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Magnetic moments of spin–1/2 triply heavy baryons: a study of light-cone QCD and quark–diquark model

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Abstract

In this study, the magnetic moments of the spin-1/2 triply heavy baryons have been calculated using both light-cone QCD sum rules and quark–diquark model. Theoretical investigations on magnetic moments of the triply heavy baryons are crucial as their results can help us better understand their internal structure and the dynamics of the QCD as the theory of the strong interaction. We compare the results extracted for the magnetic moment with the existing theoretical predictions. It is seen that the obtained magnetic moment values are quite compatible with the results in the literature.

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References

  1. R. Aaij et al., Observation of the doubly charmed baryon \(\Xi _{cc}^{++}\). Phys. Rev. Lett. 119(11), 112001 (2017). https://doi.org/10.1103/PhysRevLett.119.112001arXiv:1707.01621

    Article  ADS  Google Scholar 

  2. R. Aaij et al., Observation of structure in the \(J /\psi \) -pair mass spectrum. Sci. Bull. 65(23), 1983–1993 (2020). https://doi.org/10.1016/j.scib.2020.08.032arXiv:2006.16957

    Article  Google Scholar 

  3. S.P. Baranov, V.L. Slad, Production of triply charmed Omega(ccc) baryons in e+ e- annihilation. Phys. Atom. Nucl. 67, 808–814 (2004). https://doi.org/10.1134/1.1707141arXiv:0603090 [hep-ph]

    Article  ADS  Google Scholar 

  4. V.A. Saleev, Omega(ccc) production via fragmentation at LHC. Mod. Phys. Lett. A 14, 2615–2620 (1999). https://doi.org/10.1142/S0217732399002741arXiv:9906515 [hep-ph]

    Article  ADS  Google Scholar 

  5. M.A. Gomshi Nobary, Fragmentation production of Omega(ccc) and Omega(bbb) baryons, Phys. Lett. B 559, 239–244 (2003). [Erratum: Phys. Lett. B 598, 294–294 (2004)]. https://doi.org/10.1016/j.physletb.2002.12.001. arXiv:0408122 [hep-ph]

  6. M.A. Gomshi Nobary, R. Sepahvand, Fragmentation of triply heavy baryons. Phys. Rev. D 71, 034024 (2005). https://doi.org/10.1103/PhysRevD.71.034024arXiv:0406148 [hep-ph]

    Article  ADS  Google Scholar 

  7. M.A. Gomshi Nobary, R. Sepahvand, An Ivestigation of triply heavy baryon production at hadron colliders. Nucl. Phys. B 741, 34–41 (2006). https://doi.org/10.1016/j.nuclphysb.2006.01.043arXiv:0508115 [hep-ph]

    Article  ADS  Google Scholar 

  8. Y.-Q. Chen, S.-Z. Wu, Production of triply heavy baryons at LHC, JHEP 08, 144 (2011). [Erratum: JHEP 09, 089 (2011)]. https://doi.org/10.1007/JHEP08(2011)144. arXiv:1106.0193

  9. H. He, Y. Liu, P. Zhuang, \(\Omega _{ccc}\) production in high energy nuclear collisions. Phys. Lett. B 746, 59–63 (2015). https://doi.org/10.1016/j.physletb.2015.04.049arXiv:1409.1009

    Article  ADS  Google Scholar 

  10. J. Zhao, P. Zhuang, Multicharmed Baryon production in high energy nuclear collisions. Few Body Syst. 58(2), 100 (2017). https://doi.org/10.1007/s00601-017-1255-9

    Article  ADS  Google Scholar 

  11. J.M. Flynn, E. Hernandez, J. Nieves, Triply heavy baryons and heavy quark spin symmetry. Phys. Rev. D 85, 014012 (2012). https://doi.org/10.1103/PhysRevD.85.014012arXiv:1110.2962

