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(2020) Rapid Communications 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 ¯ ¯ à 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 Æ 0.7−0 6 MeV; results. As well as revealing the new Pþð4312Þ state, the . c Γ ¼ 9 8 Æ 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 Æ 1 3þ4.1 c Pc M . −4.7 MeV; Pþð4440Þ and Pþð4457Þ, with the two-peak structure c c Γ ¼ 20 6 Æ 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 Æ 0 6þ4.1 Pc M . −1.7 MeV; þ5.7 Γ ¼ 6.4 Æ 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¯ à 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¯ Ã, 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 ¯ Ã0 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 ¯ Ã 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 − ¯ à ½ÁÁÁ 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 Ã 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 ¯ à ¯ 2 wave ΣcD and the relative P(S − D)-wave Λcð2595ÞD are studied with the one-pion exchange potential (OPEP) in ½ÁÁÁ ¯ 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 à 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.
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