PHYSICAL REVIEW D 101, 091502(R) (2020) Rapid Communications

Pc pentaquarks with chiral tensor and quark dynamics

Yasuhiro Yamaguchi ,1,* Hugo García-Tecocoatzi ,2 Alessandro Giachino,3,4 Atsushi Hosaka ,5,6 † ‡ Elena Santopinto ,3, Sachiko Takeuchi ,7,1,5 and Makoto Takizawa 8,1,9, 1Theoretical Research Division, Nishina Center, RIKEN, Hirosawa, Wako, Saitama 351-0198, Japan 2Department of Physics, University of La Plata (UNLP), 49 y 115 cc. 67, 1900 La Plata, Argentina 3Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy 4Dipartimento di Fisica dell’Universit`a di Genova, via Dodecaneso 33, 16146 Genova, Italy 5Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047, Japan 6Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan 7Japan College of Social Work, Kiyose, Tokyo 204-8555, Japan 8Showa Pharmaceutical University, Machida, Tokyo 194-8543, Japan 9J-PARC Branch, KEK Theory Center, Institute for Particle and Nuclear Studies, KEK, Tokai, Ibaraki 319-1106, Japan

(Received 10 July 2019; revised manuscript received 14 September 2019; accepted 24 March 2020; published 7 May 2020) ¯ ðÞ ðÞ ¯ ðÞ We investigate the hidden-charm pentaquarks as superpositions of ΛcD and Σc D (isospin I ¼ 1=2) meson-baryon channels coupled to a uudcc¯ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of þ þ þ ¯ ¯ Pc ð4312Þ, Pc ð4440Þ and Pc ð4457Þ with the dominant components of ΣcD and ΣcD with spin-parity P − − − assignments J ¼ 1=2 , 3=2 and 1=2 , respectively. We analyze basic properties of the Pc’s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.

DOI: 10.1103/PhysRevD.101.091502

þ In 2015, the Large Hadron Collider beauty experiment a broad state Pc ð4380Þ (width ∼200 MeV), in the new (LHCb) Collaboration observed two hidden-charm penta- analysis using higher-order polynomial functions for the þð4380Þ þð4450Þ Λ0 → ψ − quarks, Pc and Pc ,in b J= K p decay background, data can be fitted equally well without the [1] and reported additional analysis efforts [2,3]. These Breit-Wigner contribution corresponding to the broad þ results have motivated hundreds of theoretical articles (just Pc ð4380Þ state. In this situation, more experimental and to make some examples see [4–33]). Recently a new theoretical studies are needed to fully understand the analysis has been reported [34] using 9 times more data structure of the observed states. from the Large Hadron Collider than the 2015 analysis. The The masses and widths of the three narrow pentaquark dataset was first analyzed in the same way as before and the states are as follows [34]: þ parameters of the previously reported Pc ð4450Þ and þ P ð4380Þ structures were consistent with the original þ þ6.8 c Pc ð4312Þ∶ M ¼ 4311.9 0.7−0 6 MeV; results. As well as revealing the new Pþð4312Þ state, the . c Γ ¼ 9 8 2 7þ3.7 ; analysis also uncovered a more complex structure of . . −4.5 MeV þ P ð4450Þ, consisting of two narrow nearby separate peaks, þð4440Þ∶ ¼ 4440 3 1 3þ4.1 c Pc M . . −4.7 MeV; Pþð4440Þ and Pþð4457Þ, with the two-peak structure c c Γ ¼ 20 6 4 9þ8.7 ; hypothesis having a statistical significance of 5.4 sigma . . −10.1 MeV with respect to the single-peak structure hypothesis. As for þð4457Þ∶ ¼ 4457 3 0 6þ4.1 Pc M . . −1.7 MeV; þ5.7 Γ ¼ 6.4 2.0−1 9 MeV: *[email protected] . † [email protected] ‡ þð4312Þ [email protected] As discussed by LHCb [34], Pc is just below the ¯ þ ΣcD threshold, while the higher ones Pc ð4440Þ and Published by the American Physical Society under the terms of Pþð4457Þ are both below the Σ D¯ threshold. This change the Creative Commons Attribution 4.0 International license. c c Further distribution of this work must maintain attribution to of the experimental observation motivated new theoretical the author(s) and the published article’s title, journal citation, investigations [35–44]. Among them, [35,36,41,44] are and DOI. Funded by SCOAP3. taking the hadronic-molecule approach. In [35] the authors