    Article  ADS  Google Scholar 

  12. W. Wang, J. Xu, Weak decays of triply heavy baryons. Phys. Rev. D 97(9), 093007 (2018). https://doi.org/10.1103/PhysRevD.97.093007arXiv:1803.01476

    Article  ADS  Google Scholar 

  13. S. Cho et al., Exotic hadrons from heavy ion collisions. Prog. Part. Nucl. Phys. 95, 279–322 (2017). https://doi.org/10.1016/j.ppnp.2017.02.002arXiv:1702.00486

    Article  ADS  Google Scholar 

  14. S. Meinel, Excited-state spectroscopy of triply-bottom baryons from lattice QCD. Phys. Rev. D 85, 114510 (2012). https://doi.org/10.1103/PhysRevD.85.114510arXiv:1202.1312

    Article  ADS  Google Scholar 

  15. R.A. Briceno, H.-W. Lin, D.R. Bolton, Charmed-Baryon Spectroscopy from Lattice QCD with \(N_f=2+1+1\) Flavors. Phys. Rev. D 86, 094504 (2012). https://doi.org/10.1103/PhysRevD.86.094504arXiv:1207.3536

    Article  ADS  Google Scholar 

  16. Y. Namekawa et al., Charmed baryons at the physical point in 2+1 flavor lattice QCD. Phys. Rev. D 87(9), 094512 (2013). https://doi.org/10.1103/PhysRevD.87.094512arXiv:1301.4743

    Article  ADS  Google Scholar 

  17. C. Alexandrou, V. Drach, K. Jansen, C. Kallidonis, G. Koutsou, Baryon spectrum with \(N_f=2+1+1\) twisted mass fermions. Phys. Rev. D 90(7), 074501 (2014). https://doi.org/10.1103/PhysRevD.90.074501arXiv:1406.4310

    Article  ADS  Google Scholar 

  18. M. Padmanath, R.G. Edwards, N. Mathur, M. Peardon, Spectroscopy of triply-charmed baryons from lattice QCD. Phys. Rev. D 90(7), 074504 (2014). https://doi.org/10.1103/PhysRevD.90.074504arXiv:1307.7022

    Article  ADS  Google Scholar 

  19. Z.S. Brown, W. Detmold, S. Meinel, K. Orginos, Charmed bottom baryon spectroscopy from lattice QCD. Phys. Rev. D 90(9), 094507 (2014). https://doi.org/10.1103/PhysRevD.90.094507arXiv:1409.0497

    Article  ADS  Google Scholar 

  20. K.U. Can, G. Erkol, M. Oka, T.T. Takahashi, Look inside charmed-strange baryons from lattice QCD. Phys. Rev. D 92(11), 114515 (2015). https://doi.org/10.1103/PhysRevD.92.114515arXiv:1508.03048

    Article  ADS  Google Scholar 

  21. N. Mathur, M. Padmanath, S. Mondal, Precise predictions of charmed-bottom hadrons from lattice QCD. Phys. Rev. Lett. 121(20), 202002 (2018). https://doi.org/10.1103/PhysRevLett.121.202002arXiv:1806.04151

    Article  ADS  Google Scholar 

  22. J.-R. Zhang, M.-Q. Huang, Deciphering triply heavy baryons in terms of QCD sum rules. Phys. Lett. B 674, 28–35 (2009). https://doi.org/10.1016/j.physletb.2009.02.056arXiv:0902.3297

    Article  ADS  Google Scholar 

  23. Z.-G. Wang, Analysis of the triply heavy Baryon States with QCD sum rules. Commun. Theor. Phys. 58, 723–731 (2012). https://doi.org/10.1088/0253-6102/58/5/17arXiv:1112.2274

    Article  ADS  MATH  Google Scholar 

  24. T.M. Aliev, K. Azizi, M. Savci, Masses and residues of the triply heavy spin-1/2 Baryons. JHEP 04, 042 (2013). https://doi.org/10.1007/JHEP04(2013)042arXiv:1212.6065

