturally as bound states of quarkonia excitations and ordinary baryons. The LHCb $P_c(4450)$ pentaquark is interpreted as a $ψ'$-nucleon bound state with spin-parity $J^P=3/2^-$. The partial decay width $Γ(P_c(4450)\to J/ψ+N)\approx 11$ MeV is calculated and turned out to be in agreement with the experimental data for $P_c(4450)$. The $P_c(4450)$ pentaquark is predicted to be a member of one of the two almost degenerate hidden-charm baryon octets with spin-parities $J^{P}=1/2^-,3/2^-$.…
$P_c$ resonances are studied in the approach of quark model and group theory. It is found that there are totally 17 possible pentaquark states with the quark contents $q^3Q \bar Q$ ($q$ are $u$ and $d$ quarks; $Q$ is $c$ quark) in the compact pentaquark picture, where the hidden heavy pentaquark states may take the color singlet-singlet ($[111]_{qqq}\otimes [111]_{c \bar c}$) and color octet-octet ($[21]_{qqq}\otimes [21]_{c \bar c}$) configurations. The partial decay widths of hidden heavy pentaquark states are calculated for all possible decay channels. The results show that the $pJ/ψ$ is th…
We investigate the possible existence of the spin 3/2 pentaquark states using interpolating currents with K-N color-octet structure in the framework of QCD finite energy sum rule (FESR). We pay special attention to the convergence of the operator product expansion.
Many new physics models with strongly interacting sectors predict a mass hierarchy between the lightest vector meson and the lightest pseudoscalar mesons. We examine the power of jet substructure tools to extend the 7 TeV LHC sensitivity to these new states for the case of QCD octet mesons, considering both two gluon and two b-jet decay modes for the pseudoscalar mesons. We develop both a simple dijet search using only the jet mass and a more sophisticated jet substructure analysis, both of which can discover the composite octets in a dijet-like signature. The reach depends on the mass hierarc…
Identifying the Roper N(1440) and N(1710) as the pentaquark octet and anti-decuplet, respectively, we analyze their main decay modes in the diquark picture. The ratio of the partial decay widths is largely consistent with the nearly ideal mixing of the Jaffe-Wilczek diquark model, which then allows to predict the width of the radiative decay of N(1440), $Γ_{10}(N\to pγ)=1/4 Γ_{12}(N\to nγ)=0.25-0.31$ MeV. We then show that the three-body radiative decay of the pentaquark anti-decuplet is quite enhanced due to its mixing with the pentaquark octet. We find for the $J^P={1/2}^+$ pentaquark anti-d…
Recent LHCb experiments have shown us that there are two resonances in the $J/ψp$ channel in the $Λ_b$ decay, whose spin and parity are most probably (3/2$^-$ 5/2$^+$). In this work, we investigate the $I(J^P)=1/2(1/2^-)$, $1/2(3/2^-)$, and $1/2(5/2^-)$ $uudc{\bar c}$ pentaquark states by employing the quark cluster model. It is found that the color-octet isospin-1/2 spin-3/2 $uud$ configuration gives an attraction to such five-quark systems. This configuration together with the color-octet $c{\bar c}$ pair gives structures around the $Σ_c^{(*)}{\bar D}{}^{(*)}$ thresholds: one bound state, tw…
We study one possible production mechanism for hidden charm pentaquark in e+e- collision, where it is produced via a color-octet c \bar c pair fragmentation. The pentaquark production at B factory energy is dominated by e+e- to c \bar c g to Pc + X. At Z^0 pole, for the pentaquark production, there are several partonic processes playing significant role. Our results show that it is possible to search for the direct pentaquark production signal at e+e- colliders, which is important to understand the properties of pentaquark.