2470-0010=2020=101(9)=091502(7) 091502-1 Published by the American Physical Society YASUHIRO YAMAGUCHI et al. PHYS. REV. D 101, 091502 (2020) explore several scenarios for the structures of the quark and chiral symmetries. The interaction Lagrangian pentaquark states by means of QCD sum rules. They between the ground state heavy mesons, D¯ and D¯ , and the propose to interpret all the four pentaquarks as molecular pions can be written in a compact form [46–49], þ þ states, in particular they interpret Pc ð4440Þ and Pc ð4457Þ þþ ¯ − þ ¯ 0 L ¼ M ½ γ γ μ ¯ ð Þ as Σc D and Σc D molecular states, both with πHH gA Tr Hb μ 5AbaHa ; 1 JP ¼ 3=2−.In[36] pentaquark states are studied with a ¯ μ ¯ μ ¯ local hidden gauge based interaction in a coupled-channel where Ha ¼½Daμγ − Daγ5ð1 þ γμv Þ=2 and Ha ¼ ¯ ðÞ ðÞ ¯ ðÞ γ †γ approach by including the Nηc, NJ=ψ, ΛcD and Σc D 0Ha 0 are the heavy meson fields containing the spin þ P ¯ meson-baryon channels. They assign Pc ð4440Þ to J ¼ multiplet of pseudoscalar and vector meson fields Da and − þ P − ¯ ½ 1=2 and Pc ð4457Þ to J ¼ 3=2 . Although these assign- Daμ. The trace Tr is taken over the gamma matrices. ments agree with experimental decay widths, the mass of The subscript a denotes the light quark flavor, and vμ is the þ Pc ð4440Þ is overestimated by about 13 MeV, which is four-velocity of the heavy quark inside the heavy meson; M more than the double of the experimental error on the gA is the axial vector coupling constant for heavy mesons, þð4440Þ Pc mass of about 5 MeV. Most importantly, the which was determined by the D → Dπ strong decay to be mass difference between Pþð4440Þ and Pþð4457Þ, approx- M ¼ 0 59 – μ ¼ i ½ξ†∂ ξ − ξ∂ ξ† c c gA . [48 50], and A 2 μ μ , with imately 17 MeV, is not reproduced by this model in which, ξ ¼ expð iπˆ Þ, is the pion axial vector current; πˆ is the þ 2fπ instead, the two states are almost degenerate. Pc ð4440Þ flavor matrix of the pion field and fπ ¼ 92.3 MeV is the þð4457Þ ΣðÞ ¯ ðÞ and Pc are considered as the c D hadronic- pion decay constant. The effective Lagrangian which molecule states in a quasipotential Bethe-Salpeter equation describes the interaction between Σc and Λc heavy baryons approach [41]. They use the meson-exchange interaction and the pions is [51,52] with π, η, ρ, ω and σ mesons and reproduce the observed masses reasonably. Their spin-parity assignments are 3 L ¼ ð Þεμνλκ ½ ¯ þ ½¯ μ Λˆ þ þ − þ − πBB g1 ivκ tr SμAνSλ g4tr S Aμ c H:c:; Pc ð4440Þ as 1=2 and Pc ð4457Þ as 3=2 , respectively. 2 Coupled-channel molecular states of the relative S − D(P)- ð Þ ¯ ¯ 2 wave ΣcD and the relative P(S − D)-wave Λcð2595ÞD are studied with the one-pion exchange potential (OPEP) in ½ ¯ where tr denotes the trace performed in flavor space. [44] as the Λcð2595ÞD threshold is very close to the ¯ þ The superfields Sμ and Sμ are represented by Pc ð4457Þ mass. The model predicts two bound states, þ − 1 which they argue correspond to P ð4440Þ(JP ¼ 3=2 ) ˆ ˆ ¯ † c Sμ ¼ Σ μ − pffiffiffi ðγμ þ vμÞγ5Σ ; Sμ ¼ Sμγ0: ð3Þ þ P þ c c and Pc ð4457Þ(J ¼ 1=2 ). 3 In Ref. [45] we studied the hidden-charm pentaquarks by ðÞ ðÞ Λˆ Σˆ ¯ ðÞ ¯ ðÞ Here, the heavy baryon fields c and ðμÞ, are coupling the ΛcD and Σc D meson-baryon channels c to a uudcc¯ compact core with a meson-baryon binding   0 Λþ interaction satisfying the heavy quark and chiral sym- Λˆ ¼ c ; ð4Þ c −Λþ 0 metries. In that work we expressed the hidden-charm c pentaquark masses and decay widths as functions of one 0 1 ðÞþþ ðÞþ free parameter, which is proportional to the coupling Σ p1ffiffi Σ B cðμÞ 2 cðμÞ C strength between the meson-baryon and 5-quark-core Σˆ ðÞ ¼ @ A ð Þ cðμÞ ðÞþ ðÞ0 : 5 states. Interestingly enough, we find that the model has pre- p1ffiffi Σ Σ 2 ðμÞ ðμÞ dicted the masses and decay widths consistently with the c c new data with the following quantum number assignments: pffiffiffi P − P − P − As shown in [52], g1 ¼ð 8=3Þg4 ¼ 1. The internal J þ ¼ 1=2 , J þ ¼ 3=2 and J þ ¼ 1=2 . Pc ð4312Þ Pc ð4440Þ Pc ð4457Þ þ structure of hadrons is parametrized by a dipole form Our assignments of the quantum numbers for the P ð4440Þ 2 2 c ðΛ qÞ¼Λ −mπ q þ factor at each vertex, F ; Λ2þq2 , where mπ and are and Pc ð4457Þ states are different from those in other hadronic-molecule approaches. the mass and three-momentum of an incoming pion and the Λ The purpose of the present article is to study the origin of heavy hadron cutoffs H are determined by the ratio þ þ the mass difference between P ð4440Þ and P ð4457Þ by between the sizes of the heavy hadron, rH, and the nucleon, c c Λ Λ ¼ Λ ∼ Λ ∼ Λ performing the calculations with and without the tensor rN, N= H rH=rN. We obtained Λc Σc N for the Λ ¼ 1 35Λ ¯ ðÞ term of the OPEP. The importance of the tensor force is charmed baryons and D¯ . N for the D meson, emphasized as “chiral tensor dynamics”. where the nucleon cutoff is determined to reproduce the Let us briefly overview the main ingredients of the model deuteron-binding energy by the OPEP as ΛN ¼ 837 MeV of Ref. [45]. The best established interaction between the [53–55]. The explicit form of the OPEP VπðqÞ between the meson and the baryon is provided by OPEP, which is meson-baryon (MB) channels in the momentum space is as obtained by the effective Lagrangians satisfying the heavy follows:

