Surveying exotic pentaquarks with the typical $QQqq\bar{q}$ configuration

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 predictions present here can be tested.

In the quark model, the doubly charmed baryon Ξ cc (J P = 1 2 + or 3 2 + ) is in a 20-plet representation of the flavor SU (4) classification [30]. Although its study started 40 years ago [31], its existence is confirmed very recently [32][33][34]. The confirmation from LHCb motivates further theoretical studies on the possible stable T QQ (QQqq) states, which had been predicted in various models. Both the Ξ cc baryon and the T QQ meson contain a heavy diquark. Now we would like to add one more light quark component and discuss the spectra of the doubly heavy pentaquarks within a simple model. The so- * Electronic address: xiangliu@lzu.edu.cn † Electronic address: yrliu@sdu.edu.cn ‡ Electronic address: zhusl@pku.edu.cn called heavy diquark-antiquark symmetry was used to relate the mass splittings of QQq and QQqq in Ref. [35]. Hopefully, the present investigation can also be helpful to further study on such a symmetry in multiquark systems.
Compared to the QQq baryon, the QQqqq pentaquark state should be heavier. However, the complicated interactions within multiquark systems may lower the mass, which probably makes it difficult to distinguish experimentally a conventional baryon from a pentaquark baryon just from the mass consideration. One example for this feature is the five newly observed Ω c states [36,37]. They can be accommodated in both 3q configuration [38][39][40][41][42][43][44][45][46] and 5q configuration [47][48][49][50][51][52][53] and much more measurements are needed to resolve their nature. As a theoretical prediction, the basic features for the pentaquark spectra may be useful for us to understand possible structures of heavy quark hadrons.
For the doubly heavy five-quark systems, we have a compact QQqqq configuration and two baryon-meson moleucle configurations, (QQq)(qq) and (Qqq)(Qq). As for the latter molecule configuration, there are theoretical studies in the meson exchange methods [54][55][56]. Here, we discuss the mass splittings of the compact QQqqq pentaquark states by considering the color-magnetic interactions between quarks and estimate their rough positions. It is still an open question how to distinguish the two configurations. For example, if we compare the prediction for the Λ-type hidden charm state in the molecule picture [57] and the estimation for the mass of the lowest ccuds compact pentaquark [58], one gets consistent results. However, the numbers of possible states in these two pictures are different. The present study should be useful in looking for genuine pentaquark states rather than molecules. This paper is organised as follows. In Sec. II, we construct the f lavor ⊗ color ⊗ spin wave functions for the QQqqq pentaquark states. In Sec. III, the relevant Hamiltonians for various systems are presented. In Sec. IV, we give numerical results and discuss the mass spectra of the pentaquark states and their strong decay channels. Finally, we present a summary in Sec. V.

