Abstract
We study diquarks on the lattice in the background of a static quark, in a gauge-invariant formalism with quark masses down to almost physical mπ. We determine mass differences between diquark channels as well as diquark-quark mass differences. The lightest and next-to-lightest diquarks have “good” scalar, \( {\overline{3}}_F \), \( {\overline{3}}_c \), J P = 0+, and “bad” axial vector, 6F, \( {\overline{3}}_c \), J P = 1+, quantum numbers, and a bad-good mass difference for ud flavors, 198(4) MeV, in excellent agreement with phenomenological determinations. Quark-quark attraction is found only in the “good” diquark channel. We extract a corresponding diquark size of ∼ 0.6 fm and perform a first exploration of the “good” diquark shape, which is shown to be spherical. Our results provide quantitative support for modeling the low-lying baryon spectrum using good light diquark effective degrees of freedom.
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R. L. Jaffe, Exotica, Phys. Rept. 409 (2005) 1 [hep-ph/0409065] [INSPIRE].
A. Ali, J. S. Lange and S. Stone, Exotics: Heavy Pentaquarks and Tetraquarks, Prog. Part. Nucl. Phys. 97 (2017) 123 [arXiv:1706.00610] [INSPIRE].
M. Y. Barabanov et al., Diquark correlations in hadron physics: Origin, impact and evidence, Prog. Part. Nucl. Phys. 116 (2021) 103835 [arXiv:2008.07630] [INSPIRE].
M. Gell-Mann, A Schematic Model of Baryons and Mesons, Phys. Lett. 8 (1964) 214 [INSPIRE].
M. Ida and R. Kobayashi, Baryon resonances in a quark model, Prog. Theor. Phys. 36 (1966) 846 [INSPIRE].
D. B. Lichtenberg, W. Namgung, E. Predazzi and J. G. Wills, Baryon Masses in a Relativistic Quark-Diquark Model, Phys. Rev. Lett. 48 (1982) 1653 [INSPIRE].
R. T. Cahill, C. D. Roberts and J. Praschifka, Calculation of Diquark Masses in QCD, Phys. Rev. D 36 (1987) 2804 [INSPIRE].
P. Maris, Effective masses of diquarks, Few Body Syst. 32 (2002) 41 [nucl-th/0204020] [INSPIRE].
E. Santopinto, An Interacting quark-diquark model of baryons, Phys. Rev. C 72 (2005) 022201 [hep-ph/0412319] [INSPIRE].
A. De Rujula, H. Georgi and S. L. Glashow, Hadron Masses in a Gauge Theory, Phys. Rev. D 12 (1975) 147 [INSPIRE].
T. A. DeGrand, R. L. Jaffe, K. Johnson and J. E. Kiskis, Masses and Other Parameters of the Light Hadrons, Phys. Rev. D 12 (1975) 2060 [INSPIRE].
G. ’t Hooft, Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle, Phys. Rev. D 14 (1976) 3432 [Erratum ibid. 18 (1978) 2199] [INSPIRE].
E. V. Shuryak, The Role of Instantons in Quantum Chromodynamics. 1. Physical Vacuum, Nucl. Phys. B 203 (1982) 93 [INSPIRE].
T. Schäfer and E. V. Shuryak, Instantons in QCD, Rev. Mod. Phys. 70 (1998) 323 [hep-ph/9610451] [INSPIRE].
M. Hess, F. Karsch, E. Laermann and I. Wetzorke, Diquark masses from lattice QCD, Phys. Rev. D 58 (1998) 111502 [hep-lat/9804023] [INSPIRE].
Y. Bi et al., Diquark mass differences from unquenched lattice QCD, Chin. Phys. C 40 (2016) 073106 [arXiv:1510.07354] [INSPIRE].
R. Babich, N. Garron, C. Hölbling, J. Howard, L. Lellouch and C. Rebbi, Diquark correlations in baryons on the lattice with overlap quarks, Phys. Rev. D 76 (2007) 074021 [hep-lat/0701023] [INSPIRE].
K. B. Teo and J. W. Negele, The Definition and lattice measurement of hadron wave functions, Nucl. Phys. B Proc. Suppl. 34 (1994) 390 [INSPIRE].
J. W. Negele, Hadron structure in lattice QCD: Exploring the gluon wave functional, in NSTAR2000: The Physics of Excited Nucleons, Newport News, U.S.A., February 16–19, 2000, pp. 368–377 [hep-lat/0007026] [INSPIRE].