    Article  ADS  Google Scholar 

  25. T.M. Aliev, K. Azizi, M. Savcı, Properties of triply heavy spin-3/2 baryons. J. Phys. G 41, 065003 (2014). https://doi.org/10.1088/0954-3899/41/6/065003arXiv:1404.2091

    Article  ADS  Google Scholar 

  26. Z.-G. Wang, Analysis of the triply-heavy baryon states with the QCD sum rules. AAPPS Bull. 31, 5 (2021). https://doi.org/10.1007/s43673-021-00006-3arXiv:2010.08939

    Article  Google Scholar 

  27. N. Alomayrah, T. Barakat, The excited states of triply-heavy baryons in QCD sum rules. Eur. Phys. J. A 56(3), 76 (2020). https://doi.org/10.1140/epja/s10050-020-00062-7

    Article  ADS  Google Scholar 

  28. R.-H. Wu, Y.-S. Zuo, C. Meng, Y.-Q. Ma, K.-T. Chao, NLO effects for \(\Omega \) QQQ baryons in QCD sum rules. Chin. Phys. C 45(9), 093103 (2021). https://doi.org/10.1088/1674-1137/ac0b3carXiv:2104.07384

    Article  ADS  Google Scholar 

  29. P. Hasenfratz, R.R. Horgan, J. Kuti, J.M. Richard, Heavy baryon spectroscopy in the QCD bag model. Phys. Lett. B 94, 401–404 (1980). https://doi.org/10.1016/0370-2693(80)90906-5

    Article  ADS  Google Scholar 

  30. B. Silvestre-Brac, Spectrum and static properties of heavy baryons. Few Body Syst. 20, 1–25 (1996). https://doi.org/10.1007/s006010050028

    Article  ADS  Google Scholar 

  31. S. Migura, D. Merten, B. Metsch, H.-R. Petry, Charmed baryons in a relativistic quark model. Eur. Phys. J. A 28, 41 (2006). https://doi.org/10.1140/epja/i2006-10017-9arXiv:0602153 [hep-ph]

    Article  ADS  Google Scholar 

  32. Y. Jia, Variational study of weakly coupled triply heavy baryons. JHEP 10, 073 (2006). https://doi.org/10.1088/1126-6708/2006/10/073arXiv:0607290 [hep-ph]

    Article  ADS  Google Scholar 

  33. W. Roberts, M. Pervin, Heavy baryons in a quark model. Int. J. Mod. Phys. A 23, 2817–2860 (2008). https://doi.org/10.1142/S0217751X08041219arXiv:0711.2492

    Article  ADS  MATH  Google Scholar 

  34. A.P. Martynenko, Ground-state triply and doubly heavy baryons in a relativistic three-quark model. Phys. Lett. B 663, 317–321 (2008). https://doi.org/10.1016/j.physletb.2008.04.030arXiv:0708.2033

    Article  ADS  Google Scholar 

  35. B. Patel, A. Majethiya, P.C. Vinodkumar, Masses and magnetic moments of triply heavy flavour baryons in hypercentral model. Pramana 72, 679–688 (2009). https://doi.org/10.1007/s12043-009-0061-4arXiv:0808.2880

    Article  ADS  Google Scholar 

  36. A. Bernotas, V. Simonis, Heavy hadron spectroscopy and the bag model. Lith. J. Phys. 49, 19–28 (2009). https://doi.org/10.3952/lithjphys.49110arXiv:0808.1220

    Article  Google Scholar 

  37. F.J. Llanes-Estrada, O.I. Pavlova, R. Williams, A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential. Eur. Phys. J. C 72, 2019 (2012). https://doi.org/10.1140/epjc/s10052-012-2019-9arXiv:1111.7087

    Article  ADS  Google Scholar 

  38. J. Vijande, A. Valcarce, H. Garcilazo, Constituent-quark model description of triply heavy baryon nonperturbative lattice QCD data. Phys. Rev. D 91(5), 054011 (2015). https://doi.org/10.1103/PhysRevD.91.054011arXiv:1507.03735

