Abstract
We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to mπ = 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Therefore, there is no strong indication for any bound state or narrow resonance in the channels we study.
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References
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
G. Rupp and E. van Beveren, Why static bound-state calculations of tetraquarks should be met with scepticism, Chin. Phys. C 41 (2017) 053104 [arXiv:1611.00793] [INSPIRE].
N. Brambilla et al., QCD and strongly coupled gauge theories: challenges and perspectives, Eur. Phys. J. C 74 (2014) 2981 [arXiv:1404.3723] [INSPIRE].
H.-X. Chen, W. Chen, X. Liu and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rept. 639 (2016) 1 [arXiv:1601.02092] [INSPIRE].
A. Esposito, A. Pilloni and A.D. Polosa, Multiquark resonances, Phys. Rept. 668 (2016) 1 [arXiv:1611.07920] [INSPIRE].
R.F. Lebed, R.E. Mitchell and E.S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93 (2017) 143 [arXiv:1610.04528] [INSPIRE].
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao and B.-S. Zou, Hadronic molecules, arXiv:1705.00141 [INSPIRE].
S.L. Olsen, T. Skwarnicki and D. Zieminska, Non-standard heavy mesons and baryons, an experimental review, arXiv:1708.04012 [INSPIRE].
M.A. Moinester, How to search for doubly charmed baryons and tetraquarks, Z. Phys. A 355 (1996) 349 [hep-ph/9506405] [INSPIRE].
A. Del Fabbro, D. Janc, M. Rosina and D. Treleani, Production and detection of doubly charmed tetraquarks, Phys. Rev. D 71 (2005) 014008 [hep-ph/0408258] [INSPIRE].
T. Hyodo, Y.-R. Liu, M. Oka, K. Sudoh and S. Yasui, Production of doubly charmed tetraquarks with exotic color configurations in electron-positron collisions, Phys. Lett. B 721 (2013) 56 [arXiv:1209.6207] [INSPIRE].
A. Esposito, M. Papinutto, A. Pilloni, A.D. Polosa and N. Tantalo, Doubly charmed tetraquarks in B c and Ξbc decays, Phys. Rev. D 88 (2013) 054029 [arXiv:1307.2873] [INSPIRE].
M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].
M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B 364 (1991) 237 [INSPIRE].
R.A. Briceno, J.J. Dudek and R.D. Young, Scattering processes and resonances from lattice QCD, arXiv:1706.06223 [INSPIRE].
J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards and C.E. Thomas, Toward the excited meson spectrum of dynamical QCD, Phys. Rev. D 82 (2010) 034508 [arXiv:1004.4930] [INSPIRE].
C.E. Thomas, R.G. Edwards and J.J. Dudek, Helicity operators for mesons in flight on the lattice, Phys. Rev. D 85 (2012) 014507 [arXiv:1107.1930] [INSPIRE].
J.J. Dudek, R.G. Edwards and C.E. Thomas, S and D-wave phase shifts in isospin-2 ππ scattering from lattice QCD, Phys. Rev. D 86 (2012) 034031 [arXiv:1203.6041] [INSPIRE].
Hadron Spectrum collaboration, J.J. Dudek, R.G. Edwards and C.E. Thomas, Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD, Phys. Rev. D 87 (2013) 034505 [arXiv:1212.0830] [INSPIRE].
Hadron Spectrum collaboration, J.J. Dudek, R.G. Edwards, C.E. Thomas and D.J. Wilson, Resonances in coupled πK-ηK scattering from quantum chromodynamics, Phys. Rev. Lett. 113 (2014) 182001 [arXiv:1406.4158] [INSPIRE].
D.J. Wilson, J.J. Dudek, R.G. Edwards and C.E. Thomas, Resonances in coupled πK, ηK scattering from lattice QCD, Phys. Rev. D 91 (2015) 054008 [arXiv:1411.2004] [INSPIRE].
D.J. Wilson, R.A. Briceno, J.J. Dudek, R.G. Edwards and C.E. Thomas, Coupled ππ, \( K\;\overline{K} \) scattering in P -wave and the ρ resonance from lattice QCD, Phys. Rev. D 92 (2015) 094502 [arXiv:1507.02599] [INSPIRE].
Hadron Spectrum collaboration, J.J. Dudek, R.G. Edwards and D.J. Wilson, An a 0 resonance in strongly coupled πη, \( K\;\overline{K} \) scattering from lattice QCD, Phys. Rev. D 93 (2016) 094506 [arXiv:1602.05122] [INSPIRE].
R.A. Briceno, J.J. Dudek, R.G. Edwards and D.J. Wilson, Isoscalar ππ scattering and the σ meson resonance from QCD, Phys. Rev. Lett. 118 (2017) 022002 [arXiv:1607.05900] [INSPIRE].
G. Moir, M. Peardon, S.M. Ryan, C.E. Thomas and D.J. Wilson, Coupled-channel Dπ, Dη and \( {D}_s\overline{K} \) scattering from lattice QCD, JHEP 10 (2016) 011 [arXiv:1607.07093] [INSPIRE].
