$D \Xi$ and $D^* \Xi$ Molecular States from One Boson Exchange

We explore the existence of $D \Xi$ and $D^* \Xi$ molecular states within the one boson exchange model. We regularize the potential derived in this model with a form factor and a cut-off of the order of $1\,{\rm GeV}$. To determine the cut-off, we use the condition that the $X(3872)$ is reproduced as a pole in the $J^{PC} = 1^{++}$ $D^*\bar{D}$ amplitude. From this we find that the $J^P= {\frac{1}{2}}^{-}$ $D^*\,\Xi$ system is on the verge of binding and has an unnaturally large scattering length. For the $J^P= {\frac{1}{2}}^{-}$ $D\,\Xi$ and the $J^P= {\frac{3}{2}}^{-}$ $D^*\,\Xi$ systems the attraction is not enough to form a bound state. From heavy quark symmetry and the quark model we can extend the previous model to the $P \Xi_{QQ}$ and $P^* \Xi_{QQ}$ systems, with $P = D, \bar{B}$, $P^* = D^*, \bar{B}^*$ and $\Xi_{QQ} = \Xi_{cc}, \Xi_{bb}$. In this case we predict a series of triply heavy pentaquark-like molecules.


I. INTRODUCTION
The discovery of the X(3872) by the Belle Collaboration [1] fifteen years ago represented the first hidden charm state that did not fit into the charmonium spectrum. Afterwards experiments have found a series of similar states, informally known as XYZ states. They cannot be easily accommodated in the naive quark model and other components have to be invoked to explain their masses, decay widths and production rates, see [2] for a recent review. A few are tetraquark-like, such as the Z c (3900) [3,4], Z c (4020) [5,6], Z b (10610) and Z b (10650) [7,8], while recently two pentaquark-like states have been observed, the P c (4380) and P c (4450) [9]. A few of them have the interesting feature of being close to an open flavour threshold. The most notable example is the X(3872), located almost on top of the D 0D0 * threshold, but the list also includes the Z c (3900) (DD * ) and Z c (4020) (D * D * ), the Z b (10610) (BB * ) and Z b (10650) (B * B * ) and the P c (4450) near theD * Σ c threshold. This characteristic has led to the conjecture that the previous states might be hadronic molecules.
Recently the LHCb Collaboration has observed five narrow states Ω c (3000) 0 , Ω c (3050) 0 , Ω c (3066) 0 , Ω c (3090) 0 , and Ω c (3119) 0 [29], where four of them have also been recently confirmed from an analysis of the Belle data [30]. These states can be accomodated as excited Ω c baryons [31,32], as compact baryons in which the ss strange quark pair forms a diquark [33] or as molecular states [34][35][36][37][38]. The LHCb data also hint at a structure around 3188 MeV, which is near the DΞ threshold (3179 − 3191 MeV), and could be a bound state of DΞ. Wang et al. [39] used the Bethe-Salpeter formalism to study the S −wave DΞ interaction and they found two bound states, one isoscalar and one isovector, respectively, which could contribute to the 3188 MeV structure near the five new narrow Ω c states. Debastiani and Liang [34,40] used an extension of the chiral unitary model to calculate the interactions between DΞ, D * Ξ ,BΞ,B * Ξ plus other channels, and obtained one zero width state with J P = 1/2 − , 3/2 − , which couples mostly to D * Ξ andB * Ξ and another state with J P = 1 2 − , which couples mostly to DΞ andBΞ.
In this work we study possible bound states near the thresholds of DΞ, D * Ξ,BΞ andB * Ξ within the one boson exchange (OBE) model, where we will also consider the replacement of Ξ by Ξ cc or Ξ bb to explore the existence of heavy molecules containing two and three charm/bottom quarks. The OBE model is an intuitive framework in which a few of the most quantitative succesful descriptions of the nuclear force have been achieved [41,42]. Nowadays it has been superseded by the effective field theory (EFT) approaches [43,44], which have two theoretical advantages over the OBE model: (i) the possibility of making a priori error estimates and (ii) the lowenergy equivalence with quantum chromodynamics. However the EFT approach requires a large number of data to fix the low energy constants that substitute the exchange of light mesons such as the σ, ρ and ω. This means that in situations where hadron-hadron scattering data is poor, such as hadron molecules, the OBE potential has the advantage of providing a model of the short-range dynamics of these systems, at the price of sacrificing the systematicity of EFT. As a matter of fact the seminal works that pioneered the idea of hadronic molecules [10,11] were indeed based on the OBE model and a few modern explorations rely heavily on this model [18,19,24].
