Skip to main content
SpringerLink
Log in

Rigorous bounds on quark masses within a nonrelativistic approach

  • Published:
Zeitschrift für Physik C Particles and Fields

Abstract

By applying the Feynman-Hellmann theorem to\(q\bar q\) systems we find the following bounds on quark mass differences from the spectrum ofall quarkonium states

$$\begin{gathered} 0.27 \leqq m_s - m_u \leqq 0.45GeV \hfill \\ 1.23 \leqq m_c - m_s \leqq 1.46GeV \hfill \\ 3.30 \leqq m_b - m_c \leqq 3.55GeV. \hfill \\ \end{gathered}$$

As best values we derive

$$\begin{gathered} m_u = m_d = 0.31GeV,m_s = 0.62GeV, \hfill \\ m_c = 1.91GeV,m_b = 5.27GeV. \hfill \\ \end{gathered}$$

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Grosse, A. Martin: Phys. Rep.60,341 (1980)

    Google Scholar 

  2. C. Quigg, J.L. Rosner: Phys. Rep.56, 167 (1979)

    Google Scholar 

  3. M. Krammer, H. Krasemann: Acta Phys. Austr. Suppl. xx (1979)

  4. V.A. Novikov et al.: Phys. Rep.41C, 1 (1978)

    Google Scholar 

  5. R. Barbieri, R. Kögerler, Z. Kunszt, R. Gatto: Nucl. Phys.B105, 125 (1976)

    Google Scholar 

  6. A. De Rújula, H. Georgi, S.L. Glashow: Phys. Rev.D12, 147 (1975)

    Google Scholar 

  7. H. Leutwyler, J. Stern: Phys. Lett.73B, 75 (1978); Nucl. Phys.157B, 327 (1979)

    Google Scholar 

  8. J. Gasser, H. Leutwyler: Nucl. Phys.94B, 269 (1975)

    Google Scholar 

  9. J. Gasser, H. Leutwyler, J. Jersak, J. Stern: On the spin and flavour dependence of the confining potential, University of Bern preprint, 1980

  10. P. Minkowski: Asymptotic freedom-infrared stability. University of Bern preprint, 1979

  11. R.A. Bertlmann, A. Martin: Nucl. Phys.B168, 111 (1980)

    Google Scholar 

  12. S. Ono: Phys. Rev.D20, 2975 (1979)

    Google Scholar 

  13. R.A. Bertlmann, S. Ono: Phys. Lett.96B, 123 (1980)

    Google Scholar 

  14. A. Martin: Phys. Lett.88B, 133 (1979)

    Google Scholar 

  15. A. Martin: Phys. Lett.93B, 338 (1980)

    Google Scholar 

  16. R.P. Feynman: Phys. Rev.56, 340 (1939)

    Google Scholar 

  17. H. Hellmann: Einführung in die Quantenchemie. Leipzig: Deuticke 1937

    Google Scholar 

  18. C. Quigg, J.L. Rosner: Phys. Lett.71B, 153 (1977)

    Google Scholar 

  19. G. Bhanot, S. Rudaz: Phys. Lett.78B, 119 (1978)

    Google Scholar 

  20. H. Krasemann, S. Ono: Nucl. Phys.B154, 283 (1979)

    Google Scholar 

  21. G. Fogleman, D.B. Lichtenberg, J.G. Wills: Lett. Nuovo Cimento,26, 369 (1979)

    Google Scholar 

  22. E. Eichten et al.: Phys. Rev. Lett.34, 369 (1975)

    Google Scholar 

  23. K. Berkelman: rapporteur talk, Madison conference, 1980

  24. E. Eichten et al.: Phys. Rev.D21, 203 (1980)

    Google Scholar 

  25. S. Ono: Phys. Rev.D23, 1118 (1981)

    Google Scholar 

  26. I. Cohen, H.J. Lipkin: Phys. Lett.93B, 56 (1980)

    Google Scholar 

  27. H. Faissner, B.R. Kim: Constituent mass and fermi motion from-distribution Aachen preprint (1980)

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, University, A-1090, Wien, Austria

    R. A. Bertlmann

  2. Institut für Theoretische Physik, RWTH, D-5100, Aachen, Germany

    Seiji Ono

Authors
  1. R. A. Bertlmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seiji Ono
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by “Fonds zur Förderung der wissenschaftlichen Forschung in Osterreich”, Project Nr. 3800

Supported by Bundesministerium für Forschung und Technologie, FRG

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bertlmann, R.A., Ono, S. Rigorous bounds on quark masses within a nonrelativistic approach. Z. Phys. C - Particles and Fields 10, 37–43 (1981). https://doi.org/10.1007/BF01545782

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01545782

Keywords

Search

Navigation