General mass formula in broken supersymmetry

S. Ferrara; L. Girardello; F. Palumbo

doi:10.1103/PhysRevD.20.403

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General mass formula in broken supersymmetry

S. Ferrara

L. Girardello^*

F. Palumbo

Laboratori Nazionali di Frascati, Istituto Nazionale di Física Nucleare, Frascati, Italy

Gordon McKay Laboratory, Harvard University, Cambridge, Massachusetts 02138

Laboratori Nazionali di Frascati, Istituto Nazionale di Física Nucleare, Frascati, Italy

^*On leave from Istituto di Fisica, Università degli Studi, Milano, and INFN, Sezione di Milano, Italy.

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Phys. Rev. D 20, 403 – Published 15 July, 1979

DOI: https://doi.org/10.1103/PhysRevD.20.403

Abstract

The mass formula $Σ J^{} {(- 1)}^{2 J} (2 J + 1) {m_{J}}^{2} = 0$ is derived for a very general class of interactions with spontaneously broken supersymmetry. It shows the vanishing of the graded trace of the square of the mass operator, with $m_{J}$ the mass associated with a (real) field of spin $J$ . This mass relation is shown to be true even in the presence of explicit breaking, provided it fulfills suitable requirements.

References (20)

B. Zumino, in Proceedings of the XVII International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974) J. Wess, in Trends in Particle Theory, Vol. 37, Lecture Notes in Physics, edited by J. Ehlers, K. Hepp, R. Kippenhahn, H. A. Werdenmüller, and J. Zittartz (Springer, Berlin, 1974) L. Corwin, Y. Ne'eman, and S. Sternberg, Rev. Mod. Phys. 47, 573 (1975) L. O'Raifeartaigh, Commun. Dublin Inst. Adv. Studies Ser. A 22, (1975) P. Fayet and S. Ferrara, Phys. Rep. 32C, 249 (1977) A. Salam and J. Strathdee, Fortsch. Phys. 26, 57 (1978)
A. SalamJ. StrathdeeSanibel Symposium on Fundamental Problems of Quantum Field Theory, Flagler Beach, Fl., 1979 Report No. LNF-79/14 (P), Laboratori Nazionali Frascati, 1979 (unpublished)
P. Fayet and S. Ferrara, Phys. Rep. 32C, 249 (1977) P. Fayet, in Proceedings of CNRS National Colloquium, Montpellier, 1977, and in New Frontiers of High Energy Physics, proceedings of Orbis Scientiae, Univ. of Miami, Coral Gables, Florida, 1978, edited by A. Perlmutter, B. Kursunoglu, and L. F. Scott (Plenum, New York, to be published) E. S. Egorian and A. A. Slavnov, Ann. Phys. (N.Y.) 116, 358 (1978)
D. V. Volkov and V. A. Soroka, Zh. Eksp. Teor. Fiz. Pis'ma Red. 18, 529 (1973) [JETP Lett. 18, 312 (1973)] B. Zumino, in Deeper Pathways in High Energy Physics, Proceedings of Orbis Scientiae, Univ. of Miami, Coral Gables, Florida, 1977, edited by A. Perlmutter and L. F. Scott (Plenum, New York, 1977) in Fundamentals of Quark Models, proceedings of the Seventeenth Scottish Universities Summer School in Physics, St. Andrews, 1976, edited by I. M. Barbour and A. T. Davies (SUSSP Publications, Edinburgh Univ., Edinburgh, 1977)
S. Deser and B. Zumino, Phys. Rev. Lett. 38, 1433 (1977)
E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Ferrara, and L. Girardello, Phys. Lett. 79B, 231 (1978) Nucl. Phys. B147, 105 (1979)
S. Ferrara and P. van Nieuwenhuizen, Phys. Lett. 74B, 333 (1978) K. S. Stelle and P. C. West, 74B, 330 (1978)
J. Scherk and J. H. Schwarz, Phys. Lett. 82B, 60 (1979) Report No. LPTENS 79/2, 1979 (unpublished)
L. O'Raifeartaigh, Nucl. Phys. B96, 331 (1975) P. Fayet, Phys. Lett. 58B, 67 (1975)
J. Wess and B. Zumino, Phys. Lett. 49B, 52 (1974)
J. Iliopoulos and B. Zumino, Nucl. Phys. B76, 310 (1974)
B. Zumino, Nucl. Phys. B89, 535 (1975)
A. Salam and J. Strathdee, Phys. Lett. 49B, 465 (1974)
J. Wess and B. Zumino, Nucl. Phys. B78, 1 (1974)
P. Fayet and J. Iliopoulos, Phys. Lett. 51B, 461 (1974)
S. Ferrara and B. Zumino, Nucl. Phys. B79, 413 (1974) A. Salam and J. Strathdee, Phys. Lett. 51B, 353 (1974)
Omitted endnote
P. Fayet, Nuovo Cimento 31A, 626 (1976)
Omitted endnote
E. Cremmer, J. Scherk, and J. H. Schwarz, Report No. LPTENS 79/11, 1979 (unpublished)