The manuscript is organized as follows: in Section II we review the OBE model as applied to the DΞ, D * Ξ plus anal-ogous systems and derive the potentials in these systems. In Section III we show the predictions we obtain for the molecular states. Finally we present our conclusions in Section IV.

II. THE ONE BOSON EXCHANGE POTENTIAL
In this section we explain the one boson exchange (OBE) model (see Ref. [42] for a review) and how it applies to the DΞ and D * Ξ systems. The OBE model is a generalization of the idea of Yukawa, namely that nuclear forces arise from the exchange of pions, to shorter distances. For that the exchange of other light mesons (besides the pion) is considered, in particular the σ scalar meson and the ρ and ω vector mesons. The reason for the development of the OBE model was the failure of the original two-pion theories in the fifties (which did not include chiral symmetry), see Ref. [45] for a historical perspective. The fundamental idea is that the bulk of the two-pion exchange potential can be described by the exchange of a heavier meson, which either couples strongly to pions or which can be interpreted as a multi-pion resonance. The idea is physically compelling and has been fairly successful at the phenomenological level, as illustrated by the nuclear potentials based on it [41,46]. There are limitations however, such as the requirement of form factors to regularize the potentials or the requirement of fine-tuning the coupling constants [47,48] (at least in the two-nucleon system). Yet the OBE potential is still perfectly able to provide a good estimation of the plausability of hadronic bound states and their location, as attested for instance in the pioneering work of Voloshin and Okun [10].

A. The Lagrangian
We begin with the interaction of the D and D * fields with the π, σ, ρ and ω mesons. First we group the fields of the D and D * in the (heavy spin symmetric) superfield with v the velocity parameter and where we have used the convenient normalization of Falk and Luke [49]. In this normalization we can write the interaction lagrangian of the H superfield with the light mesons as where the traces are in the 4x4 space spanned by the Dirac matrices when defining the superfield H. In the lagrangian above we take the normalization f π = 132 MeV, g 1 , g σ1 , g ω1 , f ω1 , g ρ1 and f ρ1 are the different couplings in the OBE model and M 1 is a mass scale that we introduce for f ω1 and f ρ1 to be dimensionless (M 1 is in principle arbitrary, but we will later take it to be the D-meson mass, i.e. M 1 = m D ). If we choose the velocity parameter to be v = (1, 0), we can substitute the superfield H v by a non-relativistic superfield H where H is a 2x2 matrix (instead of a 4x4 one). Now the lagrangian can be rewritten as Now for the Ξ field we can write the interaction lagrangian which is analogous to the one for the D and D * (and it is identical in form to the one in the nucleon-nucleon case). In the lagrangian g 2 , g σ2 , g ω2 , f ω2 , g ρ2 , f ρ2 and M 2 denote the couplings and the mass scale for the cascade baryon. Here we can use the heavy baryon formulation by making the field redefinition If we choose again v = (1, 0), we arrive at the lagrangian B. The OBE Potential The general form of the P Ξ and P * Ξ OBE potential is where the subscript indicates from which meson comes the contribution (π, σ, ρ or ω) and with ζ = ±1 a sign. We take the convention that ζ = +1 for PΞ and P * Ξ , If the vector meson and the hadrons are point-like, their vertices can be directly computed from the Lagrangian and we end up with the following potentials in momentum space In the expressions the subscript 1 and 2 is used for the P/P * heavy meson and Ξ baryon respectively. For a 1 we take with S the spin-1 angular momentum matrices. For the pion decay constant we take the f π = 132 MeV normalization. The choice of sign for the momentum space potential is such that the Lippmann-Schwinger equation reads T = V + VG 0 T , where the T-matrix is in turn normalized so that for zeroenergy scattering T → 2π a 0 /µ, with a 0 the scattering length and µ the reduced mass of the system. That is, we are using the standard non-relativistic normalization which is also used in the two-nucleon system, see for instance Ref. [42]. We can take into account the finite size of hadrons by including form factors in the calculation, that is where F 1 and F 2 are the form factors corresponding to vertex 1 and 2, i.e. the P/P * heavy meson and the Ξ baryon. The form factor can depend on the momentum transfer q, the mass of the exchanged meson m and a cut-off Λ. Here we will use a monopolar form factor of the type for both vertices, where q 2 = q 2 0 − q 2 is the 4-momentum of the exchanges meson.