091502-2 PC PENTAQUARKS WITH CHIRAL TENSOR AND QUARK … PHYS. REV. D 101, 091502 (2020)   M B ðSˆ qÞðSˆ qÞ πðqÞ¼− gA gA 1 · 2 · Tˆ Tˆ ð Þ V 2 2 2 1 · 2; 6 4fπ q þ mπ where Sˆ is the spin operator and Tˆ is the isospin operator. B gA is the axial vector coupling constant of the correspond- ing baryons.1 The coupling of the MB channels, i and j, to the five-quark (5q) channels, α, gives rise to an effective interaction, V5q, X 1 h j 5qj i¼ h j jαi hαj †j i ð Þ i V j i V 5q V j ; 7 α E − Eα where V represents the transitions between the MB and 5q 5q FIG. 1. Experimental data (EXP) [1,34] and our results of channels and Eα is the eigenenergy of a 5q channel. We masses and widths for various Pc states. The horizontal dashed further introduced the following assumption: lines show the thresholds for corresponding channels and values in the right axis are isospin averaged ones in units of MeV. The hijVjαi¼fhijαi; ð8Þ centers of the bars are located at the central values of pentaquark masses while their lengths correspond to the pentaquark widths ð4380Þ where f is the only free parameter which determines the with the exception of Pc width. overall strength of the matrix elements. In order to calculate the hijαi, we construct the meson-baryon and five-quark wave functions explicitly in the standard nonrelativistic corresponding predictions in our model. The dashed lines quark model with a harmonic oscillator confining potential. are for threshold values. Our predicted masses and the 5 decay widths are shown for the parameters f=f0 ¼ 50 and The derived potential hijV qjji turned out to give similar f=f0 ¼ 80. Here, f0 is the strength of the one-pion results to those derived from the quark cluster model [7]. Σ ¯ The energies and widths of the bound and resonant states exchange diagonal term for the cD meson-baryon chan- ¼j π ð ¼ 0Þj ∼ 6 nel, f0 CΣ ¯ r MeV (see Ref. [45]). Setting were obtained by solving the coupled-channel Schrödinger cD π 5 equation with the OPEP, V ðrÞ, and 5q potential V qðrÞ, the free parameter f=f0 at f=f0 ¼ 50, we observe that both þ þ masses and widths of Pc ð4312Þ and Pc ð4440Þ are repro- ðK þ VπðrÞþV5qðrÞÞΨðrÞ¼EΨðrÞ; ð9Þ duced within the experimental errors. However, the state þ corresponding to Pc ð4457Þ is absent in our results, where where K is the kinetic energy of the meson-baryon system the attraction is not enough. Increasing the value of f=f0 to P − ¯ and ΨðrÞ is the wave function of the meson-baryon systems 70, the state with J ¼ 1=2 appears below the ΣcD with r being the relative distance between the center of threshold, and at f=f0 ¼ 80 the mass and width of this state þ mass of the meson and that of the baryon. The coupled are in reasonable agreement with Pc ð4457Þ. However, as ðÞ ¯ ðÞ shown in Fig. 1, the attraction at f=f0 ¼ 80 is stronger than channels included are all possible ones of Σc D and ðÞ that at f=f0 ¼ 50 and hence the masses of the other states Λ D¯ which can form a given JP and isospin I ¼ 1=2. c shift downward. Equation (9) is solved by using variational method. We We find as expected that the dominant components of used the Gaussian basis functions as trial functions [56].In these states are nearby threshold channels and with the order to obtain resonance states, we employed the complex quantum numbers as follows: Σ D¯ with JP ¼ 1=2− scaling method [57]. c þð4312Þ Σ ¯ P ¼ 3 2− þð4440Þ In Fig. 1 and Table I, experimental data [1,34] and our [Pc ], cD with J = [Pc ] and with P ¼ 1 2− þð4457Þ predictions are compared. The centers of the bars in Fig. 1 J = [Pc ] meson-baryon molecular states. are located at the central values of pentaquark masses while Let us compare our results with the ones reported by their lengths correspond to the pentaquark widths with the other works. In Ref. [36], the assignments of the quantum ð4440Þ ð4457Þ exception of P ð4380Þ width, which is too large and does numbers for Pc and Pc are different from c Σ ¯ not fit into the shown energy region. The boxed numbers ours. Since these two states are located near cD threshold are the masses of the recently observed states [34], and the and both states have the narrow widths, it is natural to consider them to form the J ¼ 1=2 and 3=2 states in 3 2 1 S-wave. It is emphasized that in our model the spin = In our previous publication [20], there were a few errors in the state (4440) is lighter than the spin 1=2 state (4457). In matrix elements, which are corrected in this paper. After the corrections, however, important results of our discussions remain Ref. [37], they studied seven heavy quark multiplets of ¯ ¯ ¯ ¯ unchanged. ΣcD, ΣcD , ΣcD, and ΣcD , and considered two options of