II. COLOR-MAGNETIC INTERACTION AND WAVE FUNCTIONS
Few-body problem is difficult to deal with and there are scarce dynamical studies on pentaquark systems without substructure assumptions [59,60]. To understand systematically the basic features for the properties of multiquark states, as the first step, we here adopt a color-magnetic model and mainly focus on the mass splittings of the S -wave pentaquark states. For the pentaquark masses, we just present some estimations.
Their accurate values need further dynamical calculations. For the ground state hadrons with the same quark content, e.g. ∆ and N, their mass splitting is mainly determined by the color-magnetic interaction (CMI). The Hamiltonian in this model reads where λ a i (a = 1, · · · , 8) are the Gell-Mann matrices for the i-th quark and σ b j (b = 1, 2, 3) are the Pauli matrices for the j-th quark. For antiquarks, the λ i is replaced with − λ * i . The effective mass m i for the i-th quark includes the constituent quark mass and contributions from color-electric interactions and color confinements. The effective coupling constants C i j depend on the quark masses and the ground state spatial wave functions.
The model is an oversimplified one of the realistic quark interactions. We may check its relation with the leading order Hamiltonian in nonrelativistic approximation in Ref. [31] (ignore the electromagnetic part), H = L( r 1 , r 2 , ...) + i (m 0i + p i 2m 0i ) + 1 4 i> j α s λ i · λ j S i j . (2) Here, L is responsible for quark binding and r i , p i , and m 0i are the position, momentum, and mass of the i-th quark, respectively. S i j has the form where r = r i − r j . For S -wave hadrons, the last two lines (spin-orbit and tensor parts) have vanishing contributions. By calculating the average value with the orbital wave function Ψ 0 (L = 0), one may write the Hamiltonian as For states with the same quark content, M 0 is a constant and it can be expressed as the summation of effective quark masses M 0 = i m i . Then the model Hamiltonian we will use is obtained. In principle, the values of m i and C i j should be different for various systems. However, it is difficult to exactly calculate these parameters for a given system without knowing the spatial wave function. In the present study, they will be extracted from the masses of conventional hadrons. That is to say, we use the assumption that quark-quark interactions are the same for various systems. This assumption certainly leads to uncertainties on hadron masses. The uncertainty cause by m i does not allow us to give accurate pentaquark masses while the uncertainty in coupling parameters has smaller effects and the mass splittings should be more reliable. In order to reduce the uncertainties and obtain more appropriate estimations, we will try to use an alternative form of the mass formula. Whether this manipulation gives results close to realistic masses or not can be tested in future measurments. Obviously, we can calculate the color-magnetic matrix elements and investigate the mass spectra for the QQqqq systems if the wave functions were constructed. Now we move on to the construction of the flavor-color-spin wave function of a system, which is a direct product of SU(3) f flavor wave function, SU(3) c color wave function, and SU(2) s spin wave function. We construct these wave functions separately and then combine them together by noticing the possible constraint from the Pauli principle. We will use the diquark-diquarkantiquark bases to construct the wave function. In principle, the selection of wave function bases is irrelevant with the final results since we will diagonalize the Hamiltonian in this CMI model. Here, the notation "diquark" only means two quarks and it does not mean a compact substructure.
In flavor space, the heavy quarks are treated as SU(3) f singlet states and the light diquark may be in the flavor antisym-metric3 f or symmetric 6 f representation. For the case of the antisymmetric (symmetric) light diquark, the representations of the pentaquarks are6 f and 3 f (3 f and 15 f ). We plot the SU(3) f weight diagrams for the QQqqq systems in Fig. 1. The explicit wave functions are similar to the qqqQ tetraquark states presented in Ref. [61]. Because of the unequal quark In color space, the Young diagrams tell us that the pentaquark systems have three color singlets. Then we have three color wave functions. The direct product for the representations can be written as In the last line, the representations in the parentheses are for the heavy diquark, light diquark, and antiquark, respectively. Then the color-singlet wave functions can be constructed as where A (S ) means antisymmetric (symmetric) for the diquarks. Explicitly, we have The spin wave functions for the pentaquark states are Here in the symbol [(Q 1 Q 2 ) spin (q 3 q 4 ) spinq ] totalspin j , j is the total spin of the first four quarks. The superscript S A of χ means that the first two quarks are symmetric and the second two quarks are antisymmetric. Other superscripts are understood similarly.

III. THE HAMILTONIAN EXPRESSIONS
With the constructed wave functions, we calculate colormagnetic matrix elements on various bases. In this section, we present the obtained Hamiltonians in the matrix form. To simplify the expressions, we use the variables defined in Table  I.

Variable Definition Variable
Definition For the J P = 3 B. (ccnn) I=0q and (bbnn) I=0q states in the second class In this case, we also have three types of basis vectors to consider: can be obtained.
E. (ccns)q and (bbns)q states in the fifth class In this case, again we have six types of basis vectors, For the J P = 5 1 , and [(QQ) 6 0 (ns)¯3 1q ] 3 2

. Then one can get
F. (cbns)q states in the sixth class Since the Pauli principle has no effects in this case, the most basis vectors are involved. There are twelve types of bases,