In configuration space and for point-like interactions the components of the OBE potential take the form where the functions W Y (x) and W T (x) are defined as The effects of the finite size of the hadrons is easy to take into account by making the changes where λ = Λ/m. For the monopolar form factor of Eq. (30) we end up with As a matter of fact the structure of the OBE potential presented here is exceedingly simple. We can write it as a sum of a central, spin-spin and tensor component where for point-like interactions we have while for finite-size hadrons we substitute δ(r), W Y (x) and W T (x) by their finite-size versions.

C. Couplings
For the D and D * heavy mesons the axial coupling with the pion we take which is compatible with g 1 = 0.59 ± 0.01 ± 0.07 as extracted from the D * → Dπ decay [50,51]. The coupling to the σ meson, in the case of the nucleonnucleon interaction, can be determined from the non-linear sigma model [52] yielding For the case of the D, D * mesons and Ξ baryons we can estimate the coupling to the σ from the quark model. If we assume that σ only couples to the u and d quarks, we expect We can also deduce from SU(3) flavour symmetry and the OZI rule that From the universality of the ρ couplings (Sakurai's universality [53]) and the KSFR (Kawarabayashi-Suzuki-Fayyazuddin-Riazuddin) relation [54,55] we expect Yet there might be deviations from this value. Regarding the ρ coupling to the heavy mesons, Casalbuoni et al. [56] indicate that where β = 0.9. The ρ coupling thus obtained actually coincides with lattice QCD calculations in the heavy quark limit [57], which yield g ρ1 = 2.6 ± 0.1 ± 0.4. For the ρ and ω coupling to the cascade, there is also the possibility of obtaining it from the nucleon-nucleon case. In that case the relevant relations are (see the Appendix) In the nucleon-nucleon case the SU(3) + OZI relation is which is compatible with the analogous relation for the cascade baryon once we take into account the quark model. Yet nuclear potentials usually violate the previous relation, requiring a g ωNN ∼ 20 or larger, a discrepancy which has been long known in OBE models and usually attributed to the fact that the g ωNN used in nuclear potentials might indeed also account for some of the short-range quark-gluon exchanges [42]. Yet, this discrepancy can be understood in more modern terms within the renormalization ideas that have become commonplace after the advent of chiral EFT. The explanation lies in the fine-tuning nature of the nucleon-nucleon interaction, which translates into a fine-tuning of the ω coupling. In fact the ω coupling provides a very important central contribution to the nuclear force, which is responsible in a large part for the concrete values of the scattering lengths of the singlet and triplet channels. By combining the OBE model with modern renormalization techniques this discrepancy disappears and the SU(3) relation is recovered [48]. These findings indicate that the use of the SU(3) relations is the most judicious choice to determine the g ω couplings, at least for exploratory studies of prospective hadron molecules where we are not trying to fit fine-tuned systems.
