Heavy Quark Spin Symmetry Research Articles

Predicting the [formula omitted] bound states as the partners of [formula omitted

In this work, we investigate the SU(3) flavor symmetry, heavy quark spin symmetry and their breaking effects in the di-meson systems. We prove the existence of the [D‾s∗Ds∗]0++, [D‾s∗Ds/D‾sDs∗]1+-, and [D‾s∗Ds∗]1+- bound states as the consequence of two prerequisites in the SU(3) flavor symmetry and heavy quark spin symmetry. The first prerequisite, the X(3872) as the weakly D‾∗D/D‾D∗ bound state is supported by its mass and decay branching ratios. The second prerequisite, the existence of the [D‾sDs]0++ bound state is supported by the lattice QCD calculation and the observation of χc0(3930) by the LHCb Collaboration. We hope the future experimental analyses can search for these bound states in the B→D(s)(*)D‾(s)(*)h processes (h denotes the light hadrons). The [D‾s∗Ds∗]0++ bound state is also expected to be reconstructed in the J/ψϕ final state in the B→J/ψϕK decay.

Molecular nature of Pcs(4459) and its heavy quark spin partners

Inspired by the observation of the $P_{cs} (4459)$ state by LHCb recently, we reexamine the results of the interaction of the $J/\psi \Lambda$ channel with its coupled channels, exploiting the coupled channel unitary approach combined with heavy quark spin and local hidden gauge symmetries. By tuning the only free parameter, we find a pole of $(4459.07+i6.89)$ MeV below the $\bar D^* \Xi_c$ threshold, which was consistent well with the mass and width of the $P_{cs} (4459)$ state. Thus, we assume the $P_{cs} (4459)$ state to be a $\bar D^* \Xi_c$ bound state with the uncertainties on its degeneracy with $J^P = \frac{1}{2}^-$ and $J^P = \frac{3}{2}^-$. For the degeneracy, it would have two-poles structure, like $P_c (4450)$ before. There is another pole in the $J^P = \frac{1}{2}^-$ sector, $(4310.53+i8.23)$ MeV, corresponding to a deep bound state of $\bar D \Xi_c$. Furthermore, the previously predicted loose bound states of $\bar D \Xi'_c$, $\bar D^* \Xi'_c$, $\bar D^* \Xi^*_c$ with $J=1/2,~I=0$ and $\bar D^* \Xi'_c$, $\bar D \Xi^*_c$, $\bar D^* \Xi_c^*$ with $J=3/2,~I=0$ may exist as either bound states or unbound virtual states. We hope that future experiments can search for the $\bar D^{(*)} \Xi_c$ molecular states in their dominant decay channels of $\bar D^{(*)}_s \Lambda_c$, also in the $J/\psi \Lambda$ and $\eta_c \Lambda$ channels to reveal their different nature.

Triple- X and beyond: Hadronic systems of three and more X(3872)

The $X(3872)$ resonance has been conjectured to be a $J^{PC} = 1^{++}$ charm meson-antimeson two-body molecule. Meanwhile, there is no experimental evidence for larger, few-body compounds of multiple charm meson-antimeson pairs which would resemble larger molecules or nuclei. Here, we investigate such multi-meson states to the extent of what can be deduced theoretically from essentials of the interaction between uncharged $D^{0}$ and $D^{*0}$ mesons. From a molecular $X(3872)$, we predict a $4X$ ($4^{++}$) octamer with a binding energy \mbox{$B_{4X} > 2.08\,{\rm MeV}$,} assuming a $D^{*0} \bar{D}^0$ system close to the unitary limit (as suggested by the mass of the $X(3872)$). If we consider heavy-quark spin symmetry explicitly, the $D^{*0} \bar{D}^{*0}$ ($2^{++}$) system is close to unitarity, too. In this case, we predict a bound $3X$ ($3^{++}$) hexamer with $B_{3X} > 2.29\,{\rm MeV}$ and a more deeply bound $4X$ octamer with $B_{4X} > 11.21\,{\rm MeV}$. These results exemplify with hadronic molecules a more general phenomenon of equal-mass two-species Bose systems comprised of equal number of either type: the emergence of unbound four- and six-boson clusters in the limit of a short-range two-body interaction which acts only between bosons of different species. Finally, we also study the conditions under which a $2X$ ($2^{++}$) tetramer might form.

