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 constituent quark models for five-quark states are given. The method can also be useful in the calculation of meson-baryon scattering and the study of the five-quark components effect in baryon structure. The physical contents of different model configurations for the same multi-quark system can also be compared through the transformation between different physical bases to the same set of symmetry bases.
We study the properties of the colour triplet qqqbar quark cluster when flavour symmetry is broken. The relevance of such a cluster for some models of pentaquarks is then examined in the light of recent experimental signals.
In the paper, we study the production of pentaquark $\bar{c}q qqq$ from singly bottom baryon. The tensor representations of pentaquark $\bar{c}q qqq$ are completed at first. Under the light quark symmetry analysis, we decompose the singly charmed pentaquarks into $6$, $15$ and $15'$ multiple states, and deduce the representations of these states. Then we construct the production Hamiltonian of the multiple states in proper order. For completeness, we systematically study the production channels of pentaquark states, including the possible production amplitudes and cross section relations betwe…
In the framework of the color-magnetic interaction model, we have systematically calculated the mass splittings for the S-wave triply heavy pentaquark states with the configuration $qqQQ\bar{Q}$ $(Q=c,b;q=u,d,s)$. Their masses are estimated and their stabilities are discussed according to possible rearrangement decay patterns. Our results indicate that there may exist several stable or narrow such states. We hope the present study can help experimentalists to search for exotic pentaquarks.
We study the masses and lifetimes of doubly charmed pentaquark $P_{cc\bar qqq}(q=u,d,s)$ primarily. The operation of masses carried out by the doubly heavy triquark-diquark model, whose results suggests the existence of stable states $cc\bar s ud$ with the parity $J^P=\frac{1}{2}^-$. The roughly calculation about lifetimes show the short magnitudes, $(4.65^{+0.71}_{-0.55})\times 10^{-13}s $ for the parity $J^P=\frac{1}{2}^-$ and $(0.93^{+0.14}_{-0.11})\times 10^{-12} s $ for $J^P=\frac{3}{2}^-$. Since the pentaquark $cc\bar s ud$ is interpreted as the stable bound states against strong decays,…
We investigate the pentaquark system $qqqs \bar q$ in a framework of chiral quark model. Two structures, $(qqq)(s\bar{q})$ and $(qqs)(q\bar{q})$, with all possible color, spin, flavor configurations are considered. The calculations show that there are several possible resonance states, $Sigma π$ and $N \bar{K}$ state with $IJ^P=0\frac{1}{2}^-$, $Σ^* π$ with $IJ^P=0\frac{3}{2}^-$, $Σ^* ρ$ with $IJ^P=0\frac{5}{2}^-$, $Δ\bar{K}$ with $IJ^P=1\frac{3}{2}^-$ and $Δ\bar{K}^*$ with $IJ^P=1\frac{5}{2}^-$. Where the $N \bar{K}$ state with $IJ^P=0\frac{1}{2}^-$ can be used to explain the $Λ(1405)$, and t…
As a hot issue, exploring exotic pentaquarks is full of challenges and opportunities for both theorist and experimentalist. In this work, we focus on a type of pentaquark with the $QQqq\bar{q}$ ($Q=b,c$; $q=u,d,s$) configuration, where their mass spectrum is estimated systematically. Especially, our result indicates that there may exist some stable or narrow exotic pentaquark states. Obviously, our study may provides valuable information for further experimental search for the $QQqq\bar{q}$ pentaquarks. With the running of LHCb and forthcoming Belle II, we have a reason to believe that these p…
In this work, we carry out the study of heavy flavor pentatuarks with four heavy quarks, which have typical $QQQQ\bar q$ configuration. Within the Chromomagnetic Interaction model, the mass spectrum of these discussed $QQQQ\bar q$ pentaquarks is given. In addition to the mass spectrum analysis, we also illustrate their two-body strong decay behavior by estimating some ratios of decay channels. By these effort, we suggest that future experiment should pay attention to this kind of pentaquark.