For f ρ and f ω the estimations in the case of the charmed mesons are as follows. SU(3) and the OZI rule imply that This relation appears automatically if the lagrangians are written in terms of the vector meson nonet. Meanwhile vector meson dominance applied to the weak decays of the charmed mesons [56] bring us to with |λ| = 0.60 ± 0.11 GeV −1 and where in the second line we have written the coupling of the ρ in the normalization for which we take M 1 = m H with m H the mass of the charmed meson. If we take m H = m D , g ρ1 = 2.6 and assume that λ is positive we obtain For the cascade the estimations are more involved. The reason is that the coupling of the ρ meson to the octet baryons depends in general on two coupling constants, the symmetric and antisymmetric octet couplings 1 . In the case of the nucleon-nucleon interaction it is possible to use single vector meson dominance to obtain the relation with κ ρNN = µ p −µ n −1, κ ωNN = µ p +µ n −1, yielding κ ρNN = 3.7 and κ ωNN = −0.1. This idea can be adapted to the D and D * charmed mesons and the Ξ baryon, in which case we have The application of the previous idea implicitly assumes the convention M 2 = m Ξ , which we will follow onwards. From the experimental values µ Ξ 0 = −0.6507 (25) and µ Ξ − = −1.250 (14) listed in the PDG [58] we obtain κ ρ2 = −0.401 and κ ω2 = −0.901. Other possibility is to contrain them from the quark model, in which case we obtain which yield κ ρ2 = −3.2 and κ ω2 = −1.3, in stark contrast with the previous estimations. We can also consider the family of phenomenological soft-core potentials by the Nijmegen group [59][60][61][62][63][64] which also contain estimations for the electric and magnetic couplings of the vector mesons with the cascade. In this case we have κ ρ2 = −2.0, −0.7, −0.3 κ ω2 = −1.1, −1.9, −2.3 for the ESC04a, ESC04d and ESC08c potentials respectively 2 , though it is worth noticing that κ ω2 is obtained from a value of the omega coupling g ω2 ∼ (2 − 3) g ρ2 that is considerably larger than the SU(3) + OZI rule expectation. From the previous discussion it is apparent that there is a considerable level of uncertainty in κ ρ2 and κ ω2 . For simplicity we will use the values This choice is similar to the geometric mean of the previous determinations (κ ρ2 = −1.3 and κ ω2 = −1.5) and to the values we obtain when we compute the cascade magnetic moments at tree level in chiral perturbation theory (µ Ξ 0 = −1.60 and µ Ξ − = −0.97 [65] yielding κ ρ2 = −1.63 and κ ω2 = −1.57). We review the set of parameters we use in the OBE potential in Tables I and II. 1 The electric-type coupling of the ρ meson -the g ρ coupling -is an exception because of its universal character. 2 We have simply divided the magnetic and electric couplings κ = f /g for these potentials.   [58]. For the Ξ cc we use the experimental value of the Ξ ++ cc mass from the LHCb collaboration [66], and for the Ξ bb we use the lattice QCD determination of Ref. [67]. We round the numbers at the MeV level.   For the molecules we are considering here, the total wave function is the product of the isospin and spin-spatial wave functions where J refers to the total angular momentum of the molecule under consideration. The isospin wave function comes from the coupling of the isospin of the two hadrons in the molecule The only subtlely in the isospin wave function is when the hadron contains a light anti-quarkq, for which there will be a minus sign for one of the components of the isospin multiplet.
For instance, if we consider theD (cq) and the D (cq) we havē where the upper and lower components represent the | 1 2 + 1 2 and | 1 2 − 1 2 isospinors respectively. In constrast, for the cascade we simply have where we are using the same prescription for the isospinors. For the part of the wavefunction containing the spatial and spin pieces, we can express it as a sum of different components with the same parity and total angular momentum, i.e. a partial wave expansion where the sum over angular momentum only comprises even or odd L depending on the parity of the molecule P = (−1) L . For the partial wave projection we have adopted the spectroscopic notation 2S +1 L J , where S is the total spin, L the orbital angular momentum and J the total angular momentum. We define the | 2S +1 L J as follows where LM L S M S |JM is a Clebsch-Gordan coefficient, Y LM L (r) a spherical harmonic and |S M S the spin wavefunction, which in turn can be defined as with |S 1 M S 1 , |S 2 M S 2 are the spin wavefunction of particle 1 and 2. The mixing of partial waves with the same J but different S /L requires the tensor force. The coupling only happens in the D * Ξ andD * Ξ cases, because for DΞ andDΞ the tensor force disappears. As molecular states are expected to be more probable for S-waves, we will consider only the following partial waves: The evaluation of the spin-spin and tensor operators for these channels can be found in Table III.  (73), (74) and (75) for the definitions.