Insights into the inner structures of the fully charmed tetraquark state X(6900)

The recently discovered fully charmed tetraquark candidate $X(6900)$ is analyzed within the frameworks of effective-range expansion, compositeness relation and width saturation, and a coupled multichannel dynamical study. By taking into account constraints from heavy-quark spin symmetry, the coupled-channel amplitude including the $J/\psi J/\psi,~ \chi_{c0}\chi_{c0}$ and $\chi_{c1}\chi_{c1}$ is constructed to fit the experimental di-$J/\psi$ event distributions around the energy region near $6.9$ GeV. Another dynamical two-coupled-channel amplitude with the $J/\psi J/\psi$ and $\psi(3770) J/\psi$ is also considered to describe the same datasets. The three different theoretical approaches lead to similar conclusions that the two-meson components do not play dominant roles in the $X(6900)$. Our determinations of the resonance poles in the complex energy plane from the refined coupled-channel study are found to be consistent with the experimental analyses. The coupled-channel amplitudes also have another pole corresponding to a narrow resonance $X(6825)$ that we predict sitting below the $\chi_{c0}\chi_{c0}$ threshold and of molecular origin. We give predictions to the line shapes of the $\chi_{c0}\chi_{c0}$ and $\chi_{c1}\chi_{c1}$ channels, which could provide a useful guide for future experimental measurements.

Excited K meson, Kc(4180) , with hidden charm as a DD¯K bound state

Motivated by the recent discovery of two new states in the $B^+\rightarrow D^+D^-K^+$ decay by the LHCb Collaboration, we study the $D\bar{D}K$ three-body system by solving the Schr\"odinger equation with the Gaussian Expansion Method. We show that the $D\bar{D}K$ system can bind with quantum numbers $I(J^P)=\frac{1}{2}(0^-)$ and a binding energy of $B_3(D\bar{D}K)=48.9^{+1.4}_{-2.4}$ MeV. It can decay into $J/\psi K$ and $D_s\bar{D}^*$ via triangle diagrams, yielding a partial decay width of about 1 MeV. As a result, if discovered, it will serve as a highly nontrivial check on the nature of the many exotic hadrons discovered so far and on non-perturbative QCD as well. Assuming heavy quark spin symmetry, the same formalism is applied to study the $D\bar{D}^*K$ system, which is shown to also bind with quantum numbers $I(J^P)=\frac{1}{2}(1^-)$ and a binding energy of $B_3(D\bar{D}^*K)\simeq 77.3^{+3.1}_{-6.6}$ MeV, consistent with the results of previous works.

Insights into Zb(10610) and Zb(10650) from dipion transitions from ϒ(10860)

The dipion transitions $\Upsilon(10860)\to\pi^+\pi^-\Upsilon(nS)$ ($n=1,2,3$) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analysing experimental data on the bottomoniumlike states $Z_b(10610)$ and $Z_b(10650)$ [Phys. Rev. D 98, 074023 (2018)] and predicting the properties of their spin partners [Phys. Rev. D 99, 094013 (2019)]. In this work we use a relatively simple but realistic version of this approach, where the scattering and production amplitudes are constructed employing only short-ranged interactions between the open- and hidden-flavour channels consistent with the constraints from heavy quark spin symmetry, for an extended analysis of the experimental line shapes. In particular, the transitions from the $\Upsilon(10860)$ to the final states $\pi \pi h_b(mP)$ ($m=1,2$) and $\pi B^{(*)}\bar B^* $ already studied before, are now augmented by the $\Upsilon(10860)\to\pi^+\pi^-\Upsilon(nS)$ final states ($n=1,2,3$). This is achieved by employing dispersion theory to account for the final state interaction of the $\pi\pi$ subsystem including its coupling to the $K\bar K$ channel. Fits to the two-dimensional Dalitz plots for the $\pi^+\pi^-\Upsilon$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each $\Upsilon(nS)$ $(n=1,2,3)$ while all the parameters related to the properties of the $Z_b$'s are kept fixed from the previous study. A good overall description of the data for all $\Upsilon(10860)\to\pi^+\pi^-\Upsilon(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the $Z_b$ states.

Can discovery of hidden charm strange pentaquark states help determine the spins of Pc(4440) and Pc(4457) ?

The pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$, could be nicely arranged into a multiplet of seven molecules of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ dictated by heavy quark spin symmetry. However, the spins of $P_c(4440)$ and $P_c(4457)$ are not yet fully determined. In this work we employ the contact-range effective field theory to investigate the $SU(3)$-flavor counterparts of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$, and study the possibility whether their discovery can help determine the spins of $P_c(4457)$ and $P_c(4440)$. We find the existence of a complete hidden charm strange multiplet of $\bar{D}^{(\ast)}\Xi_{c}^{(\prime\ast)}$ molecules irrespective of the spins of $P_c(4440)$ and $P_c(4457)$. On the other hand, we find that although molecules of $\bar{D}^{(\ast)}\Xi_{c}$ are also likely, depending on the realization of the underlying dynamics, their discovery can be more useful to determine the spins of $P_{c}(4440)$ and $P_{c}(4457)$ and to tell how the heavy quark and light quark interaction depends on the spin of the light quark pair.

Zcs(3985)− as the U -spin partner of Zc(3900)− and implication of other states in the SU(3)F symmetry and heavy quark symmetry

Recently, for the first time, the BESIII Collaboration reported the strange hidden charm tetraquark states $Z_{cs}(3985)^-$ in the $K^+$ recoil-mass spectrum near the $D_{s}^{-}D^{*0}/ D_{s}^{*-}D^{0}$ mass thresholds in the processes of $e^{+}e^{-}\to K^{+}(D_{s}^{-}D^{*0}+D_{s}^{*-}D^{0})$ at $\sqrt{s}=4.681$ GeV. The significance was estimated to be 5.3 $\sigma$. We show that the newly observed $Z_{cs}(3985)^-$ state is the $U$-spin partner of $Z_c(3900)^{-}$ as a resonance within coupled-channel calculation in the $\text{SU(3)}_F$ symmetry and heavy quark spin symmetry (HQSS). In the $\text{SU(3)}_F$ symmetry, we introduce the $G_{U/V}$ parity to construct the flavor wave functions of the $Z_{cs}$ states. In a unified framework, we consider the $J/\psi\pi(K)$, $\bar{D}_{(s)}{D}^*/\bar{D}_{(s)}^*{D}$ coupled-channel effect with the contact interaction. With the masses and widths of $Z_c(3900)$ and $Z_c(4020)$, we determine all the unknown coupling constants. We obtain mass and width of $Z_{cs}(3985)$ in good agreement with the experimental results, which strongly supports the $Z_{cs}$ states as the $U/V$-spin partner states of the charged $Z_c(3900)$. We also calculate the ratio of the partial decay widths of $Z_{cs}(3985)$, which implies that the $\bar{D}_sD^*/\bar{D}^*_s D$ decay modes are dominant. We also predict the $Z_{cs}^\prime$ states with a mass around $4130$ MeV and width around $30$ MeV, which are the $U/V$-spin partner states of the charged $Z_c(4020)$ and HQSS partner states of the $Z_{cs}(3985)$. In the hidden bottom sector, we predict the strange tetraquark states $Z_{bs}$ and $Z_{bs}^\prime$ with a mass around 10700 MeV and 10750 MeV, which are the $U/V$-spin partner states of $Z_{b}(10610)^{\pm}$ and $Z_b(10650)^{\pm}$, respectively.

Pseudoscalar and vector open-charm mesons at finite temperature

Vacuum and thermal properties of pseudoscalar and vector charm mesons are analyzed within a self-consistent many-body approach, employing a chiral effective field theory that incorporates heavy-quark spin symmetry. Upon unitarization of the vacuum interaction amplitudes for the scattering of charm mesons off light mesons in a fully coupled-channel basis, new dynamically generated states are searched. The imaginary-time formalism is employed to extend the calculation to finite temperatures up to $T=150$ MeV. Medium-modified spectral shapes of the $D$, $D^*$, $D_s$ and $D_s^*$ mesons are provided. The temperature dependence of the masses and decay widths of the nonstrange $D_0^*$ (2300) and $D_1^*$(2430) mesons, both showing a double-pole structure in the complex-energy plane, is also reported, as well as that of the $D_{s0}^*$(2317) and $D_{s1}^*$(2460) resonances and other states not yet identified experimentally. Being the first calculation incorporating open-charm vector mesons at finite temperature in a self-consistent fashion, it brings up the opportunity to discuss the medium effects on the open charm sector under the perspective of chiral and heavy-quark spin symmetries.