In the framework of the color-magnetic interaction, we have systematically studied the mass splittings of the possible hidden-charm pentaquarks $qqqc\bar{c}$ ($q=u,d,s$) where the three light quarks are in a color-octet state. We find that i) the LHCb $P_c$ states fall in the mass region of the studied system; ii) most pentaquarks should be broad states since their $S$-wave open-charm decays are allowed while the lowest state is the $J^P=\frac12^-$ $Λ$-like pentaquark with probably the suppressed $η_cΛ$ decay mode only; and iii) the $J^P=\frac52^-$ states do not decay through $S$-wave and thei…
The discovery of three pentaquark peaks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- by the LHCb collaboration has a series of interesting consequences for hadron spectroscopy. If these hidden-charm objects are indeed hadronic molecules, as suspected, they will be constrained by heavy-flavor and SU(3)-flavor symmetries. The combination of these two symmetries will imply the existence of a series of five-flavor pentaquarks with quark content $\bar{b} c s d u$ and $b \bar{c} s d u$, that is, pentaquarks that contain each of the five quark flavors that hadronize. In addition, from SU(3)-fla…
We investigate three possible pentaquark candidates, one of which contains a single charm quark and the other two contain triple charm quarks in their substructure. To this end we apply QCD sum rule method and take into account both the positive and negative parity states corresponding to each possible pentaquark channel having spin $3/2$ or $1/2$. Insisting on the importance of identification of the members of pentaquark family we obtain their spectroscopic parameters such as masses and residues. These parameters are the main inputs in the searches for their electromagnetic, strong and weak i…
We present in this talk a recent analysis for the magnetic moments of the baryon antidecuplet within the framework of the chiral quark-soliton model with linear $m_s$ corrections considered. We take into account the mixing of higher representations to the collective magnetic moment operator, which comes from the SU(3) symmetry breaking. Dynamical parameters of the model are fixed by experimental data for the magnetic moments of the baryon octet as well as by the masses of the octet, decuplet and of $Θ^{+}$. The magnetic moment of $Θ^{+}$ is rather sensitive to the pion-nucleon sigma term and r…
Inspired by the newly observed $P_{ψs}^Λ(4338)$ and the reported $P_{cs}(4459)$, we indicate the existence of the molecular-type characteristic mass spectrum for hidden-charm pentaquark with strangeness. It shows that the $P_{cs}(4459)$ may contain two substructures corresponding to the $Ξ_c\bar{D}^*$ molecular states with $J^P=1/2^-$ and $3/2^-$, while there exists the corresponding $Ξ_c \bar{D}$ molecular state with $J^P=1/2^-$. As the prediction, we present another characteristic mass spectrum of the $Ξ_c^\prime\bar{D}^{(*)}$ molecular states. Experimental confirmation of these characterist…
We test a pentaquark model of the negative parity hyperon Lambda(1405). We use the model where valence four quarks and one antiquark move in a potential relativisticaly and interact with themselves and each other through gluon and NG boson. We calculate mass shift of the system and find that there are two Lambda(1405) with almost degenerate mass: one flavor singlet and one flavor octet. We calclate also sigma-term and scalar form factor of the hyperon and show their usefulness to deduce the number of valence quark in the hypeon.
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.
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 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…
The LHCb has discovered two new states with preferred $J^P$ quantum numbers $3/2^-$ and $5/2^+$ from $Λ_b$ decays. These new states can be interpreted as hidden charm pentaquarks. It has been argued that the main features of these pentaquarks can be described by diquark model. The diquark model predicts that the $3/2^-$ and $5/2^+$ are in two separate octet multiplets of flavor $SU(3)$ and there is also an additional decuplet pentaquark multiplet. Finding the states in these multiplets can provide crucial evidence for this model. The weak decays of b-baryon to a light meson and a pentaquark ca…
Encouraged by the observation of the pentaquark states $P^+_c(4380)$ and $P^+_c(4450)$, we propose a novel color flux-tube structure, pentagonal state, for pentaquark states within the framework of color flux-tube mode involving a five-body confinement potential. Numerical results on the heavy pentaquark states indicate that the states with three color flux-tube structures, diquark, octet and pentagonal structures, have the close masses, which can therefore be called QCD isomers analogous to isomers in Chemistry. The pentagonal structure has lowest energy. The state $P^+_c(4380)$ can be descri…
In this work, we employ the light-cone QCD sum rule to calculate the magnetic dipole moments of the $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$ pentaquark states by considering them as the diquark-diquark-antiquark and molecular pictures with quantum numbers $J^P = \frac{3}{2}^-$, $J^P = \frac{1}{2}^-$ and $J^P = \frac{1}{2}^-$, respectively. In the analyses, we use the diquark-diquark-antiquark and molecular form of interpolating currents, and photon distribution amplitudes to obtain the magnetic dipole moment of pentaquark states. Theoretical examinations on magnetic dipole moments of the hi…