E. The Extension to Ξ cc and Ξ bb Baryons
We can extend the OBE model to the doubly heavy baryons in two ways. The first is the quark model, in which case we derive the interactions of the Ξ cc and Ξ bb with the light mesons from the ones for the Ξ. The second is heavy antiquarkdiquark symmetry [68][69][70], in which case the derivation is from the heavy meson interactions.
In the quark model we expect the strange quark to act as an expectator in what refers to the couplings to the π, σ, ρ and ω light mesons. From this the OBE lagrangian for the Ξ cc and Ξ bb baryons is where M 2 is the same as in the original lagrangian for the cascade. In short, the couplings are the same as for the Ξ. Heavy heavy antiquark-diquark symmetry (HADS) is a manifestation of heavy quark symmetry which states that a heavy quark pair behaves as a heavy antiquark [68]. According to this symmetry the couplings of the Ξ cc and Ξ bb baryons can be deduced from those of theD,D * andB,B * heavy antimesons [69,70]. The application of HADS can actually be encapsulated in the following two relations between the lagrangian for theP andP * heavy antimesons and the Ξ QQ doubly heavy baryons where the bar over the H field indicates that we are dealing the heavy antimeson superfield. From this, the OBE lagrangian for the heavy mesons and changing the sign of the π and ω contributions to take into account their G-parity, we arrive at The comparison with the lagrangian derived from the quark model entails the following HADS predictions which can actually be checked against the quark model expectations. Owing to the choices of the couplings made before, we only have to compare five couplings: g 2 , g ρ2 , g ω2 , f ρ2 and f ω2 . These comparisons are reduced to three as g ρ2 = g ω2 from SU ( which are actually very similar. For the ρ electric-type couplings we have which differ by a 10 % only. For the magenetic-type couplings, if we employ M 2 = m Ξ in the doubly heavy sector, the comparison can be directly made in terms of κ ρ2 and κ ω2 instead of f ρ2 and f ω2 , yielding plus identical predictions for κ ω2 . In this case the difference is bigger, but both set of values remain compatible. It is important to notice there that the HADS predictions are expected to be subjected to a sizeable error of Λ QCD /(m Q v) ∼ 30 − 40% in the charm sector (instead of the standard Λ QCD /m Q ∼ 10 − 15% for HQSS) [68,70], where v is the velocity of the heavy quark in the Ξ cc baryon. For the quark model predictions the situation is a bit more murky, owing to its status as a model (as they usually lack reliable error estimations). We warn however that the apparent similarity of both set of predictions is not necessarily due to a compatibility between the two models: the choice that we have made for the couplings of the cascade have also played a role.

III. PREDICTIONS OF MOLECULAR STATES
Now we solve the Schrödinger equation for the HΞ andHΞ potentials with the coupling constant choices we have made in the previous section. For the cut-off in the form factor we will fix Λ as to reproduce the X(3872) in the isospin symmetric limit. In this limit the X(3872) is a 1 ++ DD * molecule with a binding energy of about 4 MeV, which corresponds to a binding energy of about 0 MeV if we consider isospin symmetry breaking in the masses of the charmed mesons. With the choices of the couplings previously made, we obtain the value Λ = Λ X ≃ 1.04 GeV. For this cut-off the charmed meson -cascade molecules do not bind but are prettry close to binding. The J = 1 2 − D * Ξ system is the most attractive case. It binds for Λ ≥ 1.05 GeV, which is just a tiny fraction above Λ X . Concrete calculations indicate a scattering length of a 0 = −18.7 fm, which is indeed larger than any other scale in the system. For the other two configurations of the charmed meson -cascade system we find that the J =  Fig. 1 we plot the dependence of the binding energy on the reduced mass for the different J P molecular configurations, where we also indicate the location of the thresholds. For comparison purposes we also include the mean square radius of these molecules in Fig. 1, which is important to determine whether they are actual bound states (i.e. with a size bigger than its components) or more compact objects requiring a different type of treatment.