X0(2866) as a D*K¯* molecular state

Very recently the LHCb Collaboration reported the discovery of two open charm tetraquark states, $X_{0}(2866)$ and $X_{1}(2904)$. In the present work, we study the $D^{(\ast)}$ and $\bar{K}^{(\ast)}$ interaction in the one-boson exchange model and show that the $X_{0}(2866)$ can be understood as a $D^{\ast}\bar{K}^{\ast}$ molecule with $I(J^{P})=0(0^{+})$, or at least it has a large molecular component. On the other hand, the $X_{1}(2904)$ can not be interpreted as a molecular state. Inspired by the discovery of the $X_0(2866)$ and the fact that the $D^*\bar{K}^*$ interaction is strong enough to generate a bound state, we also discuss likely existence of other open charm molecules. In the meson-meson sector, two molecules near the mass thresholds of $DD^{\ast}$ and $D^{\ast}D^{\ast}$ with $I(J^{P})=0(1^{+})$ are obtained, and using the heavy quark flavor symmetry their $\bar{B}\bar{B}^{\ast}$ and $\bar{B}^{\ast}\bar{B}^{\ast}$ counterparts are also predicted. In the meson-baryon sector, 7 open charm molecules with $I=1/2$ near the mass thresholds of $D^{(\ast)}\Sigma_{c}^{(\ast)}$ naturally appear, as dictated by the heavy quark spin symmetry.

Open-charm Euclidean correlators within heavy-meson EFT interactions

The open-charm Euclidean correlators have been computed for the first time using the thermal spectral functions extracted from a finite-temperature self-consistent unitarized approach based on a chiral effective field theory that implements heavy-quark spin symmetry. The inclusion of the full-energy dependent open-charm spectral functions in the calculation of the Euclidean correlators leads to a similar behaviour as the one obtained in lattice QCD for temperatures well below the transition deconfinement temperature. The discrepancies at temperatures close or above the transition deconfinement temperature could indicate that higher-energy states, that are not present in the open-charm spectral functions, become relevant for a quantitative description of the lattice QCD correlators at those temperatures. In fact, we find that the inclusion of a continuum of scattering states improves the comparison at small Euclidean times, whereas differences still arise for large times.

How to reveal the nature of three or more pentaquark states

Within the chiral unitary approach and with the constraints of heavy quark spin symmetry, we study the coupled channel interactions of ${\bar D}^{(*)}\Sigma_c^{(*)}$ channels, close to whose thresholds three pentaquark-like $P_c$ states have been reported by the LHCb Collaboration. In the present work, we take into account the contributions of pion exchanges via box diagrams to the interaction potentials, and therefore lift the degeneracy in the masses of ${\bar D}^*\Sigma_c^{(*)}$ spin multiplets. Fitting the $J/\psi p$ invariant mass distributions in the $\Lambda_b^0 \to J/\psi K^- p$ decay, we find that the LHCb pentaquark states can not be reproduced in the direct $J/\psi p$ production in the $\Lambda_b^0$ decay, and can only be indirectly produced in the final state interactions of the $\Lambda_b^0$ decay products, ${\bar D}^*\Sigma_c^{(*)}$, which further supports the nature of these states as $\bar{D}\Sigma_c$ molecules. Based on the fit results obtained, we study the partial decay widths/branching ratios to other decay channels, $\bar{D}^* \Lambda_c$, $\bar{D} \Lambda_c$, and $\eta_c N$, and the corresponding invariant mass distributions. The resonances with $J^P=\frac{1}{2}^-$, $P_c(4312)$, $P_c(4440)$ and the one of $\bar{D}^* \Sigma_c^*$ around 4500 MeV, have large partial decay width into $\eta_c N$, and thus, can be easily seen in the $\eta_c N$ invariant mass distributions. By contrast, the states with $J^P=\frac{3}{2}^-$, $P_c(4457)$, the (predicted) narrow $P_c(4380)$ and the bound state of $\bar{D}^* \Sigma_c^*$ with a mass of about 4520 MeV, do not decay into $\eta_c N$. Therefore, the $\eta_c N$ channel should be studied in future to provide further insights into the nature of these states, especially that of the $P_c(4440)$ and $P_c(4457)$.

Nonrelativistic effective field theory for heavy exotic hadrons

We propose an effective field theory to describe hadrons with two heavy quarks without any assumption on the typical distance between the heavy quarks with respect to the typical hadronic scale. The construction is based on Non-Relativistic QCD and inspired in the strong coupling regime of Potential Non-Relativistic QCD. We construct the effective theory at leading and next-to-leading order in the inverse heavy-quark mass expansion for arbitrary quantum numbers of the light degrees of freedom. Hence our results hold for hybrids, tetraquarks, double heavy baryons and pentaquarks, for which we also present the corresponding operators at Non-Relativistic level. At leading order, the effective theory enjoys heavy quark spin symmetry and corresponds to the Born-Oppenheimer approximation. At next-to-leading order, spin and velocity dependent terms arise, which produce splittings in the heavy-quark spin symmetry multiplets. A concrete application to double heavy baryons is presented in an accompanying paper.