IV. THE QQqqq PENTAQUARK MASS SPECTRA
Now, we determine the values of the seventeen coupling parameters (C nn , C ns , C ss , C cn , C bn , C cs , C bs , C bc , C cc , C bb , C nn , C sn = C ns , C ss , C cn , C bn , C cs , and C bs ) and the four effective quark masses (m n , m s , m c , and m b ) in order to estimate the pentaquark masses. The procedure to extract the parameters has been illustrated in Ref. [62]. From the calculated CMI matrix elements for ground state hadrons and their mass splittings, we can get most values of the coupling parameters which are shown in Table II. To determine C ss , one needs the mass of a ground pseudoscalar meson having the same quark content with φ. Since there is no such a state, here we adopt approximately C ss = C ss . Similarly, we use the approximation C QQ = C QQ (C bb = C bb = 2.9 MeV, C cc = C cc = 5.3 MeV, and C bc = C bc = 3.3 MeV) since only one doubly heavy baryon Ξ cc is observed. In Table II, the B * c has not been observed yet and we take its mass from a model calculation [63]. The effective quark masses can be extracted from the ground state baryons after the determination of the coupling parameters, and we present them in Table III.
With these parameters, we can estimate the pentaquark masses in two ways. In the first method, one substitutes the relevant parameters into M = i m i + H CM . In the second method, we employ the formula M = M re f − H CM re f + H CM , where M re f = M baryon + M meson is a reference mass scale and H CM re f = H CM baryon + H CM meson . The reference baryon and meson system should have the same constituent quarks as the considered system [64]. Although the mass formula in the second method is from that in the first method, one should note the difference in adopting them. When applying the first formula to conventional hadrons, the resulting masses are usually higher than the experimental measurements, which is illustrated in table IV. This indicates that the simple model does not incorporate attraction sufficiently. As a result, we may treat the pentaquark masses estimated with the first method as theoretical upper limits. In the second method, we use the realistic values rather than the calculated values for the hadron masses of the reference system. The attraction that the model does not incorporate is somehow phenomenologically compensated in this procedure. The estimated masses in the second method should be more reasonable than those in the first method. In the following parts, we will present numerical results obtained in both methods. To understand the decay properties in the following discussions, we will adopt some masses of the not-yet-observed doubly heavy baryons, which were obtained from several theoretical calculations. They are presented in table V.  Hadron A. The ccnnq, ccssq, bbnnq, and bbssq pentaquark states For the ccnnq (q = n, s) systems, we can use two types of threshold to estimate their masses: (charmed baryon)-(charmed meson) and (doubly charmed baryon)-(light meson). We will use M Ξ cc = 3621.4 MeV from the LHCb Collaboration [34] in the latter case. For the bbnnq systems, we only use the (bottom baryon)-(bottom meson) threshold since no doubly bottom baryon has been observed. For the ccssq and bbssq systems, only (heavy baryon)-(heavy meson) type thresholds are adopted because of the same reason. We present the estimated masses for the ccnnq, bbnnq, ccssq, and bbssq pentaquark states in Tables VI, VII, VIII, and IX, respectively. From these tables, it is obvious that different estimation approaches give different masses. The reason is that the model does not involve dynamics and contributions from other terms in the potential are not elaborately considered. For the ccnnn and bbnnn systems with I nn = 1, we get the same spectra for the case of the total isospin I = 1 2 and 3 2 , which comes from the fact that the color-magnetic interaction for a quark and an antiquark is irrelevant with the isospin.
Table VI shows us that the pentaquark masses obtained with Ξ cc π and Ξ cc K are lower than those with Σ c D and Σ c D s , respectively. This feature is consistent with the observation that more effects contribute to the effective attractions in the former systems, which can be seen from the inequalities ∆M Ξ cc + ∆M π > ∆M Σ c + ∆M D and ∆M Ξ cc + ∆M K > ∆M Σ c + ∆M D s according to table IV. If the adopted model could reproduce all the hadron masses accurately, all the mentioned approaches would give consistent pentaquark masses. At present, we are not sure which type of threshold results in more appropriate pentaquark masses. For a multiquark hadron, the effective attraction is probably not strong and maybe a higher mass is more reasonable. We plot the relative positions for the ccnnn, ccnns, bbnnn, bbnns, ccssn, ccsss, bbssn, and bbsss systems in diagrams (a)-(h) of Fig. 2, respectively. Here we select the masses obtained with the thresholds of Σ c D, Σ c D s , Σ bB , Σ bBs , Ω c D, Ω c D s , Ω bB , and Ω bBs , respectively. The thresholds relevant with rearrangement decay patterns are also displayed in the figure. The following discussions are based on the assumption that the obtained positions in this figure are all reasonable. For the figures in the other systems, we will also adopt pentaquark masses estimated with higher thresholds. One should note that the figures show only rough positions of the pentaquarks. Their properties may be changed accordingly once the positions for states in a system are determined by an observed pentaquark. However, the mass splittings should not be affected. For the ccnnn system, the I nn = 0 states are generally lower than the I nn = 1 states and the lowest state is around the Ξ cc π threshold. This pentaquark is in the mass range of excited Ξ cc states [65]. It is highly probable that an observed excited Ξ cc gets contributions from coupled channel effects. An inverted mass order that the I nn = 0 state is heavier is observed for the J = 5 2 states. This feature exists because of the stronger nn interaction in the I nn = 0 state, which can be understood    . When the isospin (spin) of an initial pentaquark state is equal to a number in the subscript (superscript) of a baryon-meson state, its decay into that baryon-meson channel through S -or D-wave is allowed by the isospin (angular momentum) conservation. We have adopted the masses estimated with the reference thresholds of (a) Σ c D, from the comparison between Eqs. (17) and (14). The bbnnn system should have similar properties. From the mass distributions in diagrams (a) and (c), we may guess roughly the mass of Ξ bb , m Ξ bb ≈ 10465 − 135 = 10330 MeV, a value consistent with Refs. [67,68]. Replacing the antiquark with ans , we get the spectra of QQnns in the diagrams (b) and (d). The difference from the QQnnn case lies only in the interaction strengths between the antiquark and other quarks. The remaining systems are obtained by exchanging s and n. All the lowest states have the quantum numbers J P = 1 2 − . In these systems, the QQnns, QQssn, and I = 3 2 QQnnn states are explicitly exotic. Now we move on to the possible rearrangement decays of the pentaquarks, which may occur through S -wave or Dwave, depending on the conservation laws. The mass, total angular momentum, isospin, and parity all together determine whether the relevant decay channels are open or not. For convenience, we label in Fig. 2 the spin and isospin of the baryonmeson states in the superscripts and subscripts of their symbols, respectively. From the quantum numbers of the decay product, it is possible to find pentaquark candidates. First, we take a look at the ccnnn system. In the case of I(J P ) = More channels will open if one includes the D-wave decay modes. However, only the observation of these decay patterns cannot prove the existence of a pentaquark state consisting of ccnnn because the initial state may also be an excited Ξ cc . In this case, the mixing between 3q state and 5q state is probably important. In the case of I = 3 2 , an observed state would be a good pentaquark candidate. The J P = 5 2 − state with either isospin is probably not a very broad pentaquark. For the bbnnn system, the situation is similar to the ccnnn system. For the ccsss and bbsss systems, the identification of a pentaquark state is not so easy. On the contrary, the pentaquark states ccnns, ccssn, bbnns, and bbssn are easier to identify since the quantum numbers are not allowed for the conventional baryons. For example, if we observed a state in the decay pattern Ξ cc K, Ξ cc K * , Λ c D s , Λ c D * s , Σ c D s , Σ c D * s , Σ * c D s , or Σ * c D * s , it would be a good candidate of a ccnns pentaquark state. From the diagrams in Fig. 2, the lowest ccnns pentaquark may be stable and the lowest one with J = 3 2 is also relatively stable. Because of the difference in coupling constants, the lowest two I = 0 bbnns pentaquarks, J P = 1/2 − and 3/2 − , probably both have strong decay patterns. This can be seen with the values m Ξ bb = 10138 MeV and m Ξ bb * = 10169 MeV obtained in Ref. [65]. If such masses are not far from the realistic values, the decay into Ξ bb K or Ξ * bb K may occur. Once the Ξ bb (Ξ * bb ) state is observed, the search for pentaquark candidates in the Ξ bb K (Ξ * bb K) channel may be performed. For the exotic ccssn and bbssn pentaquarks, only the isospin I = 1/2 is allowed. The lowest J = 1/2 state and the lowest J = 3/2 state in both systems are lower than the (Qss)-(Qn) type thresholds and such decay patterns are forbidden. However, one finds that the decay for the J = 1/2 (3/2) ccssn pentaquark into Ω ccK (Ω * ccK ) is possible if the mass m Ω cc = 3715 MeV (m Ω * cc = 3772 MeV) obtained in Ref. [65] is close to the realistic mass. Similarly, the decay for the J = 1/2 (3/2) bbssn pentaquark into Ω bbK (Ω * bbK ) is possible if one checks the threshold with m Ω bb = 10230 MeV (m Ω * bb = 10258 MeV). With the (QQs)-(sn) type channels, the identification of ccssn and bbssn pentaquarks may be performed in the future measurements.

