Abstract
The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel — the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at E = 4.12 GeV for the transitions \( J/\psi +\phi \leftrightarrow {D}_s^{\ast }+{\overline{D}}_s^{\ast } \), which can be associated with χc1 (4140), and a narrow peak at 3.98 GeV with the width 10 MeV for the transitions \( {D}_s^{-}+{D}_0^{\ast}\leftrightarrow J/\psi +{K}^{\ast -} \), which can be associated with th recently discovered Zcs (3985).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
N. Brambilla et al., The XYZ states: experimental and theoretical status and perspectives, Phys. Rept. 873 (2020) 1 [arXiv:1907.07583] [INSPIRE].
J. L. Rosner, Threshold effect and π±ψ(2S) peak, Phys. Rev. D 76 (2007) 114002 [arXiv:0708.3496] [INSPIRE].
E. Braaten and M. Lu, Line shapes of the Z(4430), Phys. Rev. D 79 (2009) 051503 [arXiv:0712.3885] [INSPIRE].
K.-M. Cheung, W.-Y. Keung and T.-C. Yuan, Bottomed analog of Z+(4433), Phys. Rev. D 76 (2007) 117501 [arXiv:0709.1312] [INSPIRE].
C. Meng and K.-T. Chao, Z+(4430) as a resonance in the \( {D}_1\left({D}_1^{\prime}\right){D}_{\ast } \) channel, arXiv:0708.4222 [INSPIRE].
G.-J. Ding, Understanding the charged meson Z(4430), arXiv:0711.1485 [INSPIRE].
G.-J. Ding, W. Huang, J.-F. Liu and M.-L. Yan, Z+(4430) and analogous heavy flavor molecules, Phys. Rev. D 79 (2009) 034026 [arXiv:0805.3822] [INSPIRE].
Y. Li, C.-D. Lu and W. Wang, Partners of Z(4430) and productions in B decays, Phys. Rev. D 77 (2008) 054001 [arXiv:0711.0497] [INSPIRE].
L. Maiani, A. D. Polosa and V. Riquer, The charged Z(4433): towards a new spectroscopy, arXiv:0708.3997 [INSPIRE].
C.-F. Qiao, A uniform description of the states recently observed at B-factories, J. Phys. G 35 (2008) 075008 [arXiv:0709.4066] [INSPIRE].
X.-H. Liu, Q. Zhao and F. E. Close, Search for tetraquark candidate Z(4430) in meson photoproduction, Phys. Rev. D 77 (2008) 094005 [arXiv:0802.2648] [INSPIRE].
X. Liu, B. Zhang and S.-L. Zhu, The two-body open charm decays of Z+(4430), Phys. Rev. D 77 (2008) 114021 [arXiv:0803.4270] [INSPIRE].
L. Maiani, A. D. Polosa and V. Riquer, The charged Z(4430) in the diquark-antidiquark picture, New J. Phys. 10 (2008) 073004 [INSPIRE].
D. V. Bugg, How resonances can synchronise with thresholds, J. Phys. G 35 (2008) 075005 [arXiv:0802.0934] [INSPIRE].
T. Matsuki, T. Morii and K. Sudoh, Is the Z+(4430) a radially excited state of Ds?, Phys. Lett. B 669 (2008) 156 [arXiv:0805.2442] [INSPIRE].
M. Cardoso and P. Bicudo, Microscopic calculation of the decay of Jaffe- Wilczek tetraquarks, and the Z(4433), AlP Conf. Proc. 1030 (2008) 352 [arXiv:0805.2260] [INSPIRE].
Y.-R. Liu and Z.-Y. Zhang, A chiral quark model study of Z+(4430) in the molecular picture, arXiv:0908.1734 [INSPIRE].
T. Branz, T. Gutsche and V. E. Lyubovitskij, Hidden-charm and radiative decays of the Z(4430) as a hadronic \( {D}_1{\overline{D}}_{\ast } \) bound state, Phys. Rev. D 82 (2010) 054025 [arXiv:1005.3168] [INSPIRE].