R.A. Briceno, J.J. Dudek, R.G. Edwards and D.J. Wilson, Isoscalar ππ, \( K\;\overline{K} \) , ηη scattering and the σ, f 0 , f 2 mesons from QCD, arXiv:1708.06667 [INSPIRE].
L. Maiani, F. Piccinini, A.D. Polosa and V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of X(3872), Phys. Rev. D 71 (2005) 014028 [hep-ph/0412098] [INSPIRE].
Y. Ikeda et al., Charmed tetraquarks T cc and T cs from dynamical lattice QCD simulations, Phys. Lett. B 729 (2014) 85 [arXiv:1311.6214] [INSPIRE].
S. Prelovsek, C.B. Lang, L. Leskovec and D. Mohler, Study of the Z + c channel using lattice QCD, Phys. Rev. D 91 (2015) 014504 [arXiv:1405.7623] [INSPIRE].
A.L. Guerrieri, M. Papinutto, A. Pilloni, A.D. Polosa and N. Tantalo, Flavored tetraquark spectroscopy, PoS(LATTICE2014)106 [arXiv:1411.2247] [INSPIRE].
M. Padmanath, C.B. Lang and S. Prelovsek, X(3872) and Y (4140) using diquark-antidiquark operators with lattice QCD, Phys. Rev. D 92 (2015) 034501 [arXiv:1503.03257] [INSPIRE].
Y. Chen et al., Low-energy scattering of the \( {\left(D\ {\overline{D}}^{\ast}\right)}^{\pm } \) system and the resonance-like structure Z c(3900), Phys. Rev. D 89 (2014) 094506 [arXiv:1403.1318] [INSPIRE].
CLQCD collaboration, Y. Chen et al., Low-energy scattering of \( {\left({D}^{\ast }{\overline{D}}^{\ast}\right)}^{\pm } \) system and the resonance-like structure Z c(4025), Phys. Rev. D 92 (2015) 054507 [arXiv:1503.02371] [INSPIRE].
HAL QCD collaboration, Y. Ikeda et al., Fate of the tetraquark candidate Z c(3900) from lattice QCD, Phys. Rev. Lett. 117 (2016) 242001 [arXiv:1602.03465] [INSPIRE].
A. Francis, R.J. Hudspith, R. Lewis and K. Maltman, Lattice prediction for deeply bound doubly heavy tetraquarks, Phys. Rev. Lett. 118 (2017) 142001 [arXiv:1607.05214] [INSPIRE].
European Twisted Mass collaboration, P. Bicudo and M. Wagner, Lattice QCD signal for a bottom-bottom tetraquark, Phys. Rev. D 87 (2013) 114511 [arXiv:1209.6274] [INSPIRE].
Z.S. Brown and K. Orginos, Tetraquark bound states in the heavy-light heavy-light system, Phys. Rev. D 86 (2012) 114506 [arXiv:1210.1953] [INSPIRE].
P. Bicudo, K. Cichy, A. Peters, B. Wagenbach and M. Wagner, Evidence for the existence of \( ud\overline{b}\overline{b} \) and the non-existence of \( ss\overline{b}\overline{b} \) and \( cc\overline{b}\overline{b} \) tetraquarks from lattice QCD, Phys. Rev. D 92 (2015) 014507 [arXiv:1505.00613] [INSPIRE].
P. Bicudo, K. Cichy, A. Peters and M. Wagner, BB interactions with static bottom quarks from lattice QCD, Phys. Rev. D 93 (2016) 034501 [arXiv:1510.03441] [INSPIRE].
A. Peters, P. Bicudo, L. Leskovec, S. Meinel and M. Wagner, Lattice QCD study of heavy-heavy-light-light tetraquark candidates, PoS(LATTICE2016)104 [arXiv:1609.00181] [INSPIRE].
P. Bicudo, J. Scheunert and M. Wagner, Including heavy spin effects in the prediction of a \( \overline{b}\overline{b}ud \) tetraquark with lattice QCD potentials, Phys. Rev. D 95 (2017) 034502 [arXiv:1612.02758] [INSPIRE].
P. Bicudo, M. Cardoso, A. Peters, M. Pflaumer and M. Wagner, \( ud\overline{b}\overline{b} \) tetraquark resonances with lattice QCD potentials and the Born-Oppenheimer approximation, Phys. Rev. D 96 (2017) 054510 [arXiv:1704.02383] [INSPIRE].
R.C. Johnson, Angular momentum on a lattice, Phys. Lett. B 114 (1982) 147 [INSPIRE].
D.C. Moore and G.T. Fleming, Angular momentum on the lattice: the case of non-zero linear momentum, Phys. Rev. D 73 (2006) 014504 [Erratum ibid. D 74 (2006) 079905] [hep-lat/0507018] [INSPIRE].
C. Michael, Adjoint sources in lattice gauge theory, Nucl. Phys. B 259 (1985) 58 [INSPIRE].
M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].
B. Blossier, M. Della Morte, G. von Hippel, T. Mendes and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, JHEP 04 (2009) 094 [arXiv:0902.1265] [INSPIRE].
