Skip to main content
SpringerLink
Log in

High energy behaviour of total cross sections in weak interactions

  • Published:
Zeitschrift für Physik C Particles and Fields

Abstract

We propose a new method for the computation of the high energy limit of the total cross section in spontaneously broken gauge theories. It is based on an evolution equation for effective couplings in dependence on the gauge boson mass. We apply this method to weak interactions in the leading logarithm approximation. Perturbation theory becomes invalid at very high energies since one of the couplings becomes strong. The obtained total cross sections obey Froissart's bound, in contrast to previous results not using the evolution equation.

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. A. Ringwald, C. Wetterich: Nucl. Phys. B 353 (1991) 303

    Google Scholar 

  2. A.A. Migdal, A.M. Polyakov, K.A. Ter-Martirosyan: Phys. Lett. 48B (1974) 229;

    Google Scholar 

  3. Henry P.I. Abarbanel et al.: Phys. Rep. 21 C (1975) 119;

    Google Scholar 

  4. W. Bardeen et al.: Phys. Rev. D 21 (1980) 1037;

    Google Scholar 

  5. L.N. Lipatov: Sov. Phys. JETP 63 (1986) 904;

    Google Scholar 

  6. L.N. Lipatov; Nucl. Phys. B 365 (1991) 614; Nucl. Phys. B (Proc. Suppl.) 29 A (1992) 89; V.S. Fadin, L.N. Lipatov: Nucl. Phys. B (Proc. Suppl.) 29 A (1992) 97; R. Kirschner, L.N. Lipatov and L. Szymanowski: Effective action for high energy scattering in QCD. (in preparation);

    Google Scholar 

  7. H. Verlinde and E. Verlinde: QCD at high energy and two-dimensional field theory, preprint PUPT-1319, 1993

  8. For a recent review see by L.N. Lipatov: Pomeron in quantum chromodynamics. In: Perturbative Quantum Chromodynamics. A.H. Mueller (Ed.) Singapore: World Scientific 1989 and references contained therein. L.N. Lipatov: Preprint LNPI-157 (1975), Yad. Fiz. 23 (1976) 642; E.A. Kuraev, L.N. Lipatov, V.S. Fadin: Phys. Lett. 60 B (1975) 50; Zh. Eksp. Teor. Fiz. 71 (1976) 840 (Sov. Phys. JETP 44 (1976) 443); 72 (1977) 337 (Sov. Phys. JETP 45 (1977) 199); B.M. McCoy, T.T. Wu: Phys. Rev. Lett. 35 (1975) 604; H. Cheng, C.Y. Lo: Phys. Rev. D15 (1977) 2959; J. Bartels: Phys. Lett. 68 B (1977) 258. L. Łukaszuk, L. Szymanowski: Nucl. Phys. B 159 (1979) 316. L. Szymanowski: Nucl. Phys. B 173 (1980) 93.

    Google Scholar 

  9. Ya.Ya. Balitski, L.N. Lipatov: Yad. Fiz. 28 (1978) 1597; Sov. J. Nucl. Phys., 288 (1978) 822

    Google Scholar 

  10. P.A. Rączka, M. Pindor; Nuovo Cimento 103A (1990) 349

    Google Scholar 

  11. J.M. Cornwall, D. Lewin G.: Phys. Rev. Lett. 30 (1973) 1268, Phys. Rev. D 10 (1974) 1145; J.M. Cornwall: Phys. Lett. B 243 (1990) 271

    Google Scholar 

  12. C. Wetterich: Nucl. Phys. B (Proc. Suppl.) 22A (1991) 43

    Google Scholar 

  13. A. Ringwald: Nucl. Phys. B 330 (1990) 1; O. Espinosa: Nucl. Phys. B 343 (1990) 310

    Google Scholar 

  14. K.G. Wilson, I.G. Kogut: Phys. Rep. 12 (1974) 75; L.P. Kadanoff: Physica 2 (1966) 263

    Google Scholar 

  15. A. Dhar, V. Gupta: Phys. Rev. D 29, 2822 (1984)

    Google Scholar 

  16. G. Grundberg: Phys. Rev. D 29 2315 (1984)

    Google Scholar 

  17. J. Mc Mahon: Bull. Am. Math. Soc. 111 (1894) 170. The coefficientsK 1,...,K 13 were tabulated by C.E. Van Orstrand: Phil. Mag. 19 (1910) 366

    Google Scholar 

  18. See e.g. H. Cheng and T.T. Wu: Expanding Protons; Scattering at High Energies. Cambridge: MIT Press 1987 and references contained therein.

    Google Scholar 

  19. R. Rączka: Nuovo Cim. 98 (1987) 297

    Google Scholar 

  20. J. Kraśkiewicz: private communication

  21. Gilewicz (ed.): Rational Approximation and its Application in Mathematics and Physics. Berlin 1987 G.A. Baker, P. Graves-Morris: Padé approximants. Encyclopedy of Mathematics and Its Applications Vol. 13 and 14, Reading, Mass. Addison-Wesley 1981

    Google Scholar 

  22. J. Kraśkiewicz, M. Pindor: Acta Phys. Pol. B23 (1992) 759

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Faculty of Physics, Warsaw University, Poland

    M. Pindor

  2. Soltan Institute for Nuclear Studies, Nuclear Theory Department, Hoza 69, PL-00681 Warsaw, Warsaw, Poland

    R. Rączka

  3. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120, Heidelberg, Germany

    C. Wetterich

Authors
  1. M. Pindor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Rączka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Wetterich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by grants BST 192 and GR-11 from the Committee of Scientific Research and G-MEN 148/90

Supported in part by the Grant No 1044/P3/P2 from the Committee of Scientific Research

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pindor, M., Rączka, R. & Wetterich, C. High energy behaviour of total cross sections in weak interactions. Z. Phys. C - Particles and Fields 61, 125–137 (1994). https://doi.org/10.1007/BF01641895

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01641895

Keywords

Search

Navigation