The previous numbers are subject to theoretical errors, which are however not easy to estimate because the OBE potential is a model after all. The coupling constants in the potential are in principle amenable to error estimations. The values we take for g ω1 and g ω2 are derived from SU(3) and the OZI rule and hence expected to have an uncertainty of about 20 %. For the couplings derived from the quark model, g σ1 and g σ2 , it is less clear which uncertainty to adscribe them, but probably a 30 % could be a good guess. For g ρ1 and g ρ2 , the error depends on how much do we expect the KSFR relation to fail, but probably a 10 % is enough. The axial coupling and its error g 1 are known experimentally, while for g 2 the er- ror is again determined from the quark model. However the independent variation of each of the couplings followed by the subsequent addition of the errors in quadrature is cumbersome because of the large number of parameters to vary (not to mention that it is not so easy to determine the error of all of them). We find instead much more convenient to simply assume a global uncertainty for the D/D * and Ξ couplings in the following way where M stands for the π, σ, ρ and ω mesons and with ∆ 1 and ∆ 2 the relative error we expect in each of the vertices. If we assume all the couplings to vary in the same direction, i.e. correlated errors, then the outcome is that there is an overall uncertainty in the X(3872) and DΞ/D * Ξ potentials. In this picture for a potential with a vertex of type i and j we will assign the error where vertex type 1 refers to a D/D * and vertex type 2 to a cascade. We will assume the uncertainties on vertex type 1 and 2 to be uncorrelated. In the previous notation, the X(3872) potential will be V 11 and the DΞ/D * Ξ potential will be V 12 .
Besides it is important to stress that the role of the couplings to the charmed mesons and the cascade play a fundamentally different role in the calculations. We are using the X(3872) and hence the couplings of the charmed mesons as a way to fix the unkown parameter Λ in the OBE model, i.e. as a sort of renormalization condition. That is, a change in the charmed meson vertex piece of the potential entails a change in Λ X from which to redo the predictions of the binding energy: where B ′ DΞ is the binding energy for Λ ′ X , where the parameters for vertex 1 in V 12 have to change congruently as how they change in V 11 . After this the error of the cascade baryon vertex (1 ± ∆ 2 ) should be added in quadrature. If we follow this procedure and assume a global ∆ 1 = 0.15, i.e. a 30% global error in the X(3872) potential, we get Λ X = 1.04 +0. 18 −0.10 MeV. If we apply this idea to vertex 2 with ∆ 2 = 0.15, the predictions and uncertainties for inverse of the DΞ, D * Ξ,BΞ andB * Ξ scattering lengths can be found in Table IV. Notice the choice of the inverse scattering length: the reason is that the scattering length diverges and then changes sign when there is a bound state. Its inverse however changes smoothly, and hence the choice. Actually the uncertainties are still compatible with the existence of bound states in the DΞ and D * Ξ systems. For the PΞ QQ and P * Ξ QQ bound states, their binding energies and uncertaintie can be consulted in Table V.
We stress that the previous conclusions are derived from the hypothesis that the X(3872) is molecular at the distances in which the OBE model applies. Besides the circumstantial fact that the X(3872) is located close to the D 0D0 * threshold, the most convincing evidence that the X is molecular is the ratio of its isospin breaking decays Γ(X → J/Ψ2π) and Γ(X → J/Ψ3π) [71]. It is relatively easy to explain this branching ratio within the molecular picture [72,73], but not so if the X(3872) is a compact charmonium-like state [74]. However the radiative decays Γ(X → J/Ψγ) and Γ(X → Ψ(2S )γ) [75] state I (J P ) 1 a 0 (MeV) state I (J P ) 1 a 0 (MeV) IV: Inverse of the scattering length for the DΞ, D * Ξ systems and their bottom counterpartsBΞ andB * Ξ and. They are deduced from the condition of reproducing the X(3872) pole in the DD * potential and by assuming a 15% error in the D/D * and Ξ vertices (where the same applies to theBΞ andB * Ξ systems). offer a different perspective of the X(3872), as they are difficult to explain without the existence of cc components in the X wave function [76]. The cc component necessary to successfully explain the radiative components is small [77], but could nonetheless represents a source of systematic uncertainty for our predictions. In this regard it has been shown that the cc short range components do not necessarily affect the long range picture of the X(3872) as a hadronic molecule [78]. This means that while these components are important at short distances, they are probably heavily suppressed at long distances. This is consistent with the approximation we are using here that the X(3872) is molecular. Thus we do not expect significant corrections to our predictions.