    Article  ADS  Google Scholar 

  39. K. Thakkar, A. Majethiya, P.C. Vinodkumar, Magnetic moments of baryons containing all heavy quarks in the quark-diquark model. Eur. Phys. J. Plus 131(9), 339 (2016). https://doi.org/10.1140/epjp/i2016-16339-4arXiv:1609.05444

    Article  Google Scholar 

  40. Z. Shah, A.K. Rai, Masses and Regge trajectories of triply heavy \(\Omega _{ccc}\) and \(\Omega _{bbb}\) baryons. Eur. Phys. J. A 53(10), 195 (2017). https://doi.org/10.1140/epja/i2017-12386-2

    Article  ADS  Google Scholar 

  41. Z. Shah, A.K. Rai, Ground and excited state masses of the \(\Omega _{bbc}\) Baryon. Few Body Syst. 59(5), 76 (2018). https://doi.org/10.1007/s00601-018-1398-3

    Article  ADS  Google Scholar 

  42. Z. Shah, A. Kumar Rai, Spectroscopy of the \(\Omega _{ccb}\) baryon in the hypercentral constituent quark model. Chin. Phys. C 42(5), 053101 (2018). https://doi.org/10.1088/1674-1137/42/5/053101arXiv:1803.02090

    Article  ADS  Google Scholar 

  43. M.-S. Liu, Q.-F. Lü, X.-H. Zhong, Triply charmed and bottom baryons in a constituent quark model. Phys. Rev. D 101(7), 074031 (2020). https://doi.org/10.1103/PhysRevD.101.074031arXiv:1912.11805

    Article  ADS  Google Scholar 

  44. G. Yang, J. Ping, P.G. Ortega, J. Segovia, Triply heavy baryons in the constituent quark model. Chin. Phys. C 44(2), 023102 (2020). https://doi.org/10.1088/1674-1137/44/2/023102arXiv:1904.10166

    Article  ADS  Google Scholar 

  45. M.C. Gordillo, F. De Soto, J. Segovia, Diffusion Monte Carlo calculations of fully-heavy multiquark bound states. Phys. Rev. D 102(11), 114007 (2020). https://doi.org/10.1103/PhysRevD.102.114007arXiv:2009.11889

    Article  ADS  Google Scholar 

  46. M. Radin, S. Babaghodrat, M. Monemzadeh, Estimation of heavy baryon masses \(\Omega \)ccc++ and \(\Omega \)bbb- by solving the Faddeev equation in a three-dimensional approach. Phys. Rev. D 90(4), 047701 (2014). https://doi.org/10.1103/PhysRevD.90.047701

    Article  ADS  Google Scholar 

  47. S.-X. Qin, C.D. Roberts, S.M. Schmidt, Spectrum of light- and heavy-baryons. Few Body Syst. 60(2), 26 (2019). https://doi.org/10.1007/s00601-019-1488-xarXiv:1902.00026

    Article  ADS  Google Scholar 

  48. P.-L. Yin, C. Chen, G.A. Krein, C.D. Roberts, J. Segovia, S.-S. Xu, Masses of ground-state mesons and baryons, including those with heavy quarks. Phys. Rev. D 100(3), 034008 (2019). https://doi.org/10.1103/PhysRevD.100.034008arXiv:1903.00160

    Article  ADS  Google Scholar 

  49. L.X. Gutiérrez-Guerrero, A. Bashir, M.A. Bedolla, E. Santopinto, Masses of light and heavy mesons and baryons: a unified picture. Phys. Rev. D 100(11), 114032 (2019). https://doi.org/10.1103/PhysRevD.100.114032arXiv:1911.09213

    Article  ADS  Google Scholar 

  50. K.-W. Wei, B. Chen, X.-H. Guo, Masses of doubly and triply charmed baryons. Phys. Rev. D 92(7), 076008 (2015). https://doi.org/10.1103/PhysRevD.92.076008arXiv:1503.05184

