FIG. 2. Potentially large contributions to mH from quadratic divergences in the Standard Model (a), couplings to grand unified theory (GUT) Higgs bosons (b), and logarithmic corrections to the latter (c).

This would be if the differences between the boson and fermion squared masses


suggesting that the supersymmetric partner particles should be accessible to present or planned accelerators.

The next section discusses in more detail the current lower limit on the lightest neutralino—a mixture of the supersymmetric partners of the photon, Z boson, and neutral Higgs bosons, which is the best candidate for the LSP (9). In addition to these supersymmetric particles per se, even the minimal supersymmetric extension of the Standard Model predicts a rich spectrum of Higgs bosons, with five physical states, of which the lightest must weigh less than about 150 GeV (1015).

This prediction underlies one of two tentative experimental indications in favor of supersymmetry. As seen in Fig. 3, precision electroweak data favor indirectly a relatively light Higgs boson weighing about 140 GeV with a factor of 2 uncertainty, which is highly consistent with the supersymmetric prediction (16). The second tentative indication comes from measurements of the gauge couplings at LEP and elsewhere shown in Fig. 4. which favor unification in a supersymmetric GUT over a theory without supersymmetry (1725). The supersymmetric GUT prediction is to 0.232, whereas a minimal nonsupersymmetric GUT predicts sin2θw0.21 to 0.22, and the LEP data find sin2θw=0.2315±0.0002.

FIG. 3. Global fit to the precision electroweak data and Fermilab measurements of mt, compared with the LEP lower limit on mH and the range expected if the Standard Model remains unmodified up to a scale Λ.

These indications are nice, but there still is no smoking “gunino”!


The LSP is expected to be stable in many models—and hence present in the Universe today as a cosmological relic from the Big Bang—because of a multiplicatively conserved quantum number called R parity (26), which is +1 for all particles and −1 for all sparticles. Its conservation is related to those of baryon and lepton numbers (B, L), because R=(−1)3B+L+2S, where S is the spin. If B and L are conserved, and thus also R parity, sparticles must always be produced in pairs (e.g., e+ e+), heavier sparticles must decay into lighter ones (e.g., μ), and the LSP is stable because it has no legal decay modes.

If the LSP had charge or strong interactions, it would bind with conventional matter to form anomalous heavy isotopes. The fact that these have not been seen suggests that the LSP must be electrically neutral and have only weak interactions. Possible scandidates include the sneutrino of spin 0, the lightest neutralino (partner of the γ, H0, Z) of spin 1/2, and the gravitino of spin 3/2 (the prefix “s” is used to denote the supersymmetric partner of some observed particle). The sneutrino has essentially been excluded by LEP experiments and the underground searches for dark matter discussed later, and the gravitino is expected in many models to be heavier than the lightest neutralino χ, so attention has focused on the χ as the LSP (9).

In simple supersymmetric models, neutralinos and charginos X± (partners of the W±, H±) are characterized by three parameters: a primordial gaugino mass m1/2, a Higgs mixing parameter μ, and the ratio tan β of two Higgs vacuum expectation values. The lightest neutralino looks simple in certain limits: as m1/20, χ, and as μ→0, χ→H, though neither of these ideal limits is compatible with the constraints from LEP and other experiments. What makes χ a particularly attractive candidate for cold dark matter is the fact that there are generic domains of parameter space where the relic cosmological density is in the interesting range: 0.1≤Ωχh2≤ 1 (9).

FIG. 4. Measurements of sin2θw. Note that the nonsupersyrametric GUT prediction disagrees significantly with the data. The minimal supersymmetric GUT prediction assumes unrealistically that all sparticles (supersymmetric particles) have masses mZ. Realistic spectra give predictions in agreement with the data.

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