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TABLE I. Comparison between the experimental mass spectrum and decay widths with our results. For our results for f=f0 ¼ 80, the values in parentheses are obtained without the OPEP tensor force, which are also shown in Fig. 2. All values except JP are in units of MeV.

EXP [1,34] Our Results for f=f0 ¼ 50 Our Results for f=f0 ¼ 80 State Mass Width JP Mass Width JP Mass Width þð4312Þ 4311 9 0 7þ6.8 9 8 2 7þ3.7 1=2− 1=2− Pc . . −0.6 . . −4.5 4313 9.6 4299 (4307) 9.4 (12) þ 4380 8 29 205 18 86 3 2− 3 2− Pc ð4380Þ = 4371 5.0 = 4350 (4365) 5.0 (3.6) þð4440Þ 4440 3 1 3þ4.1 20 6 4 9þ8.7 3 2− 3 2− Pc . . −4.7 . . −10.1 = 4440 16 = 4415 (4433) 15 (1.8) þð4457Þ 4457 3 0 6þ4.1 6 4 2 0þ5.7 1=2− Pc . . −1.7 . . −1.9 4462 (4462) 3.2 (0.96) 1=2− 4527 0.88 1=2− 4521 (4526) 2.8 (0.18) 3=2− 4524 7.6 3=2− 4511 (4521) 14 (3.4) 5=2− 4497 20 5=2− 4468 (4491) 18 (0.0)