    Article  ADS  Google Scholar 

  51. K.-W. Wei, B. Chen, N. Liu, Q.-Q. Wang, X.-H. Guo, Spectroscopy of singly, doubly, and triply bottom baryons. Phys. Rev. D 95(11), 116005 (2017). https://doi.org/10.1103/PhysRevD.95.116005arXiv:1609.02512

    Article  ADS  Google Scholar 

  52. V.L. Chernyak, I.R. Zhitnitsky, B meson exclusive decays into baryons. Nucl. Phys. B 345, 137–172 (1990). https://doi.org/10.1016/0550-3213(90)90612-H

    Article  ADS  Google Scholar 

  53. V.M. Braun, I.E. Filyanov, QCD sum rules in exclusive kinematics and pion wave function. Z. Phys. C 44, 157 (1989). https://doi.org/10.1007/BF01548594

    Article  Google Scholar 

  54. I.I. Balitsky, V.M. Braun, A.V. Kolesnichenko, Radiative decay sigma+–\(>\) p gamma in quantum chromodynamics. Nucl. Phys. B 312, 509–550 (1989). https://doi.org/10.1016/0550-3213(89)90570-1

    Article  ADS  Google Scholar 

  55. M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, QCD and Resonance Physics. Theoretical Foundations. Nucl. Phys. B 147, 385–447 (1979). https://doi.org/10.1016/0550-3213(79)90022-1

    Article  ADS  Google Scholar 

  56. H.-X. Chen, W. Chen, X. Liu, S.-L. Zhu, The hidden-charm pentaquark and tetraquark states. Phys. Rept. 639, 1–121 (2016). https://doi.org/10.1016/j.physrep.2016.05.004arXiv:1601.02092

    Article  ADS  MathSciNet  Google Scholar 

  57. P. Colangelo, A. Khodjamirian, QCD sum rules, a modern perspective 1495–1576 (2000). https://doi.org/10.1142/9789812810458_0033. arXiv:0010175 [hep-ph]

  58. M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, D.B. Lichtenberg, Diquarks. Rev. Mod. Phys. 65, 1199–1234 (1993). https://doi.org/10.1103/RevModPhys.65.1199

    Article  ADS  Google Scholar 

  59. M.Y. Barabanov et al., Diquark correlations in hadron physics: Origin, impact and evidence. Prog. Part. Nucl. Phys. 116, 103835 (2021). https://doi.org/10.1016/j.ppnp.2020.103835arXiv:2008.07630

    Article  Google Scholar 

  60. J. Carlson, J.B. Kogut, V.R. Pandharipande, A quark model for baryons based on quantum chromodynamics. Phys. Rev. D 27, 233 (1983). https://doi.org/10.1103/PhysRevD.27.233

    Article  ADS  Google Scholar 

  61. N. Isgur, G. Karl, Hyperfine interactions in negative parity baryons. Phys. Lett. B 72, 109 (1977). https://doi.org/10.1016/0370-2693(77)90074-0

    Article  ADS  Google Scholar 

  62. W. Lucha, F.F. Schoberl, D. Gromes, Bound states of quarks. Phys. Rept. 200, 127–240 (1991). https://doi.org/10.1016/0370-1573(91)90001-3

    Article  ADS  Google Scholar 

  63. P. Lundhammar, T. Ohlsson, Nonrelativistic model of tetraquarks and predictions for their masses from fits to charmed and bottom meson data. Phys. Rev. D 102(5), 054018 (2020). https://doi.org/10.1103/PhysRevD.102.054018arXiv:2006.09393

    Article  ADS  Google Scholar 

  64. N. Barik, M. Das, Magnetic moments of confined quarks and baryons in an independent-quark model based on Dirac equation with power-law potential. Phys. Rev. D 28, 2823–2829 (1983). https://doi.org/10.1103/PhysRevD.28.2823