Inclusive J/ψ and ηc production in ϒ decay at O(αs5) in nonrelativistic QCD factorization

We study $J/\psi$ and $\eta_c$ inclusive production in $\Upsilon$ decay within the framework of nonrelativistic-QCD (NRQCD) factorization. In the latter case, for which no experimental data exist so far, we also include the $h_c$ feed-down contribution. We calculate the short distance coefficients completely through $\mathcal{O}(\alpha_s^5)$. The NRQCD predictions for the branching fraction $\mathcal{B}(\Upsilon\to J/\psi+X)$ via direct production, evaluated with different sets of long-distance matrix elements (LDMEs), all agree with the experimental data in a reasonable range of renormalization scale. Using $\eta_c$ and $h_c$ LDMEs obtained from $J/\psi$ and $\chi_c$ ones via heavy-quark spin symmetry, we find that the bulk of $\mathcal{B}(\Upsilon\to\eta_c+X)$ via prompt production arises from the $c\bar{c}({}^3\!S_1^{[8]})$ Fock state. The experimental study of this decay process would, therefore, provide a particularly clean probe of the color octet mechanism of heavy-quarkonium production.

Properties of heavy mesons at finite temperature

We study the properties of heavy mesons using a unitarized approach in a hot pionic medium, based on an effective hadronic theory. The interaction between the heavy mesons and pseudoscalar Goldstone bosons is described by a chiral Lagrangian at next-to-leading order in the chiral expansion and leading order in the heavy-quark mass expansion so as to satisfy heavy-quark spin symmetry. The meson-meson scattering problem in coupled channels with finite-temperature corrections is solved in a self-consistent manner. Our results show that the masses of the ground-state charmed mesons D(0^-)D(0−) and D_s(1^-)Ds(1−) decrease in a pionic environment at T\neq 0T≠0 and they acquire a substantial width. As a consequence, the behaviour of excited mesonic states (D_{s0}^*(2317)^\pmDs0*(2317)± and D_0^*(2300)^{0,\pm}D0*(2300)0,±), generated dynamically in our heavy-light molecular model, is also modified at T\neq 0T≠0. The aim is to test our results against Lattice QCD calculations in the future.

Interpretation of the LHCb P_{c} States as Hadronic Molecules and Hints of a Narrow P_{c}(4380).

Three hidden-charm pentaquark P_{c} states, P_{c}(4312), P_{c}(4440), and P_{c}(4457) were revealed in the Λ_{b}^{0}→J/ψpK^{-} process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the J/ψp invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven Σ_{c}^{(*)}D[over ¯]^{(*)} molecular states in two spin multiplets, such that the P_{c}(4312) is mainly a Σ_{c}D[over ¯] bound state with J^{P}=1/2^{-}, while P_{c}(4440) and P_{c}(4457) are Σ_{c}D[over ¯]^{*} bound states with quantum numbers 3/2^{-} and 1/2^{-}, respectively. We also show that there is evidence for a narrow Σ_{c}^{*}D[over ¯] bound state in the data which we call P_{c}(4380), different from the broad one reported by LHCb in 2015. With this state included, all predicted Σ_{c}D[over ¯], Σ_{c}^{*}D[over ¯], and Σ_{c}D[over ¯]^{*} hadronic molecules are seen in the data, while the missing three Σ_{c}^{*}D[over ¯]^{*} states are expected to be found in future runs of the LHC or in photoproduction experiments.

Nature of the lowest-lying odd parity charmed baryon Λc(2595) and Λc(2625) resonances

We study the structure of the $\Lambda_c(2595)$ and $\Lambda_c(2625)$ resonances in the framework of an effective field theory consistent with heavy quark spin and chiral symmetries, that incorporates the interplay between $\Sigma_c^{(*)}\pi-ND^{(*)}$ baryon-meson degrees of freedom and bare P-wave $c\bar ud$ quark-model states. We show that these two resonances are not HQSS partners. The $J^P= 3/2^-$ $\Lambda_c(2625)$ should be viewed mostly as a dressed three quark state, whose origin is determined by a bare state, predicted to lie very close to the mass of the resonance. The $J^P= 1/2^-$ $\Lambda_c(2595)$ seems to have, however, a predominant molecular structure. This is because, it is either the result of the chiral $\Sigma_c\pi$ interaction, which threshold is located much more closer than the mass of the bare three-quark state, or because the light degrees of freedom in its inner structure are coupled to the unnatural $0^-$ quantum-numbers. We show that both situations can occur depending on the renormalization procedure used. We find some additional states, but the classification of the spectrum in terms of HQSS is difficult, despite having used interactions that respect this symmetry. This is because the bare quark-model state and the $\Sigma_c\pi$ threshold are located extraordinarily close to the $\Lambda_c(2625)$ and $\Lambda_c(2595)$, respectively, and hence they play totally different roles in each sector.

