Radiative corrections in grand unified theories based on <i>N=1</i> supergravity. II. Gauge theories

Ashoke Sen

doi:10.1103/PhysRevD.32.411

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Radiative corrections in grand unified theories based on N=1 supergravity. II. Gauge theories

Ashoke Sen

Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510

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Phys. Rev. D 32, 411 – Published 15 July, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.411

Abstract

The effect of radiative corrections in supersymmetric grand unified theories with soft- supersymmetry-breaking terms induced by N=1 supergravity is analyzed. It is shown that any mass hierarchy present in the limit of unbroken supersymmetry is stable under radiative corrections induced by soft-supersymmetry-breaking terms, provided the theory does not contain a light singlet field that transforms as a singlet under the unbroken subgroup of the theory below the grand-unification scale.

References (17)

A. Sen, Phys. Rev. D 30, 2608 (1984).
For a complete list of references see H. P. Nilles, Phys. Rep. 110, 1 (1984).
E. Witten, Nucl. Phys. B 188, 513 (1981); S. Dimopoulos and H. Georgi, ibid. B 193, 150 (1981); N. Sakai, Z. Phys. C 11, 153 (1981); R. K. Kaul, Phys. Lett. 109 B, 19 (1982).
E. Gildener and S. Weinberg, Phys. Rev. D 13, 3333 (1976); E. Gildener, ibid. 14, 1667 (1976).
R. Arnowitt, A. H. Chamseddine and P. Nath, Phys. Lett. 120 B, 145 (1983); S. Ferrara, D. V. Nanopoulos and C. A. Savoy, ibid. 123 B, 214 (1983); R. Barbieri and S. Cecotti, Z. Phys. C 17, 183 (1983); J. Lykken and F. Quevedo, Phys. Rev. D 29, 293 (1984); P. Moxhay and Y. Yamamoto, University of North Carolina Report No. IFP-215-UNC (unpublished); B. Gato, L. Leon, J. Perez-Mercader and M. Quiros, Nucl. Phys. B 253, 285 (1985); I. Affleck and M. Dine, Institute for Advanced Studies report (unpublished).
J. Polchinski and L. Susskind, Phys. Rev. D 26, 3661 (1982); H. P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. 124 B, 337 (1982); A. B. Lahanas, ibid. 124 B, 341 (1982); M. Dine, in Lattice Gauge Theories, Supersymmetry and Grand Unification, proceedings of the Sixth Johns Hopkins Workshop on Current Problems in Particle Theory, Florence, 1982 (Physics Department, Johns Hopkins University, Baltimore, 1982).
L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983). See also R. Arnowitt, A. H. Chamseddine and P. Nath, Nucl. Phys. B 227, 121 (1983).
M. T. Grisaru, M. Rocek and W. Siegel, Nucl. Phys. B 159, 429 (1979).
L. Girardello and M. T. Grisaru, Nucl. Phys. B 194, 65 (1982).
B. Zumino, Nucl. Phys. B 89, 535 (1975); P. West, ibid. B 106, 219 (1976); D. M. Capper and M. Ramon-Medrano, J. Phys. G 2, 269 (1976); W. Lang, Nucl. Phys. B 114, 123 (1976); S. Weinberg, Phys. Lett. 62 B, 111 (1976); E. Witten, Nucl. Phys. B 188, 513 (1981); S. Ferrara and O. Piguet, ibid. B 93, 261 (1975); M. T. Grisaru, M. Rocek, and W. Siegel, Ref. 8; B. Ovrut and J. Wess, Phys. Rev. D 25, 409 (1982).
S. Gates, M. T. Grisaru, M. Rocek, and W. Siegel, Superspace (Benjamin, New York, 1983).
A. Sen, Phys. Rev. D 31, 2100 (1985).
This is true in a general renormalizable field theory, so long as the cubic coupling between the low-mass scalar fields is of the order of the masses of these fields. Such power-law infrared divergences, however, do exist in individual graphs in supersymmetric gauge theories in a general gauge that preserves supersymmetry. In a supersymmetric Feynman-type gauge the one-loop diagrams are free from such divergences, but graphs involving two or more loops are not. Recently, a new class of nonlocal gauges have been proposed which may be free from such divergences to all orders in perturbation theory (Ref. 16). In any case, we shall assume in our analysis that such singularities are gauge artifacts, and cancel in the sum over all graphs.
M. T. Grisaru and D. Zanon, Nucl. Phys. B 252, 578 (1985).
Contribution to $P_{rho}$ from one-loop graphs involving only background gauge fields as external lines was shown to be harmless in Ref. 12. All the supersymmetry-breaking terms in the Lagrangian, on the other hand, may be treated as ``interaction'' terms in the convention of Ref. 11, and the contribution from any graph, with one or more supersymmetry-breaking vertices may be shown to depend on $V_{ρ}^{(b)}$ only through $\tilde{φ}$ ${}^{(b)}$ , Γ ${}_{α α dot}$ ${}^{(b)}$ , $W_{α}^{(b)}$ , or their complex conjugate fields. As a result, the net contribution to $P_{ρ}$ + $m_{g}$ P ${hat}_{rho}$ from one-loop graphs may also be shown to be at most of order $m_{g}^{2}$ for $z_{α}$ app $m_{g}$ .
L. F. Abbott, M. T. Grisaru and D. Zanon, Nucl. Phys. B 244, 454 (1984).
A. Sen, Phys. Lett. 148 B, 65 (1984); Phys. Rev. D 31, 900 (1985).