    Article  ADS  Google Scholar 

  65. S.N. Jena, D.P. Rath, Magnetic Moments of Light, Charmed and \(B\) Flavored Baryons in a Relativistic Logarithmic Potential. Phys. Rev. D 34, 196–200 (1986). https://doi.org/10.1103/PhysRevD.34.196

    Article  ADS  Google Scholar 

  66. B. Silvestre-Brac, Spectroscopy of baryons containing heavy quarks. Prog. Part. Nucl. Phys. 36, 263–273 (1996). https://doi.org/10.1016/0146-6410(96)00030-0

    Article  ADS  Google Scholar 

  67. A. Faessler, T. Gutsche, M.A. Ivanov, J.G. Korner, V.E. Lyubovitskij, D. Nicmorus, K. Pumsa-ard, Magnetic moments of heavy baryons in the relativistic three-quark model. Phys. Rev. D 73, 094013 (2006). https://doi.org/10.1103/PhysRevD.73.094013arXiv:0602193 [hep-ph]

    Article  ADS  Google Scholar 

  68. A. Bernotas, V. Simonis, Magnetic moments of heavy baryons in the bag model reexamined (2012). https://doi.org/10.3952/physics.v53i2.2668. arXiv:1209.2900

  69. R. Dhir, C.S. Kim, R.C. Verma, Magnetic moments of bottom baryons: Effective mass and screened charge. Phys. Rev. D 88, 094002 (2013). https://doi.org/10.1103/PhysRevD.88.094002arXiv:1309.4057

    Article  ADS  Google Scholar 

  70. V. Simonis, Improved predictions for magnetic moments and M1 decay widths of heavy hadrons (2018). arXiv:1803.01809

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Authors and Affiliations

  1. Department of Physics, Faculty of Arts and Sciences, Ondokuz Mayis University, 55200, Atakum, Samsun, Turkey

    Halil Mutuk

  2. Health Services Vocational School of Higher Education, Istanbul Aydin University, Sefakoy-Kucukcekmece, 34295, Istanbul, Turkey

    Ulaş Özdem

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  1. Halil Mutuk
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Correspondence to Ulaş Özdem.

Appendix: The explicit expressions of \(\Delta ^{QCD}\) function

Appendix: The explicit expressions of \(\Delta ^{QCD}\) function

In this appendix, we present the explicit expression for the function \(\Delta ^{QCD} \) obtained from the LCSR in subsection 2.1. It is acquired by selecting the \(\varepsilon \!\!\!/q\!\!\!/\) structure as follows