inputs, Pcð4440; 4457Þ ∼ ð3=2; 1=2Þ which they call set A plot, we have used f=f0 ¼ 80. From Fig. 2, we observe the and (1=2, 3=2) set B. In the heavy quark limit, there are two following facts. (1) The tensor force provides attraction as parameters in the Hamiltonian and so the above inputs for indicated by the results with T in Fig. 2. This is because it the two states are enough to fix the two parameters. The contributes to the energy in the second order due to channel other five states are predicted. Interestingly, their set A couplings. (2) The role of the tensor force is further predicts the other five states similarly to what our model prominent in the decay width; the agreement with the predicts. experimental data is significantly improved. Moreover, the Therefore, new LHCb results give us an opportunity to decay width increases as the spin value increases. We ¯ study the spin-dependent forces between the Σc and D .It consider it again because of coupled-channel effects due to is important to determine which of the above spin 1=2 and the OPEP tensor force. The dominant components of the 3=2 states is more deeply bound. There are two sources for obtained resonances are the S-wave state of the nearby the spin-dependent force in our model. One is the short threshold channel. The tensor coupling allows the reso- range interaction by the coupling to the 5-quark-core states. nances to decay into the D-wave channels below the The other is the long range interaction by the OPEP, resonances. Since there are many D-wave coupled channels especially the tensor term. in the higher spin states, the decay widths of these states are To examine the effects of the tensor interaction of the increased. In fact, the number of the D-wave coupled ¯ P − OPEP, we have investigated the energy of the resonant Pc channels below the ΣcD threshold is 3 for J ¼ 1=2 , ¯ P − − states of J ¼ 1=2 and 3=2 around the ΣcD threshold, and while 7 for J ¼ 3=2 ; 5=2 . ¯ of J ¼ 1=2, 3=2 and 5=2 around the ΣcD threshold From the observation in Fig. 2, we find that the short without the OPEP tensor term as shown in Fig. 2. In that range interaction is more attractive in the 3=2− state in the present model. This contrasts with what is expected for the color-spin interaction that provides more attraction for the 1=2− state. The reason is in the quark structure of hadrons as explained below. In the quark cluster model, the hadron interaction is due mainly to the two terms: one is the Pauli-blocking effect which is measured by the norm (overlap) kernels and the other is the color-spin interaction from the one gluon exchange. The former is included in the present study, and is usually dominant when the norm of the two-hadron state deviates largely from 1 [58,59]. It can be less than 1 due to the Pauli blocking (repulsive) but also can be more than 1 (attractive) because of the spectroscopic ¯ factor. For the ΣcD channel, the norm is 23=18 for the 3=2− state while it is 17=18 for the 1=2− state [45]. Namely, this contribution of the spectroscopic factor is strongly ¯ − attractive in the ΣcD 3=2 state and slightly repulsive in FIG. 2. Comparing the results with and without the tensor force ¯ − ¯ ¯ the Σ D 1=2 state. of the OPEP for the states around the ΣcD and ΣcD thresholds. c The label “without T” stands for the result without the OPEP To estimate the effect of the color-spin interaction, tensor force, while the label “with T” stands that with the OPEP which is not included in the present study, we revisit the tensor force. The same convention is adopted as in Fig. 1. coupled-channel dynamical calculation where both the