It is shown that the exotic non-qqq hadrons of pentaquark $qqqq\bar{q}$ states can be clearly distinguished from the conventional qqq-baryon resonances or their hybrids if the flavor of $\bar{q}$ is different from any of the other four quarks. We suggest the physical process $p(e,e'K^-)Z(uuud\bar{s})$, which can be investigated at the Thomas Jefferson National Accelerator Facility (JLab), as an ideal process to search for the existence or non-existence of the exotic hadron of minimal pentaquark state $Z(uuud\bar{s})$. (The search for the existence of $Z(uudd\bar{s})$ is also discussed in the p…
$QQ^\prime qq\bar q$ pentaquarks are studied in a potential model, under the hypothesis that they are composite objects of two diquarks and one antiquark. The interaction between two colored objects includes two contributions, one based on the $q\bar q$ potential in QCD, computed in the gauge/string duality approach, and another describing the spin-spin interaction. The model has been extended to investigate pentaquarks with different quark content, as $Qqqq\bar q$ and $Qqqq\bar Q$, the latter including the states observed by LHCb, $P_c(4380)^+$ and $P_c(4450)^+$, later updated, with a new dat…
$P_c$ 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 discuss the mass splittings for the $S$-wave triply heavy pentaquark states with the $QQQq\bar{q}$ $(Q=b,c;q=u,d,s)$ configuration which is a mirror structure of $Q\bar{Q}qqq$. The latter configuration is related with the nature of $P_c(4380)$ observed by the LHCb Collaboration. The considered pentaquark masses are roughly estimated with a simple method. One finds that such states are probably not narrow even if they do exist. This leaves room for molecule interpretation for a state around the low-lying threshold of a doubly heavy baryon and a heavy-light meson, e.g. $Ξ_{cc}D$, if it were o…
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 propose a new type of structure for singly heavy baryons of $Qqq\bar{q}q$ in addition to the conventional one of $Qqq$. Based on chiral symmetry of the light quarks, we show that the $Qqq\bar{q}q$ baryon offers a novel picture for heavy quark spin-singlet and flavor-antisymmetric baryons. By making use of the effective Lagrangian approach, we find $Λ_c(2765)$ and $Ξ_c(2967)$ are mostly $Qqq\bar{q}q$ while $Λ_c(2286)$ and $Ξ_c(2470)$ are mostly $Qqq$. The masses of negative-parity baryons are predicted. We also derive a sum rule and the extended Goldberger-Treiman relation that the masses of…
Developing the calculation techniques to fivefold heavy hadrons, we perform the study of novel fully-heavy $QQQQ\bar{Q}$ pentaquark states by the QCD sum rule approach that is firmly based on the QCD basic theory. Numerically, masses of fully-heavy pentaquark states are calculated to be $7.41^{+0.27}_{-0.31}~\mbox{GeV}$ for $cccc\bar{c}$ and $21.60^{+0.73}_{-0.22}~\mbox{GeV}$ for $bbbb\bar{b}$, respectively. In experiment, these predicted all-heavy pentaquark states could be searched for in the $Ω_{QQQ}η_{Q}$ invariant mass spectrum.
With the discovery of some hidden-charm pentaquark resonances by the LHCb Collaboration, investigations of pentaquark states containing heavy quarks have aroused the interest of theorists. We study herein $qqq\bar{q}Q$ ($q = u$ or $d$, $Q=c$ or $b$) pentaquark system, in the framework of the chiral quark model. In consequence, some charmed and bottomed pentaquarks are considered to exist by five-body dynamical calculations. In the charm sector, $Σ_cπ(IJ^P=0\frac{1}{2}^-)$ and $Σ_c^*π(IJ^P=0\frac{3}{2}^-)$ are possible candidates of $Λ_c(2595)$ and $Λ_c(2625)$, respectively. Besides, two high-s…
For the case of two light flavors we propose the stringy description of the system consisting of two heavy and three light quarks, with the aim of exploring the quark organization inside the system and its low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis reveals several critical separations related to the processes of string reconnection, breaking and junction annihilation. We find that a compact pentaquark configuration makes the dominant contribution to the potential of the first excited state at small separations, and for separations larger tha…
Inspired by the observed $X(2900)$, we study systematically the mass spectra of the ground pentaquark states with the $qqqq\bar{Q}$ ($Q=c,b$; $q=n,s$; $n=u,d$) configuration in the framework of the Chromomagnetic Interaction model. We present a detailed analysis of their stabilities and decay behaviors. Our results indicate that there may exist narrow states or even stable states. We hope that the present study may inspire experimentalist's interest in searching for such a type of the exotic pentaquark state.