G. Galata, Photoproduction of Z(4430) through mesonic Regge trajectories exchange, Phys. Rev. C 83 (2011) 065203 [arXiv:1102.2070] [INSPIRE].
M. Nielsen and F. S. Navarra, Charged exotic charmonium states, Mod. Phys. Lett. A 29 (2014) 1430005 [arXiv:1401.2913] [INSPIRE].
X.-W. Kang, Z.-H. Guo and J. A. Oller, General considerations on the nature of Zb(l0610) and Zb(l0650) from their pole positions, Phys. Rev. D 94 (2016) 014012 [arXiv:1603.05546] [INSPIRE].
F. K. Guo et al., Interplay of quark and meson degrees of freedom in near-threshold states: a practical parametrization for line shapes, Phys. Rev. D 93 (2016) 074031 [arXiv:1602.00940] [INSPIRE].
C. Deng, J. Ping, H. Huang and F. Wang, Systematic study of \( {Z}_c^{+} \) family from a multiquark color fiux-tube model, Phys. Rev. D 92 (2015) 034027 [arXiv:1507.06408] [INSPIRE].
F.-K. Guo, C. Hanhart, U.-G. MeiBner, Q. Wang, Q. Zhao and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90 (2018) 015004 [arXiv:1705.00141] [INSPIRE].
Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu and S.-L. Zhu, Pentaquark and tetraquark states, Frog. Part. Nucl. Phys. 107 (2019) 237 [arXiv:1903.11976] [INSPIRE].
Y. S. Kalashnikova and A. V. Nefediev, X(3872) in the molecular model, Phys. Usp. 62 (2019) 568 [Usp. Fiz. Nauk 189 (2019) 603] [arXiv:1811.01324] [INSPIRE].
A. Esposito, A. Pilloni and A. D. Polosa, Hybridized tetraquarks, Phys. Lett. B 758 (2016) 292 [arXiv:1603.07667] [INSPIRE].
A. M. Badalian, L. P. Kok, M. I. Polikarpov and Y. A. Simonov, Resonances in coupled channels in nuclear and particle physics, Phys. Rept. 82 (1982) 31 [INSPIRE].
E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane and T.-M. Yan, Charmonium: the model, Phys. Rev. D 17 (1978) 3090 [Erratum ibid. 21 (1980) 313] [INSPIRE].
E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane and T.-M. Yan, Charmonium: comparison with experiment, Phys. Rev. D 21 (1980) 203 [INSPIRE].
E. J. Eichten, K. Lane and C. Quigg, Charmonium levels near threshold and the narrow state X(3872) → π+π– J/ψ, Phys. Rev. D 69 (2004) 094019 [hep-ph/0401210] [INSPIRE].
Y. S. Kalashnikova, Coupled-channel model for charmonium levels and an option for X(3872), Phys. Rev. D 72 (2005) 034010 [hep-ph/0506270] [INSPIRE].
I. V. Danilkin and Y. A. Simonov, Channel coupling in heavy quarkonia: energy levels, mixing, widths and new states, Phys. Rev. D 81 (2010) 074027 [arXiv:0907.1088] [INSPIRE].
I. V. Danilkin and Y. A. Simonov, Dynamical origin and the pole structure of X(3872), Phys. Rev. Lett. 105 (2010) 102002 [arXiv:1006.0211] [INSPIRE].
I. V. Danilkin, V. D. Orlovsky and Y. A. Simonov, Hadron interaction with heavy quarkonia, Phys. Rev. D 85 (2012) 034012 [arXiv:1106.1552] [INSPIRE].
A. M. Badalian and B. L. G. Bakker, Dynamics of the quark-antiquark interaction and the universality of Regge trajectories, Phys. Rev. D 100 (2019) 034010 [arXiv:1901.10280] [INSPIRE].
A. M. Badalian and B. L. G. Bakker, Radial and orbital Regge trajectories in heavy quarkonia, Phys. Rev. D 100 (2019) 054036 [arXiv:1902.09174] [INSPIRE].
