78
G. Altarelli and S. Forte
[68]. In the limit of exact boson-fermion symmetry the quadratic divergences
of bosons cancel so that only log divergences remain. However, exact SUSY is
clearly unrealistic. For approximate SUSY (with soft breaking terms), which is the
basis for all practical models, is replaced by the splitting of SUSY multiplets,
2 ∼ m 2
SU SY − m 2
ord . In particular, the top loop is quenched by partial cancellation
with s-top exchange, so the s-top cannot be too heavy. (2) Technicolor [69]. The
Higgs system is a condensate of new fermions. There is no fundamental scalar
Higgs sector, hence no quadratic divergences associated to the μ 2 mass in the scalar
potential. This mechanism needs a very strong binding force, T C ∼ 10 3 QCD .
It is difficult to arrange that such nearby strong force is not showing up in precision
tests. Hence this class of models has been disfavoured by LEP, although some
special class of models have been devised aposteriori, like walking TC, top-color
assisted TC etc (for recent reviews, see, for example, [69]). (3) Extra dimensions (for
a recent review, see, for example, [70]). The idea is that M P l appears very large, or
equivalently that gravity appears very weak, because we are fooled by hidden extra
dimensions so that either the real gravity scale is reduced down to a lower scale,
even possibly down to o(1 T eV ) or the intensity of gravity is red shifted away by
an exponential warping factor [71]. This possibility is very exciting in itself and it
is really remarkable that it is compatible with experiment. It provides a very rich
framework with many different scenarios. (4) “Little Higgs” models [72]. In these
models the Higgs is a pseudo-Goldstone boson and extra symmetries allow m h = 0
only at two-loop level, so that can be as large as o(10 TeV) with the Higgs within
present bounds (the top loop is quenched by exchange of heavy vectorlike new
quarks with charge 2/3). The physics beyond the SM will be discussed in Chap. 8.
Acknowledgments I am very grateful to Giuseppe Degrassi, Paolo Gambino, Martin Grunewald,
Vittorio Lubicz for their help and advise.
References
1. S.L. Glashow, Nucl. Phys. 22 (1961) 579; S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264; A.
Salam, in Elementary Particle Theory, ed. N. Svartholm (Almquist and Wiksells, Stockholm,
1969), p. 367.
2. F. Englert, R. Brout, Phys.Rev.Lett.13, 321 (1964); P.W. Higgs, Phys.Lett. 12,132 (1964).
3. E.D.Commins, Weak interactions, Mc Graw Hill, 1973; L. V. Okun, Leptons and Quarks,
North Holland, 1982; D. Bailin, Weak Interactions, 2nd e., Hilger, 1982; H. M. Georgi, Weak
interactions and modern particle theory, Benjamin, 1984.
4. J.D. Bjorken and S. Drell, Relativistic Quantum Mechanics/Fields, Vols. I, II, McGraw-Hill,
New York, (1965).
5. Particle Data Group, The Journal of Physics G 33(2006)1.
6. G.Altarelli, T.Sjöstrand and F.Zwirner (eds.), “Physics at LEP2”, CERN Report 95-03.
7. The ALEPH, DELPHI, L3, OPAL, SLD Collaborations and the LEP Electroweak Working
Group, A Combination of Preliminary Electroweak Measurements and Constraints on the
Standard Model, hep-ex/0312023, and references therein.
8. The LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/.
G. Altarelli and S. Forte
[68]. In the limit of exact boson-fermion symmetry the quadratic divergences
of bosons cancel so that only log divergences remain. However, exact SUSY is
clearly unrealistic. For approximate SUSY (with soft breaking terms), which is the
basis for all practical models, is replaced by the splitting of SUSY multiplets,
2 ∼ m 2
SU SY − m 2
ord . In particular, the top loop is quenched by partial cancellation
with s-top exchange, so the s-top cannot be too heavy. (2) Technicolor [69]. The
Higgs system is a condensate of new fermions. There is no fundamental scalar
Higgs sector, hence no quadratic divergences associated to the μ 2 mass in the scalar
potential. This mechanism needs a very strong binding force, T C ∼ 10 3 QCD .
It is difficult to arrange that such nearby strong force is not showing up in precision
tests. Hence this class of models has been disfavoured by LEP, although some
special class of models have been devised aposteriori, like walking TC, top-color
assisted TC etc (for recent reviews, see, for example, [69]). (3) Extra dimensions (for
a recent review, see, for example, [70]). The idea is that M P l appears very large, or
equivalently that gravity appears very weak, because we are fooled by hidden extra
dimensions so that either the real gravity scale is reduced down to a lower scale,
even possibly down to o(1 T eV ) or the intensity of gravity is red shifted away by
an exponential warping factor [71]. This possibility is very exciting in itself and it
is really remarkable that it is compatible with experiment. It provides a very rich
framework with many different scenarios. (4) “Little Higgs” models [72]. In these
models the Higgs is a pseudo-Goldstone boson and extra symmetries allow m h = 0
only at two-loop level, so that can be as large as o(10 TeV) with the Higgs within
present bounds (the top loop is quenched by exchange of heavy vectorlike new
quarks with charge 2/3). The physics beyond the SM will be discussed in Chap. 8.
Acknowledgments I am very grateful to Giuseppe Degrassi, Paolo Gambino, Martin Grunewald,
Vittorio Lubicz for their help and advise.
References
1. S.L. Glashow, Nucl. Phys. 22 (1961) 579; S. Weinberg, Phys. Rev. Lett. 19 (1967) 1264; A.
Salam, in Elementary Particle Theory, ed. N. Svartholm (Almquist and Wiksells, Stockholm,
1969), p. 367.
2. F. Englert, R. Brout, Phys.Rev.Lett.13, 321 (1964); P.W. Higgs, Phys.Lett. 12,132 (1964).
3. E.D.Commins, Weak interactions, Mc Graw Hill, 1973; L. V. Okun, Leptons and Quarks,
North Holland, 1982; D. Bailin, Weak Interactions, 2nd e., Hilger, 1982; H. M. Georgi, Weak
interactions and modern particle theory, Benjamin, 1984.
4. J.D. Bjorken and S. Drell, Relativistic Quantum Mechanics/Fields, Vols. I, II, McGraw-Hill,
New York, (1965).
5. Particle Data Group, The Journal of Physics G 33(2006)1.
6. G.Altarelli, T.Sjöstrand and F.Zwirner (eds.), “Physics at LEP2”, CERN Report 95-03.
7. The ALEPH, DELPHI, L3, OPAL, SLD Collaborations and the LEP Electroweak Working
Group, A Combination of Preliminary Electroweak Measurements and Constraints on the
Standard Model, hep-ex/0312023, and references therein.
8. The LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/.