B. The bcnnq and bcssq pentaquark states
To estimate the masses of the bcnnq and bcssq states (q = n, s), we can also use two types of thresholds: (charmed baryon)-(bottom meson) and (bottom baryon)-(charmed meson). The results and relevant reference systems are presented in Tables X and XI. The masses obtained with the two types of thresholds are slightly different. We use results estimated with the (charmed baryon)-(bottom meson) type threshold for further discussions. In Fig. 3, the relative positions for these pentaquark states and relevant baryon-meson thresholds are plotted. For the bcssn and bcsss states, only one value of isospin is possible and we do not label the subscripts of the baryon-meson states into which the pentaquarks may decay.
From the diagrams (a) and (d) of Fig. 3, the bcnnn system has more than 12 possible rearrangement decay channels and the bcsss system has more than 6. However, one cannot simply distinguish a pentaquark from a conventional baryon or from a 3q and 5q mixed state just from these decay channels if the isospin is not 3/2. The discussions are similar to the previous systems. On the other hand, in the bcnns and bcssn cases, good pentaquark candidates may be searched for in their relevant decay patterns shown in the diagrams (b) and (c) of Fig. 3. If we use m Ξ bc = 6922 MeV, m Ξ bc = 6948 MeV, and m Ξ * bc = 6973 MeV [66], one finds that the lowest two bcnns pentaquarks should be stable and the lowest J P = 3/2 − state is probably narrow. Since the three I = 3/2 bcnnn states are more than 350 MeV lower than the Λ b D threshold and just above the Ξ bc π threshold, they probably have narrow widths and we may use the Ξ bc π channels to identify such pentaquarks. Similarly, the Ω bcK channels may be used to identify the bcssn pentaquarks if m Ω bc is around 7011 MeV [66].