A. Y. Dubin, A. B. Kaidalov and Y. A. Simonov, The QCD string with quarks. 1. Spinless quarks, Phys. Atom. Nucl. 56 (1993) 1745 [Yad. Fiz. 56 (1993) 213] [hep-ph/9311344] [INSPIRE].
A. Y. Dubin, A. B. Kaidalov and Y. A. Simonov, Dynamical regimes of the QCD string with quarks, Phys. Lett. B 323 (1994) 41 [INSPIRE].
Y. A. Simonov, Exact relativistic Green’s functions for the time-independent potentials, Phys. Rev. D 99 (2019) 096025 [arXiv:1902.05364] [INSPIRE].
S. S. Afonin, Towards understanding spectral degeneracies in nonstrange hadrons. Part I. Mesons as hadron strings versus phenomenology, Mod. Phys. Lett. A 22 (2007) 1359 [hep-ph/0701089] [INSPIRE].
S. S. Afonin and T. D. Solomko, The large-Nc limit of borelized spectral sum rules and the slope of radial Regge trajectories, Int. J. Mod. Phys. A 33 (2018) 1850115 [arXiv:1805.03089] [INSPIRE].
Y. A. Simonov, Relativistic path integral and relativistic Hamiltonians in QCD and QED, Phys. Rev. D 88 (2013) 025028 [arXiv:1303.4952] [INSPIRE].
Y. A. Simonov, Spin interactions in mesons in strong magnetic field, Phys. Rev. D 88 (2013) 053004 [arXiv:1304.0365] [INSPIRE].
Y. A. Simonov, Exact relativistic Green’s functions for the time-independent potentials, Phys. Rev. D 99 (2019) 096025 [arXiv:1902.05364] [INSPIRE].
M. S. Lukashov and Y. A. Simonov, Scalar mesons in a chiral theory with quark degrees of freedom, Phys. Rev. D 101 (2020) 094028 [arXiv:1909.10384] [INSPIRE].
A. M. Badalian, M. S. Lukashov and Y. A. Simonov, Relativistic Cornell-type mechanism of exotic scalar resonances, Phys. Rev. D 102 (2020) 094012 [arXiv:2001.07113] [INSPIRE].
Y. A. Simonov, Di-pion decays of heavy quarkonium in the field correlator method, Phys. Atom. Nucl. 71 (2008) 1048 [arXiv:0711.3626] [INSPIRE].
Y. A. Simonov, Relativistic theory of string breaking in QCD, Phys. Rev. D 84 (2011) 065013 [arXiv:1103.4028] [INSPIRE].
LHCb collaboration, Observation of J/ψϕ structures consistent with exotic states from amplitude analysis of B+ → J/ψϕK+ decays, Phys. Rev. Lett. 118 (2017) 022003 [arXiv:1606.07895] [INSPIRE].
CDF collaboration, Observation of the Y(4140) structure in the J/ψϕ mass spectrum in B± → J/ψϕK± decays, Mod. Phys. Lett. A 32 (2017) 1750139 [arXiv:1101.6058] [INSPIRE].
D0 collaboration, Inclusive production of the X(4140) state in \( p\overline{p} \) collisions at D0, Phys. Rev. Lett. 115 (2015) 232001 [arXiv:1508.07846] [INSPIRE].
CMS collaboration, Observation of a peaking structure in the J/ψϕ mass spectrum from B± → J/ψϕK± decays, Phys. Lett. B 734 (2014) 261 [arXiv:1309.6920] [INSPIRE].
BESIII collaboration, Observation of a charged charmonium-like structure in e+e–π+π– J/ψ at \( \sqrt{s} \) = 4.26 GeV, Phys. Rev. Lett. 110 (2013) 252001 [arXiv:1303.5949] [INSPIRE].
Belle collaboration, Study of e+e– → π+π– J/ψ and observation of a charged charmonium-like state at Belle, Phys. Rev. Lett. 110 (2013) 252002 [Erratum ibid. 111 (2013) 019901] [arXiv:1304.0121] [INSPIRE].