We study baryo-charmonium [$η_{\rm c}$- and $J/ψ$-$N^*$, $η_{\rm c}(2S)$-, $ψ(2S)$- and $χ_{\rm c}(1P)$-$N$] and baryo-bottomonium [$η_{\rm b}(2S)$-, $Υ(2S)$- and $χ_{\rm b}(1P)$-$N$] bound states, where $N$ is the nucleon and $N^*$ a nucleon resonance. In the baryo-quarkonium model, the five $qqq Q \bar Q$ quarks are arranged in terms of a heavy quarkonium core, $Q \bar Q$, embedded in light baryonic matter, $qqq$, with $q = u$ or $d$. The interaction between the $Q \bar Q$ core and the light baryon can be written in terms of the QCD multipole expansion. The spectrum of baryo-charmonium state…
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.
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…
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…
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…
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.
By comparing SU(3)-breaking scales of linear mass formulae, it is shown that the lowest vector, axial-vector, and scalar mesons all have a $\bar{q}q$ configuration, while the ground-state octet and decuplet baryons are $qqq$. Also, the quark-level linear $σ$ model is employed to predict similar $\bar{q}q$ and $qqq$ states. Finally, the approximate mass degeneracy of the scalar $a_0$(980) and $f_0$(980) mesons is demonstrated to be accidental.
We identify essential differences between the pentaquark and chiral soliton models of \10bar$_5$ and {\bf 8}$_5$ pentaquarks and conventional {\bf 8}$_3$ states, which are experimentally measurable. We show how the decays of $Ξ_5$ states in particular can test models of the pentaquarks, recommend study of the relative branching ratios of e.g. $Ξ^{-}_5 \to Ξ^-π^0:Ξ^0π^-$, and predict that the decay amplitude $Ξ_5 \to Ξ^*π$ is zero at leading order in pentaquark models for any mixture of \10bar and the associated {\bf 8}$_5$. We also include a pedagogic discussion of wavefunctions in the pentaqu…
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…
We evaluate the static $qq\bar{q}\bar{q}$ and $qqqq\bar{q}$ potentials in the quenched theory at $β=5.8$ and $β=6.0$ on a lattice of size $16^3\times 32$. We compare the static potentials to the sum of two meson potentials for the tetraquark system and to the sum of the baryonic and mesonic potentials for the pentaquark state, as well as, with the confining potential obtained in the strong coupling expansion.
We give the explicit wave functions of the $qqqq\bar{q}$ components of the C=+1, J=1/2 charmed baryons, $Σ_{c}$, $Λ_{c}$ and $Ξ_{c}^{a}$, and calculate the magnetic moments by adding the 5q components contributions, and we also compute the magnetic moments of the $Σ_{b}$ and $Σ_{b}^{*}$ baryons. The influence of the additional light and strange $q\bar{q}$ pairs is investigated. It's obvious that the constituent quark masses of the charm and beauty quarks are much heavier than that of the light and strange quarks, consequently, the hidden flavor contributions to the baryons magnetic moments may…
Using the gauge/gravity duality, we investigate the string breaking and dissolution of two heavy quarks coupled to a light quark at finite temperature. It is found that there exist three configurations of QQq with the increase of separate distance for heavy quarks in the confined phase. Besides, the string breaking occurs at the distance $L_{\rm{QQq}} = 1.27 \rm{fm}$($T = 0.1 \rm{GeV}$) for the decay mode $\rm{Q Q q \rightarrow Q q q+Q \bar{q}}$. In the deconfined phase, QQq will melt at a certain distance then becomes free quarks. At last, we compare the potential of QQq with that of $\rm{Q\b…
The Interaction of Moving $\mathbf{Q\bar{Q}}$ and QQq in the Thermal Plasma
School of Nuclear Science and Technology, University of South China（南华大学核科学技术学院）；Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室）；INFN – Istituto Nazionale di Fisica Nucleare – Sezione di Bari（意大利国家核物理研究所巴里分部）
Baryons of the type Qqqqq-bar (where Q = c,b and q = u,d,s quarks) forming anti-decapenta (15)-plets with spin-parity one half-plus are predicted on simple theoretical considerations. The lightest members of these multiplets are explicitly exotic doublets cuuds-bar, cudds-bar with mass about 2420 MeV, and buuds-bar, budds-bar with mass about 5750 MeV, only 130 MeV heavier than Lambda_c and Lambda_b, respectively, and thus stable against strong decays. Although the production rate is probably very low, these remarkable pentaquarks can be looked for at LHC, Fermilab, B-factories, RHIC and elsewh…
In this article, we illustrate how to calculate the hadronic coupling constants of the pentaquark states with the QCD sum rules based on rigorous quark-hadron quality, then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with the spin-parity $J^P={\frac{1}{2}}^-$ in details, and calculate the partial decay widths. The total width $Γ(P_c)=14.32\pm3.31\,\rm{MeV}$ is compatible with the experimental value $Γ_{P_c(4312)} = 9.8\pm2.7^{+ 3.7}_{- 4.5} \mbox{ MeV}$ from the LHCb collaboration, and favors assigning the $P_c(4312)$ to be t…
Several recent experiments have reported evidence for a narrow baryon resonance with positive strangeness ($Θ^+$) at a mass of 1.54 GeV/$c^2$. Baryons with $S=+1$ cannot be conventional $qqq$ states and the reports have thus generated much theoretical speculation about the nature of possible $S=+1$ baryons, including a 5-quark, or pentaquark, interpretation. We show that narrow enhancements in the $K^+n$ effective mass spectrum can be generated as kinematic reflections resulting from the decay of mesons, such as the $f_2(1275)$, the $a_2(1320)$ and the $ρ_3(1690)$.