[c1] B. Zumino, in Proceedings of the XVII International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974) J. Wess, in Trends in Particle Theory, Vol. 37, Lecture Notes in Physics, edited by J. Ehlers, K. Hepp, R. Kippenhahn, H. A. Werdenmüller, and J. Zittartz (Springer, Berlin, 1974) L. Corwin, Y. Ne'eman, and S. Sternberg, Rev. Mod. Phys. 47, 573 (1975) L. O'Raifeartaigh, Commun. Dublin Inst. Adv. Studies Ser. A 22, (1975) P. Fayet and S. Ferrara, Phys. Rep. 32C, 249 (1977) A. Salam and J. Strathdee, Fortsch. Phys. 26, 57 (1978)

[c2] A. SalamJ. StrathdeeSanibel Symposium on Fundamental Problems of Quantum Field Theory, Flagler Beach, Fl., 1979 Report No. LNF-79/14 (P), Laboratori Nazionali Frascati, 1979 (unpublished)

[c3] P. Fayet and S. Ferrara, Phys. Rep. 32C, 249 (1977) P. Fayet, in Proceedings of CNRS National Colloquium, Montpellier, 1977, and in New Frontiers of High Energy Physics, proceedings of Orbis Scientiae, Univ. of Miami, Coral Gables, Florida, 1978, edited by A. Perlmutter, B. Kursunoglu, and L. F. Scott (Plenum, New York, to be published) E. S. Egorian and A. A. Slavnov, Ann. Phys. (N.Y.) 116, 358 (1978)

[c4] D. V. Volkov and V. A. Soroka, Zh. Eksp. Teor. Fiz. Pis'ma Red. 18, 529 (1973) [JETP Lett. 18, 312 (1973)] B. Zumino, in Deeper Pathways in High Energy Physics, Proceedings of Orbis Scientiae, Univ. of Miami, Coral Gables, Florida, 1977, edited by A. Perlmutter and L. F. Scott (Plenum, New York, 1977) in Fundamentals of Quark Models, proceedings of the Seventeenth Scottish Universities Summer School in Physics, St. Andrews, 1976, edited by I. M. Barbour and A. T. Davies (SUSSP Publications, Edinburgh Univ., Edinburgh, 1977)

[c5] S. Deser and B. Zumino, Phys. Rev. Lett. 38, 1433 (1977)

[c6] E. Cremmer, B. Julia, J. Scherk, P. van Nieuwenhuizen, S. Ferrara, and L. Girardello, Phys. Lett. 79B, 231 (1978) Nucl. Phys. B147, 105 (1979)

[c7] S. Ferrara and P. van Nieuwenhuizen, Phys. Lett. 74B, 333 (1978) K. S. Stelle and P. C. West, 74B, 330 (1978)

[c8] J. Scherk and J. H. Schwarz, Phys. Lett. 82B, 60 (1979) Report No. LPTENS 79/2, 1979 (unpublished)

[c9] L. O'Raifeartaigh, Nucl. Phys. B96, 331 (1975) P. Fayet, Phys. Lett. 58B, 67 (1975)

[c10] J. Wess and B. Zumino, Phys. Lett. 49B, 52 (1974)

[c11] J. Iliopoulos and B. Zumino, Nucl. Phys. B76, 310 (1974)

[c12] B. Zumino, Nucl. Phys. B89, 535 (1975)

[c13] A. Salam and J. Strathdee, Phys. Lett. 49B, 465 (1974)

[c14] J. Wess and B. Zumino, Nucl. Phys. B78, 1 (1974)

[c15] P. Fayet and J. Iliopoulos, Phys. Lett. 51B, 461 (1974)

[c16] S. Ferrara and B. Zumino, Nucl. Phys. B79, 413 (1974) A. Salam and J. Strathdee, Phys. Lett. 51B, 353 (1974)

[c17] Omitted endnote

[c18] P. Fayet, Nuovo Cimento 31A, 626 (1976)

[c19] Omitted endnote

[c20] E. Cremmer, J. Scherk, and J. H. Schwarz, Report No. LPTENS 79/11, 1979 (unpublished)

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General mass formula in broken supersymmetry

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