Nuclear Physics and Atomic Energy

ядерна ф≥зика та енергетика
Nuclear Physics and Atomic Energy

  ISSN: 1818-331X (Print), 2074-0565 (Online)
  Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine
  Languages: Ukrainian, English, Russian
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Nucl. Phys. At. Energy 2017, volume 18, issue 3, pages 222-229.
Section: Nuclear Physics.
Received: 01.06.2017; Accepted: 12.10.2017; Published online: 28.12.2017.
PDF Full text (ru)

Evaluation of the two lightest quark masses

V. A. Babenko*, N. M. Petrov

Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

*Corresponding author. E-mail address:;

Abstract: Simple relations between the masses of the two lightest up and down quarks were obtained on the basis of the simple physically based model compatible with the present-day theory of strong interactions, i.e. with quantum chromodynamics. Relations between the u and d quark masses, on one hand, and nucleon and pion masses, on the other hand, are also established. Thus, the obtained in such a way elementary formula mu/md = 1/(1+√2), relating u and d quark masses, appears to be in excellent agreement with a number of theoretical calculations of the ratio mu/md of the lightest quark masses. The u and d quark masses mu = 1.903 MeV, md = 4.594 MeV, calculated with the help of the obtained relations, are also in very good agreement with the modern evaluations and calculations of these quantities. The average of the u and d quark masses m̅ud = ΔMπ/√2 ≅ 3.248 MeV, obtained in the proposed approach, is in good agreement with previous calculations too.

Keywords: quantum chromodynamics, Standard Model of Particle Physics, quark, quark masses, hadron, nucleon, pion.


1. M. Gell-Mann. A Schematic Model of Baryons and Mesons. Phys. Lett. 8(3) (1964) 214.

2. G. Zweig. An SU3 Model for Strong Interaction Symmetry and its Breaking. CERN Report 8182/TH.401, 1964. 20 p.

3. J.J.J. Kokkedee. The Quark Model (New York: W.A. Benjamin, 1969) 239 p. Google Books

4. F.J. Yndurain. Quantum Chromodynamics: An Introduction to the Theory of Quarks and Gluons (New York-Berlin-Heidelberg-Tokyo: Springer-Verlag, 1983) 228 p.

5. L.B. Okun. Elementary Particle Physics (Moskva: Nauka, 1988) 272 p. (Rus) Google Books

6. V.V. Anisovich et al. Quark Model and High Energy Collisions (London-Singapore: World Scientific, 2004) 530 p. Google Books

7. C. Patrignani et al. (Particle Data Group). Review of Particle Physics. Chin. Phys. C 40(10) (2016) 100001.

8. D.J. Gross, S.B. Treiman, F. Wilczek. Light-Quark Masses and Isospin Violation. Phys. Rev. D 19(7) (1979) 2188.

9. S. Durr et al. Lattice QCD at the Physical Point: Light Quark Masses. Phys. Lett. B 701(2) (2011) 265.

10. V.G. Bornyakov et al. Color Confinement and Hadron Structure in Lattice Chromodynamics. Physics-Uspekhi 47(1) (2004) 17.

11. S. Durr et al. Ab Initio Determination of Light Hadron Masses. Science 322(5905) (2008) 1224.

12. C. Gattringer, C.B. Lang. Quantum Chromodynamics on the Lattice (Berlin-Heidelberg: Springer-Verlag, 2010) 343 p.

13. V.G. Bornyakov, M.I. Polikarpov. Computing Methods in Lattice Quantum Chromodynamics. Theoretical Physics 11 (2010) 64. (Rus)[7]%20Bornyakov.pdf

14. A. Bazavov et al. Nonperturbative QCD Simulations with 2 + 1 Flavors of Improved Staggered Quarks. Rev. Mod. Phys. 82(2) (2010) 1349.

15. E.M. Henley, L.K. Morrison. n-n and n-p Scattering Lengths and Charge Independence. Phys. Rev. 141(4) (1966) 1489.

16. T.E.O. Ericson, G.A. Miller. Charge Dependence of Nuclear Forces. Phys. Lett. B 132(1-3) (1983) 32.

17. R. Machleidt, M.K. Banerjee. Charge Dependence of the πNN Coupling Constant and Charge Dependence of the Nucleon-Nucleon Interaction. Few-Body Syst. 28(3) (2000) 139.