IV. SUMMARY
In this work we have considered the DΞ and D * Ξ systems from the point of view of the OBE model and looked for possible molecular states and their locations. The OBE potential is traditionally regularized with a form factor and a cut-off. The cut-off is expected to be in the 1 GeV range, but there is a considerable uncertainty with respect to its value that translates into wildly different predictions. To reduce this uncertainty we have determined the cut-off from the condition of reproducing the X(3872) as a 1 ++ D * D molecular state, yielding Λ = 1.04 +0. 18 −0.10 GeV. With this we find that the 1 2 − D * Ξ state is on the verge of binding, which translates into an unusually large scattering length of −18.7 fm. If we consider the theoretical uncertainties it turns out that this molecule might very well bind, with the probability of binding being slightly smaller than the probability of not binding. This molecule has also been predicted in Ref. [34]. The 1 2 − DΞ and 3 2 − D * Ξ are unlikely to bind, though their interaction is indeed attractive as can be deduced from their scattering lenghts. As a consequence the interpretation of the Ω c (3188) enhancement as a DΞ bound state [39] is disfavoured. The conclusion about a possible 3 2 − D * Ξ molecule is also different from Ref. [34], where it is predicted, but the previous work includes a series of coupled channels that increase the binding by a small amount. Besides, there is the possibility that these two molecules bind within the uncertainties of our model. The previous findings can be easily extended to systems in which the D and D * are substituted by a B and B * or where instead of the cascade Ξ we have a doubly heavy baryon Ξ cc or Ξ bb . These systems have a large reduced mass and are thus more likely to bind. For the Ω b -like molecular state,BΞ and B * Ξ, we find that the 1 2 −B * Ξ binds withing the errors of the present model, where this state have also been predicted in [40]. The other two configurations might bind as well, but this is contingent on the uncertainties. For the triply heavy molecules we find the 1 2 − P * Ξ QQ system to be the most attractive, binding in all cases. The other two configurations -1 2 − PΞ QQ and 3 2 − P * Ξ QQ -are less attractive. For the triply charmed pentaquark case the previous two configurations are probably close to the unitary limit, where their central values for the binding energy are 0.3 and 0.2 MeV respectively. For the triply bottom pentaquarks, all configurations bind within the theoretical uncertainties of the present model. Triply heavy pentaquarks have been considered previously in the literature. In Ref. [70] HADS is applied to the X(3872) as a D * D molecule to deduce the existence of possible PΞ QQ , P * Ξ QQ , PΞ * QQ and P * Ξ * QQ bound states. From the X(3872) the existence of isoscalar 5 2 − P * Ξ * QQ pentaquarklike molecules can indeed be deduced, while for the other J P combinations the information that can be obtained from the X(3872) is insufficient to predict more states. In this context the OBE model provides a phenomenological estimation of this missing dynamics, which allows us to fully explore the PΞ QQ and P * Ξ QQ cases. mesons can be written as [79]: L Mqq = g πqq (ūiγ 5 uπ 0 −diγ 5 dπ 0 ) (A1) + g ωqq (ūγ µ uω µ +dγ u dω µ ) + g ρqq (ūγ µ uρ 0µ −dγ µ dρ 0µ ) + g σqq (ūuσ +ddσ), where g πqq , g ρqq , g ωqq and g σqq are the couplings of the light q = u, d quarks to the light mesons. The lagrangian above assumes a non-derivative coupling with the pion, which is non chirally symmetric. This is inconsequential as the chiral derivative coupling leads to the same tree level description, i.e. the same one pion exchange potential. To obtain the relations between g Mqq and g Mhh , where the later refers to the couplings with an arbitrary hadron h, we require the interaction vertices calculated at the quark and hadron levels be the same, i.e.,