C. Alexandrou, P. de Forcrand and A. Tsapalis, Probing hadron wave functions in lattice QCD, Phys. Rev. D 66 (2002) 094503 [hep-lat/0206026] [INSPIRE].
K. Orginos, Diquark properties from lattice QCD, PoS LAT2005 (2006) 054 [hep-lat/0510082] [INSPIRE].
C. Alexandrou, P. de Forcrand and B. Lucini, Searching for diquarks in hadrons, PoS LAT2005 (2006) 053 [hep-lat/0509113] [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].
J. Green, J. Negele, M. Engelhardt and P. Varilly, Spatial diquark correlations in a hadron, PoS LATTICE2010 (2010) 140 [arXiv:1012.2353] [INSPIRE].
J. Green, M. Engelhardt, J. Negele and P. Varilly, Diquark correlations in a hadron from lattice QCD, AIP Conf. Proc. 1441 (2012) 172 [INSPIRE].
R. Fukuda and P. de Forcrand, Searching for evidence of diquark states using lattice QCD simulations, PoS LATTICE2016 (2017) 121 [INSPIRE].
PACS-CS collaboration, 2+1 Flavor Lattice QCD toward the Physical Point, Phys. Rev. D 79 (2009) 034503 [arXiv:0807.1661] [INSPIRE].
PACS-CS collaboration, Charmed baryons at the physical point in 2+1 flavor lattice QCD, Phys. Rev. D 87 (2013) 094512 [arXiv:1301.4743] [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].
A. Francis, R. J. Hudspith, R. Lewis and K. Maltman, Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD, Phys. Rev. D 99 (2019) 054505 [arXiv:1810.10550] [INSPIRE].
M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [INSPIRE].
M. Donnellan, F. Knechtli, B. Leder and R. Sommer, Determination of the Static Potential with Dynamical Fermions, Nucl. Phys. B 849 (2011) 45 [arXiv:1012.3037] [INSPIRE].
B. Blossier and A. Gérardin, Density distributions in the B meson, Phys. Rev. D 94 (2016) 074504 [arXiv:1604.02891] [INSPIRE].
M. De Sanctis, J. Ferretti, E. Santopinto and A. Vassallo, Electromagnetic form factors in the relativistic interacting quark-diquark model of baryons, Phys. Rev. C 84 (2011) 055201 [INSPIRE].
M. Padmanath, Heavy baryon spectroscopy from lattice QCD, arXiv:1905.10168 [INSPIRE].
C. Alexandrou and C. Kallidonis, Low-lying baryon masses using Nf = 2 twisted mass clover-improved fermions directly at the physical pion mass, Phys. Rev. D 96 (2017) 034511 [arXiv:1704.02647] [INSPIRE].
R. J. Hudspith, A. Francis, R. Lewis and K. Maltman, Heavy and light spectroscopy near the physical point, Part I: Charm and bottom baryons, PoS LATTICE2016 (2017) 133 [INSPIRE].
M. Karliner and J. L. Rosner, Discovery of doubly-charmed Ξcc baryon implies a stable \( \left( bb\overline{u}\overline{d}\right) \) tetraquark, Phys. Rev. Lett. 119 (2017) 202001 [arXiv:1707.07666] [INSPIRE].
E. J. Eichten and C. Quigg, Heavy-quark symmetry implies stable heavy tetraquark mesons \( {Q}_i{Q}_j{\overline{q}}_k{\overline{q}}_l \), Phys. Rev. Lett. 119 (2017) 202002 [arXiv:1707.09575] [INSPIRE].
A. Czarnecki, B. Leng and M. B. Voloshin, Stability of tetrons, Phys. Lett. B 778 (2018) 233 [arXiv:1708.04594] [INSPIRE].
ETM collaboration, Static-static-light-light tetraquarks in lattice QCD, Acta Phys. Polon. Supp. 4 (2011) 747 [arXiv:1103.5147] [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 and M. Wagner, BB interactions with static bottom quarks from Lattice QCD, Phys. Rev. D 93 (2016) 034501 [arXiv:1510.03441] [INSPIRE].
European Twisted Mass collaboration, Lattice QCD signal for a bottom-bottom tetraquark, Phys. Rev. D 87 (2013) 114511 [arXiv:1209.6274] [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, 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. Junnarkar, N. Mathur and M. Padmanath, Study of doubly heavy tetraquarks in Lattice QCD, Phys. Rev. D 99 (2019) 034507 [arXiv:1810.12285] [INSPIRE].