We study the stability of the different quark substructures in a quark cluster approach to pentaquark states considering the color-magnetic spin-spin interactions between quarks. The most likely configuration is found to be a triquark-diquark one where the two quarks of the diquark are coupled to spin zero and anti-triplet representations of flavor and color, and the triquark has spin one-half and belongs to the triplet representation of color and to anti-sextet of flavor. To ensure total antisymmetry under the interchange of identical particles, triquark and diquark are in relative p-wave. Us…
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…
We study the five-quark system composed of $qqs\bar{Q}Q$ configuration ($q = u$ or $d$, $Q=b$ or $c$), in the framework of the chiral quark model. In consequence, a series of bound states with heavy flavors are predicted by precise five-body dynamical calculations. We found that taking color-octet structure into consideration always provides more bounding energy than color-singlet structure, and the more heavier quark prevents, the easier to form the bound states. We suggest $qqs\bar{b}b$ configuration is a compact $\bar{b}b$-pair surrounded by three other quarks, while $qqs\bar{b}c$, $qqs\bar…
Recently the observation of a new pentaquark state, the hidden-charmed strange $P_{cs}(4459)^0$, was reported by the LHCb Collaboration. The spin-parity quantum numbers of this state were not determined as a result of insufficient statistics. To shed light on its quantum numbers, we investigate its decay, $P_{cs}(4459)^0 \rightarrow J/ψΛ$, the mode that this state has been observed, within the QCD sum rule framework. We obtain the width of this decay assigning the spin-parity quantum numbers of $P_{cs}(4459)^0$ state as $J^P=\frac{1}{2}^-$ and its substructure as diquark-diquark-antiquark. To …
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 stud…
There are different assumptions on the substructure of the pentaquarks $P_c(4380)$ and $P_c(4450)$, newly founded in $J/ψN $ invariant mass by the LHCb collaboration, giving consistent mass results with the experimental observations. The experimental data and recent theoretical studies on their mass suggest interpretation of these states as spin-3/2 negative-parity and spin-5/2 positive-parity pentaquarks, respectively. There may exist opposite-parity states corresponding to these particles, as well. Despite a lot of studies, however, the nature and internal organization of these pentaquarks i…
We examine several assignments of spin and parity for the pentaquark Theta+ state (J^P=1/2^{+,-}, 3/2^{+,-}) in connection with known baryon resonances. Assuming that the Theta+ belongs to an antidecuplet representation which mixes with an octet, we calculate the mass spectra of the flavor partners of the Theta+ based on the SU(3) symmetry. The decay widths of the Theta+ and nucleon partners are analyzed for the consistency check of the mixing angle obtained from the masses. It is found that a suitable choice of the mixing angle successfully reproduces the observed masses of Theta(1540) and Xi…
We make an exhaustive investigation on the pentaquark states $qqqc\bar{c}$ ($q=u, d$ and $s$) and discuss the effect of color structures in a multiquark color flux-tube model. We exhibit a novel picture of the structure and properties of the states $P_c$ and $P_{cs}$ observed by the LHCb Collaboration. We can describe the states as the compact pentaquark states in the model. The spin-parity of the group of $P_c(4312)^+$ and $P_c(4337)^+$ is $\frac{1}{2}^-$ while that of the group of $P_c(4380)^+$, $P_c(4440)^+$ and $P_c(4457)^+$ is $\frac{3}{2}^-$. Their structures are pentagon, diquark, penta…
Within the framework of the generalized linear sigma model with glueballs recently proposed [1,2], we study the schematic spectroscopy of scalar and pseudoscalar mesons in the SU(3) flavor limit and explore their quark and glue contents. In this framework, for both scalars and pseudoscalars, the two octet physical states are admixtures of quark-antiquark and four-quark components, and the three singlet states contain quark-antiquark, four-quark and glue components. We identify the two scalar octets with $a_0(980)$ and $a_0(1450)$ and the two pseudoscalar octets with $π(137)$ and $π(1300)$. We …
The spin and orbital angular momentum carried by different quark flavors in the nucleon are calculated in the SU(3) chiral quark model with symmetry-breaking. The similar calculation is also performed for other octet and decuplet baryons. Furthermore, the flavor and spin contents for charm and anti-charm quarks are predicted in the SU(4) symmetry breaking chiral quark model.
On the possibility of testing the two-peak structure of the LHCb hidden-charm strange pentaquark $P_{cs}(4459)^0$ in near-threshold antikaon-induced charmonium production on protons and nuclei
We have used the light-cone formulation of Chiral-Quark Soliton Model to investigate the vector and axial content of octet, decuplet and the hypothetical antidecuplet in the flavor SU(3) symmetry limit. We have extended previous works by computing the 7Q contribution to vector and axial charges for the octet and antidecuplet but stayed at the 5Q sector for the decuplet where the full computation needs much more time. As expected the 7Q component has a weaker impact on the quantities but still changes them by a few percent. We give also a detailed decomposition of those charges into flavor, val…
