4.6 Beyond the Standard Model 203and aslepton respectively. Similarly, for every gauge particle we have a fermionic
superpartner with spin 1/ 2 ,called agaugino. Among these,gluinosare superpart-
ners of gluons, andwinosand thebinoare the superpartners of the gauge bosons of
the electroweak group. The gauginos mediate the interaction of the scalar particles
and their fermionic partners, with a strength determined by the gauge coupling
constant. The Higgs particle is accompanied by ahiggsino. The lightest neutral
combination of -inos(mass eigenstate), called theneutralino, must be stable; if
supersymmetry were broken at the electroweak scale, it would interact weakly with
ordinary matter. Therefore, the neutralino is an ideal candidate for cold dark matter.
To conclude our brief excursion to the “s- and -inozoo,” we should mention the
gravitino –the spin 3/2 superpartner of the graviton which could also serve as a
dark matter particle. Thus we see that supersymmetric theories provide us with
the weakly interacting massive particles necessary to explain dark matter in the
universe.
Some remarkable properties of supersymmetric theories arise from the fact that
the numbers of fermionic and bosonic degrees of freedom in these theories are equal.
For instance, the superpartner of the left-handed fermion is a complex scalar field
and they both have two degrees of freedom. The energy of the vacuum fluctuations
per degree of freedom is the same in magnitude but opposite in sign for fermions and
bosons of the same mass. Therefore, in supersymmetric theories the fermion and
boson contributions cancel each other and the total vacuum energy density vanishes.
In other words, the cosmological term is exactly zero. This is true, however, only if
supersymmetry remains unbroken. But supersymmetry is broken and as a result the
expected mismatch in vacuum energy densities, arising from the mass difference of
the superpartners, is of order^4 SUSY,whereSUSYis the supersymmetry breaking
scale. IfSUSY∼1TeV,the cosmological constant is about∼ 10 −^64 in Planck
units. This number is still about 60 orders of magnitude larger than the observational
limit. Thus we see that supersymmetry, while a step in the right direction, does not
quite solve the cosmological constant problem.
The last remark we wish to make here concerns the behavior of the running
coupling constants in the minimal supersymmetric extension of the Standard Model.
The additional supersymmetric particles influence the rate of running of the strong
and electroweak coupling constants. As a result, the three constants meet at a single
point with impressive accuracy (Figure 4.20). This revives our hopes of Grand
Unification and gives an indication that we may be on the right track.
4.6.1 Dark matter candidates
Nucleosynthesis and CMB data clearly indicate that most of the matter in the
universe is dark and nonbaryonic. There is no shortage of particle physics candidates