A qqq BSE formalism based on DBχS of an input 4-fermion Lagrangian of `current' u,d quarks interacting pairwise via gluon-exchange-propagator in its {\it non-perturbative} regime, is employed for the calculation of baryon self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green's function techniques. This is a 3-body extension of an earlier q{\bar q} (2-body) result on the exact 3D-4D interconnection for the respective BS wave functions under 3D kernel support, precalibrated to both q{\bar q} and qqq spe…
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…
The role of $q\bar q$ components in the nucleon and the N(1440) resonance is studied by explicit coupling of the lowest positive parity $qqqq\bar q$ state to the $qqq$ components in the harmonic oscillator quark model. The lowest energy $qqqq\bar q$ component, where the 4-quark subsystem has the flavor-spin symmetry $[4]_{FS}[22]_F[22]_S$, is close in energy to the lowest positive parity excitation of the nucleon in the $qqq$ quark model. The confining interaction leads to a strong mixing of the $qqqq\bar q$ system and the positive parity excited state of the $qqq$ system. This result is in li…
Pentaquark baryons $Θ^{+}$ and $Ξ^{--}$ are studied in the dual gravity theory of QCD in which simple mass formulae of pentaquarks are derived in the Maldacena prototype model for supersymmetric QCD and a more realistic model for ordinary QCD. In this approach it is possible to explain the extremely narrow decay widths of pentaquarks. With the aim of constructing more reliable mass formulae, a sketch is given on spin and the hyperfine interaction in the string picture.
In this article, we study the $\bar{D}Σ_c$, $\bar{D}Σ_c^*$, $\bar{D}^{*}Σ_c$ and $\bar{D}^{*}Σ_c^*$ pentaquark molecular states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension $13$ in a consistent way. The present calculations support assigning the $P_c(4312)$ to be the $\bar{D}Σ_c$ pentaquark molecular state with $J^P={\frac{1}{2}}^-$, assigning the $P_c(4380)$ to be the $\bar{D}Σ_c^*$ pentaquark molecular state with $J^P={\frac{3}{2}}^-$, assigning the $P_c(4440/4457)$ to be the $\bar{D}^{*}Σ_c$ pentaquark molecular state with $…
In this talk I report on a computation of the spectra of exotic pentaquarks and radial excitations of the low--lying ${1/2}^+$ and ${3/2}^+$ baryons in a chiral soliton model.
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.
An attempt to study recently observed Pentaquark baryons is performed in the dual string theory of QCD. Mass formulae for Pentaquark baryons are naively estimated in the Maldacena's prototype model for supersymmetric QCD and a more realistic model for the ordinary QCD.
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 investigate the pentaquark($P$) exotic baryons as soliton-antiflavored heavy mesons bound states in the limit of infinitely heavy meson mass. Our approach respects the chiral symmetry as well as the heavy quark symmetry. The results reveal a possibility for the loosely bound non-strange $P$-baryon(s).
A review is given to pentaquark mass predictions in quark models and QCD. It is pointed out that no successful quark model prediction is available for low-lying pentaquark states. Some new results of direct application of QCD, QCD sum rules and lattice QCD, are also presented.