C. The ccnsq and bbnsq pentaquark states
In the mass estimation for the ccnsq (q = n, s) system, we use two types of thresholds: (charmed baryon)-(charmed meson) and (doubly charmed baryon)-(light meson). For the bbnsq system, we only adopt the (bottom baryon)-(bottom meson) type threshold. The pentaquark masses estimated with the help of the doubly charmed baryon are smaller than those with the (charmed baryon)-(charmed meson) type threshold. We present the numerical results for the ccnsq and bbnsq systems in Tables XII and                                       When the isospin (spin) of an initial pentaquark state is equal to a number in the subscript (superscript) of a baryon-meson state, its decay into that baryon-meson channel through S -or D-wave is allowed by the isospin (angular momentum) conservation. We have adopted the masses estimated with the reference thresholds of (a) Σ cB , (b) Σ cBs , (c) Ω cB , and (d) Ω cBs . XIII, respectively. The relative positions for these pentaquark states and the relevant rearrangement decay states are shown in Fig. 4. From the figure, we can see that both the heaviest state and the lightest state are the J P = 1 2 − pentaquarks in each system. Because all these systems contain a quark-antiquark pair, it is not easy to distinguish a pentaquark state from a 3q baryon state if the isospin of the decay product is less than 1. Also, the widths of the lowest pentaquark states are probably not narrow if we take m Ω cc = 3715 MeV and m Ω bb = 10230 MeV [65]. In Ref. [69], a bound state with I = 0 below the Ξ ccK threshold is predicted. If experiments observed one state with the quark content ccnsn, irrespective of its nature, its partner states could also be searched for in the Ω cc π, Ω cc K, Ω bb π, and Ω bb K channels and whether they exist or not can test the simple model we use.

D. The bcnsq pentaquark states
For the bcnsq states, the wave functions do not get constraints from the Pauli principle and the number of wave function bases for a given quantum number is bigger than that for other systems. After diagonalizing the Hamiltonian, one gets numbers of possible pentaquark states. Here we use two types of thresholds to estimate their masses: (charmed baryon)-(bottom meson) and (bottom baryon)-(charmed meson). The results are presented in Table XIV. One finds that these two types of thresholds lead to comparable values. With the masses from the (charmed baryon)-(bottom meson) type thresholds, we plot the relative positions for these pentaquarks and their relevant decay patterns in Fig. 5. The quantum numbers of the heaviest state and the lightest state are both J P = 1 2 − . The mass of the lightest state for the bcnsn system is around 7313 MeV which is above the thresholds of Ω bc π, Ω bc π, and Ω * bc π and is much lower than other two-body baryon-meson thresholds if we adopt the masses obtained in Ref. [66]. This feature is helpful for us to identify compact I = 1 pentaquarks once the bcs type baryons can be used to spectrum reconstruction. On the other hand, the identification of a bcnss pentaquark is not easy since it may share the same decay products with an excited Ξ bc baryon.   When the spin of an initial pentaquark state is equal to a number in the superscript of a baryon-meson state, its decay into that baryon-meson channel through S -or D-wave is allowed by the angular momentum conservation. We have adopted the masses estimated with the reference thresholds of (a) Ξ c D, (b) Ξ c D s , (c) Ξ bB , and (d) Ξ bB s .