T. Xiao, S. Dobbs, A. Tomaradze and K. K. Seth, Observation of the charged hadron \( {Z}_c^{\pm } \)(3900) and evidence for the neutral \( {Z}_c^0 \)(3900) in e+e– → ππ J/ψ at \( \sqrt{s} \) = 4170MeV, Phys. Lett. B 727 (2013) 366 [arXiv:1304. 3036] [INSPIRE].
BESIII collaboration, Observation of e+e– → π0π0hc and a neutral charmonium-like structure Zc(4020)0, Phys. Rev. Lett. 113 (2014) 212002 [arXiv:1409.6577] [INSPIRE].
BESIII collaboration, Observation of a charged charmonium-like structure Zc(4020) and search for the Zc(3900) in e+e– → π+π–hc, Phys. Rev. Lett. 111 (2013) 242001 [arXiv:1309.1896] [INSPIRE].
G. C. Rossi and G. Veneziano, Tetra-quarks, penta-quarks and the like: old and new views, in The hadronic vacuum polarization from lattice QCD at high precision: a topical workshop of the muon g – 2 theory initiative, (2020) [arXiv:2011.09774] [INSPIRE].
M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson and D. B. Lichtenberg, Diquarks, Rev. Mod. Phys. 65 (1993) 1199 [INSPIRE].
S. Fleck, B. Silvestre-Brac and J. M. Richard, Search for diquark clustering in baryons, Phys. Rev. D 38 (1988) 1519 [INSPIRE].
E. Santopinto and J. Ferretti, Strange and nonstrange baryon spectra in the relativistic interacting quark-diquark model with a Gursey and Radicati-inspired exchange interaction, Phys. Rev. C 92 (2015) 025202 [arXiv:1412.7571] [INSPIRE].
C. Gutierrez and M. De Sanctis, A study of a relativistic quark-diquark model for the nucleon, Eur. Phys. J. A 50 (2014) 169 [INSPIRE].
C. Alexandrou, P. de Forcrand and B. Lucini, Evidence for diquarks in lattice QCD, Phys. Rev. Lett. 97 (2006) 222002 [hep-lat/0609004] [INSPIRE].
E. Megías, E. Ruiz Arriola and L. L. Salcedo, Quark-diquark string tension, excited baryonic resonances and thermal fluctuations, Phys. Scripta 95 (2020) 074005 [arXiv:2002.10871] [INSPIRE].
LHCb collaboration, Observation of J/ψp resonances consistent with pentaquark states in \( {\Lambda}_b^0 \) → J/ψK–p decays, Phys. Rev. Lett. 115 (2015) 072001 [arXiv:1507.03414] [INSPIRE].
LHCb collaboration, Observation of a narrow pentaquark state, Pc(4312)+, and of two-peak structure of the Pc(4450)+, Phys. Rev. Lett. 122 (2019) 222001 [arXiv:1904.03947] [INSPIRE].
U. Skerbis and S. Prelovsek, Nucleon-J/ψ and nucleon-ηc scattering in Pc pentaquark channels from LQCD, Phys. Rev. D 99 (2019) 094505 [arXiv:1811.02285] [INSPIRE].
H.-X. Chen, W. Chen and S.-L. Zhu, Possible interpretations of the Pc(4312), Pc(4440), and Pc(4457), Phys. Rev. D 100 (2019) 051501 [arXiv:1903.11001] [INSPIRE].
M.-Z. Liu et al., Emergence of a complete heavy-quark spin symmetry multiplet: seven molecular pentaquarks in light of the latest LHCb analysis, Phys. Rev. Lett. 122 (2019) 242001 [arXiv:1903.11560] [INSPIRE].
F.-K. Guo, H.-J. Jing, U.-G. Meißner and S. Sakai, Isospin breaking decays as a diagnosis of the hadronic molecular structure of the Pc(4457) , Phys. Rev. D 99 (2019) 091501 [arXiv:1903.11503] [INSPIRE].
J. He, Study of Pc(4457), Pc(4440), and Pc(4312) in a quasipotential Bethe-Salpeter equation approach, Eur. Phys. J. C 79 (2019) 393 [arXiv:1903.11872] [INSPIRE].