Heavy quark spin multiplet structure of Pc-like pentaquarks as a P-wave hadronic molecular state

Abstract We study the heavy quark spin (HQS) multiplet structure of P-wave $Q\bar{Q}qqq$-type pentaquarks treated as molecules of a heavy meson and a heavy baryon. We define the light-cloud spin (LCS) basis decomposing the meson–baryon spin wave function into LCS and HQS parts. Introducing the LCS basis, we find HQS multiplets classified by the LCS: five HQS singlets, two HQS doublets, and three HQS triplets. We construct the one-pion exchange potential respecting the heavy quark spin and chiral symmetries to demonstrate which HQS multiplets are realized as a bound state. By solving the coupled channel Schrödinger equations, we study the heavy meson–baryon systems with $I=1/2$ and $J^P=(1/2^+, 3/2^+, 5/2^+, 7/2^+)$. The bound states which have the same LCS structure are degenerate at the heavy quark limit, and the degeneracy is resolved for finite mass. This HQS multiplet structure will be measured in future experiments.

Prediction of hidden charm strange molecular baryon states with heavy quark spin symmetry

We have studied the meson-baryon S−wave interaction in the isoscalar hidden-charm strange sector with the coupled-channels, ηcΛ, J/ψΛ, D¯Ξc, D¯sΛc, D¯Ξc′, D¯⁎Ξc, D¯s⁎Λc, D¯⁎Ξc′, D¯⁎Ξc⁎ in JP=1/2−, J/ψΛ, D¯⁎Ξc, D¯s⁎Λc, D¯⁎Ξc′, D¯Ξc⁎, D¯⁎Ξc⁎ in 3/2− and D¯⁎Ξc⁎ in 5/2−. We impose constraints of heavy quark spin symmetry in the interaction and obtain the non vanishing matrix elements from an extension of the local hidden gauge approach to the charm sector. The ultraviolet divergences are renormalized using the same meson-baryon-loops regulator previously employed in the non-strange hidden charm sector, where a good reproduction of the properties of the newly discovered pentaquark states is obtained. We obtain five states of 1/2−, four of 3/2− and one of 5/2−, which could be compared in the near future with forthcoming LHCb experiments. The 5/2−, three of the 3/2− and another three of the 1/2− resonances are originated from isoscalar D¯(⁎)Ξc′ and D¯(⁎)Ξc⁎ interactions. They should be located just few MeV below the corresponding thresholds (4446, 4513, 4588 and 4655 MeV), and would be SU(3)-siblings of the isospin 1/2 D¯(⁎)Σc(⁎) quasi-bound states previously found, and that provided a robust theoretical description of the Pc(4440), Pc(4457) and Pc(4312) LHCb exotic states. The another two 1/2− and 3/2− states obtained in this work are result of the D¯(⁎)Ξc−Ds(⁎)Λc coupled-channels isoscalar interaction, are significantly broader than the others, with widths of the order of 15 MeV, being D¯s(⁎)Λc the dominant decay channel.

Spin-isospin Kondo effects for Σc and Σc* baryons and D¯ and D¯* mesons

We study the Kondo effect for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon in nuclear matter. In terms of the spin and isospin ($\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$) symmetry, the heavy-quark spin symmetry and the S-wave interaction, we provide the general form of the Lagrangian for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon and a nucleon. We analyze the renormalization equation at the one-loop level, and find that the coexistence of spin exchange and isospin exchange magnifies the Kondo effect in comparison with the case where the spin-exchange interaction and the isospin-exchange interaction exist separately. We demonstrate that the solution exists for the ideal sets of the coupling constants, including the $\mathrm{SU}(4)$ symmetry as an extension of the $\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$ symmetry. We also conduct a similar analysis for the Kondo effect of a $\bar{D}$ ($\bar{D}^{\ast}$) meson in nuclear matter. On the basis of the obtained result, we conjecture that there could exist a "mapping" from the heavy meson (baryon) in vacuum onto the heavy baryon (meson) in nuclear matter.