$$\begin{aligned} \Delta ^{QCD}&=\frac{3 (-1 + t)^2}{83886080 \pi ^6} \Bigg [3 e_ {Q^\prime } m_ {Q^\prime } \Big (I[5, 1, 3] - 3 I[5, 1, 4] +3 I[5, 1, 5] - I[5, 1, 6] \nonumber \\&\quad -3(I[5, 2, 3] - 2 I[5, 2, 4] + I[5, 2, 5] \nonumber \\&\quad - I[5, 3, 3] +I[5, 3, 4]) - I[5, 4, 3]\Big ) \nonumber \\&\quad +e_Q m_ {Q^\prime } \Big (I[5, 2, 2] - 2 I[5, 2, 3] + I[5, 2, 4] -3 I[5, 3, 2] \nonumber \\&\quad +4 I[5, 3, 3] - I[5, 3, 4]+ 3 I[5, 4, 2] -2 I[5, 4, 3] - I[5, 5, 2]\Big ) \nonumber \\&\quad -e_ {Q^\prime } m_Q \Big (-I[5, 2, 2] + 2 I[5, 2, 3] - I[5, 2, 4] +3 I[5, 3, 2] \nonumber \\&\quad -4 I[5, 3, 3] + I[5, 3, 4] - 3 I[5, 4, 2] +2 I[5, 4, 3] + I[5, 5, 2]\Big ) \nonumber \\&\quad -e_Q m_Q \Big (3072 I[5, 3, 1] + 11 I[5, 3, 2] - 28 I[5, 3, 3]\nonumber \\&\quad +20 I[5, 3, 4] + 3072 I[5, 4, 1] - 22 I[5, 4, 2] +28 I[5, 4, 3] \nonumber \\&\quad + 3072 I[5, 5, 1] + 11 I[5, 5, 2]+3072 I[5, 6, 1]\Big )\Bigg ]\nonumber \\&\quad +\frac{m_Q^2 m_ {Q^\prime }}{20971520 \pi ^6} \Bigg [- e_ {Q^\prime } (1 + t)^2\Big (I[4, 1, 2] - 2 I[4, 1, 3] +I[4, 1, 4] \nonumber \\&\quad - 2 I[4, 2, 2] + 2 I[4, 2, 3] + I[4, 3, 2]\Big ) \nonumber \\&\quad +e_Q \Big (256 (1 + t)^2 I[4, 2, 1] +(3 - 2 t + 3 t^2) I[4, 2, 2]\nonumber \\&\quad - 4 I[4, 2, 3] - 4 t^2 I[4, 2, 3] + 256 I[4, 3, 1] +512 t I[4, 3, 1] \nonumber \\&\quad + 256 t^2 I[4, 3, 1] - 3 I[4, 3, 2] +2 t I[4, 3, 2] -3t^2 I[4, 3, 2] +256 (1 + t)^2 I[4, 4, 1]\Big )\Bigg ]\nonumber \\&\quad +\frac{\langle g_s^2 G^2 \rangle }{113246208 \pi ^6} (-1 + t) \Bigg [14 (-1 + t) e_Q m_ {Q^\prime } \nonumber \\&\quad \Big (I[3, 1, 2] - 2 I[3, 1, 3] +I[3, 1, 4] - 2 I[3, 2, 2] + 2 I[3, 2, 3] + I[3, 3, 2]\Big ) \nonumber \\&\quad +3 (-1 + t) e_ {Q^\prime } m_ {Q^\prime } \Big (I[3, 1, 2] -2 I[3, 1, 3] + I[3, 1, 4] \nonumber \\&\quad -2 I[3, 2, 2] + 2 I[3, 2, 3] +I[3, 3, 2]\Big )\nonumber \\&\quad - (1 +t) e_ {Q^\prime } m_Q \Big (64 I[3, 2, 1] - I[3, 2, 2] +2 I[3, 2, 3] \nonumber \\&\quad + 64 I[3, 3, 1] + I[3, 3, 2] +64 I[3, 4, 1]\Big ) \nonumber \\&\quad - (1 +t) e_Q m_Q \Big (832 I[3, 2, 1] + 8 I[3, 2, 2] +5 I[3, 2, 3] \nonumber \\&\quad + 832 I[3, 3, 1] - 8 I[3, 3, 2] +832 I[3, 4, 1]\Big )\Bigg ]. \end{aligned}$$
(27)

The functions I[n, m, l] is defined as:

$$\begin{aligned} I[n,m,l]=\int ^{s_0}_{\alpha } ds \int _0^1 dv \int _0^1 dw \,\big (\alpha + s\big )^n v^m w^l \end{aligned}$$
(28)

where \(\alpha = (2m_Q+m_{Q^\prime })^2 \).

It should be noted that in the expressions given in Eq. (27), we have given only the terms that make significant contributions to the numerical values of the magnetic moments. Contributions not given here are taken into account in numerical calculations, but for simplicity they are not shown in the text.

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Mutuk, H., Özdem, U. Magnetic moments of spin–1/2 triply heavy baryons: a study of light-cone QCD and quark–diquark model. Eur. Phys. J. Plus 137, 508 (2022). https://doi.org/10.1140/epjp/s13360-022-02724-5

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