L. Leskovec, S. Meinel, M. Pflaumer and M. Wagner, Lattice QCD investigation of a doubly-bottom \( \overline{b}\overline{b} ud \) tetraquark with quantum numbers I(J P) = 0(1+), Phys. Rev. D 100 (2019) 014503 [arXiv:1904.04197] [INSPIRE].
R. J. Hudspith, B. Colquhoun, A. Francis, R. Lewis and K. Maltman, A lattice investigation of exotic tetraquark channels, Phys. Rev. D 102 (2020) 114506 [arXiv:2006.14294] [INSPIRE].
P. Mohanta and S. Basak, Construction of \( bb\overline{u}\overline{d} \) tetraquark states on lattice with NRQCD bottom and HISQ up and down quarks, Phys. Rev. D 102 (2020) 094516 [arXiv:2008.11146] [INSPIRE].
P. Bicudo, A. Peters, S. Velten and M. Wagner, Importance of meson-meson and of diquark-antidiquark creation operators for a \( \overline{b}\overline{b} ud \) tetraquark, Phys. Rev. D 103 (2021) 114506 [arXiv:2101.00723] [INSPIRE].
LHCb collaboration, Observation of an exotic narrow doubly charmed tetraquark, arXiv:2109.01038 [INSPIRE].
LHCb collaboration, Study of the doubly charmed tetraquark \( {T}_{cc}^{+} \), arXiv:2109.01056 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
C. J. Burden, L. Qian, C. D. Roberts, P. C. Tandy and M. J. Thomson, Ground state spectrum of light quark mesons, Phys. Rev. C 55 (1997) 2649 [nucl-th/9605027] [INSPIRE].
P. Maris, Diquark properties and their role in hadrons, AIP Conf. Proc. 768 (2005) 256 [nucl-th/0412059] [INSPIRE].
G. Eichmann, I. C. Cloet, R. Alkofer, A. Krassnigg and C. D. Roberts, Toward unifying the description of meson and baryon properties, Phys. Rev. C 79 (2009) 012202 [arXiv:0810.1222] [INSPIRE].
H. L. L. Roberts, L. Chang, I. C. Cloet and C. D. Roberts, Masses of ground and excited-state hadrons, Few Body Syst. 51 (2011) 1 [arXiv:1101.4244] [INSPIRE].
G. Eichmann, C. S. Fischer and H. Sanchis-Alepuz, Light baryons and their excitations, Phys. Rev. D 94 (2016) 094033 [arXiv:1607.05748] [INSPIRE].
D. B. Lichtenberg, R. Roncaglia and E. Predazzi, Diquark model of exotic mesons, in 3rd International Workshop on Diquarks and other Models of Compositeness (DIQUARKS III), pp. 146–155, 11, 1996 [hep-ph/9611428] [INSPIRE].
J. Ferretti, A. Vassallo and E. Santopinto, Relativistic quark-diquark model of baryons, Phys. Rev. C 83 (2011) 065204 [INSPIRE].
D. Ebert, R. N. Faustov and V. O. Galkin, Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture, Phys. Rev. D 84 (2011) 014025 [arXiv:1105.0583] [INSPIRE].
S. Godfrey and N. Isgur, Mesons in a Relativized Quark Model with Chromodynamics, Phys. Rev. D 32 (1985) 189 [INSPIRE].
J. Ferretti, Effective Degrees of Freedom in Baryon and Meson Spectroscopy, Few Body Syst. 60 (2019) 17 [INSPIRE].
A. Francis, R. J. Hudspith, R. Lewis and K. Maltman, Heavy and light spectroscopy near the physical point, Part II: Tetraquarks, PoS LATTICE2016 (2016) 132 [INSPIRE].
RBC, UKQCD collaboration, Fourier Accelerated Conjugate Gradient Lattice Gauge Fixing, Comput. Phys. Commun. 187 (2015) 115 [arXiv:1405.5812] [INSPIRE].
A. Hasenfratz and F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking, Phys. Rev. D 64 (2001) 034504 [hep-lat/0103029] [INSPIRE].
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Francis, A., de Forcrand, P., Lewis, R. et al. Diquark properties from full QCD lattice simulations. J. High Energ. Phys. 2022, 62 (2022). https://doi.org/10.1007/JHEP05(2022)062
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DOI: https://doi.org/10.1007/JHEP05(2022)062