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Pauli-blocking and color-spin effects are included (but ¯ ¯ ðÞ ðÞ ¯ ðÞ terms of the ΛcD potential, the ΛcD − Σc D cou- without the OPEP) [7]. There a sharp cusp structure was pling induces the OPEP and the attraction from the tensor 3 2− Σ ¯ observed for the = state at the cD threshold while not term is also produced in the Λ D¯ ðÞ channel. In future for 1=2− state, implying some attraction for the 3=2− state c − experiments, it is interesting to search for such resonances while there is little for 1=2 state. This is because the color- below the Λ D¯ threshold. spin force which is attractive for the spin 1=2− state has c In conclusion, by coupling the open charm meson- been overcome by the Pauli-blocking effect that acts in a baryon channels to a compact uudcc¯ core with an inter- reversed manner. Therefore, the effect of the color-spin action satisfying the heavy quark and chiral symmetries, we force is not dominant for these resonant states. It is predict the masses and decay widths of the three new interesting to investigate the system with a model which pentaquark states reported in [34]. Both the masses and includes both of the above quark model features with the widths of these three hidden-charm pentaquark states we OPEP, which is now underway. − have obtained are in reasonable agreement with the Although we have obtained the JP ¼ 3=2 state at ¼ 50 experimental results. We point out that the three pentaquark 4371 MeV and at 4350 MeV when f and 80, P ¼1 2− P ¼ states have quantum numbers J þð4312Þ = , J þð4440Þ respectively, we do not consider that this state corresponds Pc Pc þ þ − P − to the LHCb’s P ð4380Þ state. The observed P ð4380Þ has 3=2 , and J þ ¼ 1=2 and the dominant molecular c c Pc ð4457Þ a width of about 200 MeV while that of our predicted state þ ¯ þ component of Pc ð4312Þ is the ΣcD and that of Pc ð4440Þ is only about 5 MeV. In the first LHCb analysis [1], though þ ¯ and Pc ð4457Þ is ΣcD . We find that the short range the higher Pc states were treated as one state, the opposite interaction by the coupling to the 5-quark-core states plays parity assignments were preferred for lower and higher Pc a major role in determining the ordering of the multiplet states. On the other hand, all the states we have obtained states, while the long range force of the pion tensor force here have the same parity minus. In the new LHCb analysis plays a major role in producing the decay widths, which are [34], using higher-order polynomials for the background, consistent with the data. The importance of what we þð4380Þ data could be fitted without the broad Pc Breit- referred to as the chiral tensor dynamics is a universal Wigner resonance contribution. Therefore, further theoreti- feature for the heavy hadrons with light quarks. Such cal as well as experimental studies are necessary for the dynamical studies in coupled-channel problems should be þð4380Þ Pc state. properly performed for further understanding of heavy In addition to the three states observed in the LHCb, we hadron systems. obtained four more states including the one corresponding þ ¯ ðÞ to Pc ð4380Þ near (below) the ΣcD thresholds as shown ¯ ðÞ ACKNOWLEDGMENTS in Fig. 1 and Table I. Due to the spins of Σc and D , J ¼ 3=2 and 1 (or 0), respectively, they naturally form The authors thank T. J. Burns for useful comments. either triplet states, J ¼ 5=2; 3=2; 1=2, or a singlet state of The authors also acknowledge financial support from J ¼ 3=2. A possible reason that those states are not seen Consejo Nacional de Ciencia y Tecnología, Mexico Σ would be due to a wider width of c. In fact, the width of (postdoctoral fellowship for H. G.-T.). This work is Σ Σ the c is about 15 MeV, while that of the c is less than supported in part by the Special Postdoctoral Researcher Σ Λ π 2MeV[50]. Furthermore c decays to c . Therefore, it (SPDR) and iTHEMS Programs of RIKEN (Y. Y.) and by ¯ ðÞ may be difficult to observe the ΣcD resonance states in Grant-in-Aid for Scientific Research of Japan Society for the J=ψp channel. One may have to look into the J=ψpπ the Promotion of Science No. 16K05361 (C) (S. T. and channel to observe the pentaquark states consisting mostly M. T.), No. JP17K05441 (C), and Grants-in-Aid for ¯ ðÞ of the ΣcD components. Scientific Research on Innovative Areas of the Ministry ðÞ ¯ ðÞ In addition to the seven Σc D states predicted in the of Education, Culture, Sports, Science and Technology, present study, we obtained two more narrow resonance Japan (No. 18H05407) (A. H.). This work is also supported ¯ “ states below the ΛcD threshold in Ref. [45], while such in part by the Research Center for Nuclear Physics, resonances have not been reported in experiments yet. Osaka University Collaboration Research network Although the OPEP does not contribute to the diagonal (COREnet).”

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