Z.-H. Guo and J. A. Oller, Anatomy of the newly observed hidden-charm pentaquark states: Pc(4312), Pc(4440) and Pc(4457), Phys. Lett. B 793 (2019) 144 [arXiv:1904.00851] [INSPIRE].
JPAC collaboration, Interpretation of the LHCb Pc(4312)+ signal, Phys. Rev. Lett. 123 (2019) 092001 [arXiv:1904.10021] [INSPIRE].
Z.-G. Wang, Analysis of the Pc(4312), Pc(4440), Pc(4457) and related hidden-charm pentaquark states with QCD sum rules, Int. J. Mod. Phys. A 35 (2020) 2050003 [arXiv:1905.02892] [INSPIRE].
F.-L. Wang, R. Chen, Z.-W. Liu and X. Liu, Probing new types of Pc states inspired by the interaction between S-wave charmed baryon and anti-charmed meson in a \( \overline{T} \) doublet, Phys. Rev. C 101 (2020) 025201 [arXiv:1905.03636] [INSPIRE].
J.-B. Cheng and Y.-R. Liu, Pc(4457)+, Pc(4440)+, and Pc(4312)+: molecules or compact pentaquarks?, Phys. Rev. D 100 (2019) 054002 [arXiv:1905.08605] [INSPIRE].
J.-J. Wu, T. S. H. Lee and B.-S. Zou, Nucleon resonances with hidden charm in 'YP reactions, Phys. Rev. C 100 (2019) 035206 [arXiv:1906.05375] [INSPIRE].
C. W. Xiao, J. Nieves and E. Oset, Heavy quark spin symmetric molecular states from \( {\overline{D}}^{\left(\ast \right)}{\Sigma}_c^{\left(\ast \right)} \) and other coupled channels in the light of the recent LHCb pentaquarks, Phys. Rev. D 100 (2019) 014021 [arXiv:1904.01296] [INSPIRE].
M. B. Voloshin, Some decay properties of hidden-charm pentaquarks as baryon-meson molecules, Phys. Rev. D 100 (2019) 034020 [arXiv:1907.01476] [INSPIRE].
Y.-J. Xu, C.-Y. Cui, Y.-L. Liu and M.-Q. Huang, Partial decay widths of Pc(4312) as a \( \overline{D}{\Sigma}_c \) molecular state, Phys. Rev. D 102 (2020) 034028 [arXiv:1907.05097] [INSPIRE].
M.-Z. Liu, T.-W. Wu, M. Sánchez Sánchez, M. P. Valderrama, L.-S. Geng and J.-J. Xie, Spin-parities of the Pc(4440) and Pc(4457) in the one-boson-exchange model, Phys. Rev. D 103 (2021) 054004 [arXiv:1907.06093] [INSPIRE].
M.-L. Du et al., Interpretation of the LHCb Pc states as hadronic molecules and hints of a narrow Pc(4380), Phys. Rev. Lett. 124 (2020) 072001 [arXiv:1910.11846] [INSPIRE].
B.-T. Zhang, J.-S. Wang and Y.-L. Ma, Pentaquark states from bound state approach with chiral partner structure, arXiv:2002.10954 [INSPIRE].
S.-Q. Kuang, L.-Y. Dai, X.-W. Kang and D.-L. Yao, Pole analysis on the hadron spectroscopy of Λb → J/ΨpK–, Eur. Phys. J. C 80 (2020) 433 [arXiv:2002.11959] [INSPIRE].
BESIII collaboration, Observation of a near-threshold structure in the K+ recoil-mass spectra in e+e– → K+(\( {D}_s^{-}{D}^{\ast 0}+{D}_s^{\ast -}{D}^0 \)), Phys. Rev. Lett. 126 (2021) 102001 [arXiv:2011.07855] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2011.12326
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Simonov, Y.A. Recoupling mechanism for exotic mesons and baryons. J. High Energ. Phys. 2021, 51 (2021). https://doi.org/10.1007/JHEP04(2021)051
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)051