V. DISCUSSIONS AND SUMMARY
Up to now, some candidates of the tetraquark states have been confirmed by different experiments. The observation of the P c (4380) and P c (4450) at LHCb gave us significant evidence for the existence of pentaquak states and opened a new door for studying hidden-charm exotic states. More possible pentaquarks have been predicted in various theoretical calculations and await further confirmation. In this paper, motivated by the P c (4380) and P c (4450) and the observation of the Ξ cc at LHCb, we have discussed the doubly heavy QQqqq pentaquark states in a CMI model and shown their possible rearrangement decay patterns. Although the model we adopt is simple and is not a dynamical model, it may give us some qualitative properties with which the experimentalists may be used to search for such exotic baryons. In the early stage studies on the multiquark properties, chromomagnetic effects were also intensively considered as the primary contribution in an attempt to explain the narrow hadronic resonances [70]. In recent years, this model as a widely used method was adopted to study the multiquark states, such as the investigations in Refs. [71][72][73][74][75][76][77][78].
In the estimation of the rough masses, we have used two approaches for comparison: one with the quark masses and the other with a reference threshold. The results obtained with the former approach are larger and can be treated as theoretical upper limits. In the estimation with the latter approach, we mainly adopt the (heavy baryon)-(heavy meson) type thresholds. Although no enough experimental data for the doubly heavy 3q baryons are available, we may employ the masses calculated in the quark model [65,66]. For the investigated systems, we find that stable pentaquarks with I = 0 are possible in the bcnns case. The lowest threshold of the rearrangement decay product is for the Ξ bc K state while the lowest pentaquarks can be below such thresholds. The typical examples are the two lowest I = 0 bcnns states in Fig. 3 (b) and the I = 0 ccnns state in Fig. 2 (b). In the Q 1 Q 2 nnn and Q 1 Q 2 nsn cases, the lowest threshold of the rearrangement decay product is for the Ξ Q 1 Q 2 π or Ω Q 1 Q 2 π, but the lowest pentaquarks we obtain are hard to be below such thresholds. Good news is that the lowest pentaquark may be below the (heavy baryon)-(heavy meson) threshold and one may search for such pentaquarks with the strong decay modes containing a pion. In the Q 1 Q 2 ssn and Q 1 Q 2 nss cases, the lowest pentaquarks may be above the Ω Q 1 Q 2K or Ω Q 1 Q 2 K threshold and can be discov-eried with the decay modes containing a kaon. Contrary to the above systems, the strong decay channel with lowest threshold in the Q 1 Q 2 sss case may be the (heavy baryon)-(heavy meson) type. Since the doubly heavy baryons are very difficult to be used to reconstruct pentaquark spectra, maybe one should notice the Q 1 Q 2 sss pentaquarks experimentally. Alternatively, the J = 5/2 pentaquarks may be searched for first since they have many D-wave decay modes but one or two Swave decay modes and probably they are not so broad. This feature is similar to the hidden-charm pentaquarks [58].
In the study of multiquark states, the number of color-spin structures may be more than ten. The mixing or channelcoupling effects could be important. The lowest pentaquarks we obtain get contributions from such effects significantly. Whether there are substructures in multiquark states and whether the configuration mixing effects are that important need more studies. In the near future, further experimental and theoretical studies on pentaquarks are still important, especially with the running of LHC at 13 TeV and the forthcoming BelleII.
In summary, we have studied preliminarily the mass spectra of doubly heavy pentaquark states in a color-magnetic model. We find candidates of possible narrow states. If they do exist, When the spin of an initial pentaquark state is equal to a number in the superscript of a baryon-meson state, its decay into that baryon-meson channel through S -or D-wave is allowed by the angular momentum conservation. We have adopted the masses estimated with the reference thresholds of (a) Ξ b D and (b) Ξ b D s . the identification may be not difficult from their exotic quantum numbers. We hope that the present study may inspire experimental exploration to exotic states.