J.J. Dudek, R.G. Edwards, N. Mathur and D.G. Richards, Charmonium excited state spectrum in lattice QCD, Phys. Rev. D 77 (2008) 034501 [arXiv:0707.4162] [INSPIRE].
D.C. Moore and G.T. Fleming, Multiparticle states and the hadron spectrum on the lattice, Phys. Rev. D 74 (2006) 054504 [hep-lat/0607004] [INSPIRE].
Hadron Spectrum collaboration, M. Peardon et al., A novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80 (2009) 054506 [arXiv:0905.2160] [INSPIRE].
J.J. Dudek, R.G. Edwards, B. Joo, M.J. Peardon, D.G. Richards and C.E. Thomas, Isoscalar meson spectroscopy from lattice QCD, Phys. Rev. D 83 (2011) 111502 [arXiv:1102.4299] [INSPIRE].
Hadron Spectrum collaboration, L. Liu et al., Excited and exotic charmonium spectroscopy from lattice QCD, JHEP 07 (2012) 126 [arXiv:1204.5425] [INSPIRE].
L. Levkova and C. DeTar, Charm annihilation effects on the hyperfine splitting in charmonium, Phys. Rev. D 83 (2011) 074504 [arXiv:1012.1837] [INSPIRE].
R.G. Edwards, B. Joó and H.-W. Lin, Tuning for three-flavors of anisotropic clover fermions with stout-link smearing, Phys. Rev. D 78 (2008) 054501 [arXiv:0803.3960] [INSPIRE].
Hadron Spectrum collaboration, H.-W. Lin et al., First results from 2 + 1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass, Phys. Rev. D 79 (2009) 034502 [arXiv:0810.3588] [INSPIRE].
R.G. Edwards, J.J. Dudek, D.G. Richards and S.J. Wallace, Excited state baryon spectroscopy from lattice QCD, Phys. Rev. D 84 (2011) 074508 [arXiv:1104.5152] [INSPIRE].
G. Moir, M. Peardon, S.M. Ryan, C.E. Thomas and L. Liu, Excited spectroscopy of charmed mesons from lattice QCD, JHEP 05 (2013) 021 [arXiv:1301.7670] [INSPIRE].
A.J. Woss and C.E. Thomas, Utilising optimised operators and distillation to extract scattering phase shifts, PoS(LATTICE2016)134 [arXiv:1612.05437] [INSPIRE].
L. Maiani, F. Piccinini, A.D. Polosa and V. Riquer, The Z(4430) and a new paradigm for spin interactions in tetraquarks, Phys. Rev. D 89 (2014) 114010 [arXiv:1405.1551] [INSPIRE].
M. Karliner and J.L. Rosner, Discovery of doubly-charmed Ξcc baryon implies a stable \( \left(bb\overline{u}\overline{d}\right) \) tetraquark, arXiv:1707.07666 [INSPIRE].
E.J. Eichten and C. Quigg, Heavy-quark symmetry implies stable heavy tetraquark mesons \( {Q}_i{Q}_j{\overline{q}}_k{\overline{q}}_l \), arXiv:1707.09575 [INSPIRE].
A. Czarnecki, B. Leng and M.B. Voloshin, Stability of tetrons, arXiv:1708.04594 [INSPIRE].
C. Morningstar et al., Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD, Phys. Rev. D 83 (2011) 114505 [arXiv:1104.3870] [INSPIRE].
SciDAC, LHPC and UKQCD collaborations, R.G. Edwards and B. Joó, The Chroma software system for lattice QCD, Nucl. Phys. Proc. Suppl. 140 (2005) 832 [hep-lat/0409003] [INSPIRE].
M.A. Clark, R. Babich, K. Barros, R.C. Brower and C. Rebbi, Solving lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181 (2010) 1517 [arXiv:0911.3191] [INSPIRE].
R. Babich, M.A. Clark and B. Joó, Parallelizing the QUDA library for multi-GPU calculations in lattice quantum chromodynamics, arXiv:1011.0024 [INSPIRE].
J.J. de Swart, The octet model and its Clebsch-Gordan coefficients, Rev. Mod. Phys. 35 (1963) 916 [Erratum ibid. 37 (1965) 326] [INSPIRE].
T.A. Kaeding, Tables of SU(3) isoscalar factors, Atom. Data Nucl. Data Tabl. 61 (1995) 233 [nucl-th/9502037] [INSPIRE].
R.L. Jaffe, Exotica, Phys. Rept. 409 (2005) 1 [hep-ph/0409065] [INSPIRE].
A.V. Manohar and M.B. Wise, Exotic \( QQ\overline{q}\overline{q} \) states in QCD, Nucl. Phys. B 399 (1993) 17 [hep-ph/9212236] [INSPIRE].
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Cheung, G.K.C., Thomas, C.E., Dudek, J.J. et al. Tetraquark operators in lattice QCD and exotic flavour states in the charm sector. J. High Energ. Phys. 2017, 33 (2017). https://doi.org/10.1007/JHEP11(2017)033
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DOI: https://doi.org/10.1007/JHEP11(2017)033