[c1] A. Sen, Phys. Rev. D 30, 2608 (1984).

[c2] For a complete list of references see H. P. Nilles, Phys. Rep. 110, 1 (1984).

[c3] E. Witten, Nucl. Phys. B 188, 513 (1981); S. Dimopoulos and H. Georgi, ibid. B 193, 150 (1981); N. Sakai, Z. Phys. C 11, 153 (1981); R. K. Kaul, Phys. Lett. 109 B, 19 (1982).

[c4] E. Gildener and S. Weinberg, Phys. Rev. D 13, 3333 (1976); E. Gildener, ibid. 14, 1667 (1976).

[c5] R. Arnowitt, A. H. Chamseddine and P. Nath, Phys. Lett. 120 B, 145 (1983); S. Ferrara, D. V. Nanopoulos and C. A. Savoy, ibid. 123 B, 214 (1983); R. Barbieri and S. Cecotti, Z. Phys. C 17, 183 (1983); J. Lykken and F. Quevedo, Phys. Rev. D 29, 293 (1984); P. Moxhay and Y. Yamamoto, University of North Carolina Report No. IFP-215-UNC (unpublished); B. Gato, L. Leon, J. Perez-Mercader and M. Quiros, Nucl. Phys. B 253, 285 (1985); I. Affleck and M. Dine, Institute for Advanced Studies report (unpublished).

[c6] J. Polchinski and L. Susskind, Phys. Rev. D 26, 3661 (1982); H. P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. 124 B, 337 (1982); A. B. Lahanas, ibid. 124 B, 341 (1982); M. Dine, in Lattice Gauge Theories, Supersymmetry and Grand Unification, proceedings of the Sixth Johns Hopkins Workshop on Current Problems in Particle Theory, Florence, 1982 (Physics Department, Johns Hopkins University, Baltimore, 1982).

[c7] L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983). See also R. Arnowitt, A. H. Chamseddine and P. Nath, Nucl. Phys. B 227, 121 (1983).

[c8] M. T. Grisaru, M. Rocek and W. Siegel, Nucl. Phys. B 159, 429 (1979).

[c9] L. Girardello and M. T. Grisaru, Nucl. Phys. B 194, 65 (1982).

[c10] B. Zumino, Nucl. Phys. B 89, 535 (1975); P. West, ibid. B 106, 219 (1976); D. M. Capper and M. Ramon-Medrano, J. Phys. G 2, 269 (1976); W. Lang, Nucl. Phys. B 114, 123 (1976); S. Weinberg, Phys. Lett. 62 B, 111 (1976); E. Witten, Nucl. Phys. B 188, 513 (1981); S. Ferrara and O. Piguet, ibid. B 93, 261 (1975); M. T. Grisaru, M. Rocek, and W. Siegel, Ref. 8; B. Ovrut and J. Wess, Phys. Rev. D 25, 409 (1982).

[c11] S. Gates, M. T. Grisaru, M. Rocek, and W. Siegel, Superspace (Benjamin, New York, 1983).

[c12] A. Sen, Phys. Rev. D 31, 2100 (1985).

[c13] This is true in a general renormalizable field theory, so long as the cubic coupling between the low-mass scalar fields is of the order of the masses of these fields. Such power-law infrared divergences, however, do exist in individual graphs in supersymmetric gauge theories in a general gauge that preserves supersymmetry. In a supersymmetric Feynman-type gauge the one-loop diagrams are free from such divergences, but graphs involving two or more loops are not. Recently, a new class of nonlocal gauges have been proposed which may be free from such divergences to all orders in perturbation theory (Ref. 16). In any case, we shall assume in our analysis that such singularities are gauge artifacts, and cancel in the sum over all graphs.

[c14] M. T. Grisaru and D. Zanon, Nucl. Phys. B 252, 578 (1985).

[c15] Contribution to $P_{rho}$ from one-loop graphs involving only background gauge fields as external lines was shown to be harmless in Ref. 12. All the supersymmetry-breaking terms in the Lagrangian, on the other hand, may be treated as ``interaction'' terms in the convention of Ref. 11, and the contribution from any graph, with one or more supersymmetry-breaking vertices may be shown to depend on $V_{ρ}^{(b)}$ only through $\tilde{φ}$ ${}^{(b)}$ , Γ ${}_{α α dot}$ ${}^{(b)}$ , $W_{α}^{(b)}$ , or their complex conjugate fields. As a result, the net contribution to $P_{ρ}$ + $m_{g}$ P ${hat}_{rho}$ from one-loop graphs may also be shown to be at most of order $m_{g}^{2}$ for $z_{α}$ app $m_{g}$ .

[c16] L. F. Abbott, M. T. Grisaru and D. Zanon, Nucl. Phys. B 244, 454 (1984).

[c17] A. Sen, Phys. Lett. 148 B, 65 (1984); Phys. Rev. D 31, 900 (1985).

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Radiative corrections in grand unified theories based on N=1 supergravity. II. Gauge theories

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