18. V.A. Babenko, N.M. Petrov. Isospin Breaking in the Pion-Nucleon Coupling Constant and the Nucleon-Nucleon Scattering Length. Yaderna Fizyka ta Energetyka (Nucl. Phys. At. Energy) 17(2) (2016) 143. (Rus)

19. V.A. Babenko, N.M. Petrov. Relation between the Charged and Neutral Pion-Nucleon Coupling Constants in the Yukawa Model. Physics of Particles and Nuclei Letters. 14(1) (2017) 58.

20. V.A. Babenko, N.M. Petrov. On the Impact of Mass Difference between the Pions (π±0) and the Nucleons (n-p) on the Charge Independence Breaking of Nuclear Forces. Yaderna Fizyka ta Energetyka (Nucl. Phys. At. Energy) 18(1) (2017) 13. (Rus)

21. B.L. Ioffe. QCD (Quantum Chromodynamics) at Low Energies. Prog. Part. Nucl. Phys. 56(1) (2006) 232.

22. D.R. Nelson, G.T. Fleming, G.W. Kilcup. Up Quark Mass in Lattice QCD with Three Light Dynamical Quarks and Implications for Strong CP Invariance. Phys. Rev. Lett. 90(2) (2003) 021601.

23. N.F. Nasrallah. Glue Content and Mixing Angle of the η-η' System: the Effect of the Isoscalar 0- Continuum. Phys. Rev. D 70(11) (2004) 116001.

24. C. Aubin et al. Light Pseudoscalar Decay Constants, Quark Masses, and Low Energy Constants from Three-Flavor Lattice QCD. Phys. Rev. D 70(11) (2004) 114501.

25. D.-N. Gao, B.A. Li, M.-L. Yan. Electromagnetic Mass Splittings of π, a1, K, K1(1400), and K(892). Phys. Rev. D 56(7) (1997) 4115.

26. J. Bijnens, J. Prades, E. de Rafael. Light Quark Masses in QCD. Phys. Lett. B 348(1-2) (1995) 226.

27. S. Basak et al. Electromagnetic Effects on the Light Hadron Spectrum. J. Phys.: Conf. Ser. 640 (2015) 012052.

28. J. Amoros, J. Bijnens, P. Talavera. QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios. Nucl. Phys. B 602(1-2) (2001) 87.

29. N. Carrasko et al. Up, Down, Strange and Charm Quark Masses with Nf = 2 + 1 + 1 Twisted Mass Lattice QCD. Nucl. Phys. B 887 (2014) 19.

30. T. Blum et al. Electromagnetic Mass Splittings of the Low Lying Hadrons and Quark Masses from 2 + 1 Flavor Lattice QCD + QED. Phys. Rev. D 82(9) (2010) 094508.

31. J. Gasser, H. Leutwyler. Quark Masses. Phys. Rep. 87(3) (1982) 77.

32. A. Duncan, E. Eichten, H. Thacker. Electromagnetic Splittings and Light Quark Masses in Lattice QCD. Phys. Rev. Lett. 76(21) (1996) 3894.

33. H. Leutwyler. The Ratios of the Light Quark Masses. Phys. Lett. B 378(1-4) (1996) 313.

34. T. Blum et al. Determination of Light Quark Masses from the Electromagnetic Splitting of Pseudoscalar Meson Masses Computed with Two Flavors of Domain Wall Fermions. Phys. Rev. D 76(11) (2007) 114508.

35. C.A. Dominguez. Determination of Light Quark Masses in QCD. Int. J. Mod. Phys. A 25(29) (2010) 5223.

36. S. Aoki et al. 1 + 1 + 1 Flavor QCD + QED Simulation at the Physical Points. Phys. Rev. D 86(3) (2012) 034507.

37. M.A. Shifman, A.I. Vainshtein, V.I. Zakharov. QCD and Resonance Physics: the ρ-ω Mixing. Nucl. Phys. B 147(5) (1979) 519.

38. S. Durr et al. Lattice QCD at the Physical Point: Simulation and Analysis Details. J. High Energy Phys. 08 (2011) 148.

39. G.V. Efimov et al. About Isotopic Invariance Violation. Preprint JINR –2-83-420 (Dubna, 1983) 16 p. (Rus)