Is there a Desert beyond the Mountains?

  • C. H. Llewellyn Smith


The steps in the argument which lead to the possibility of a “desert” containing no new physics between 102 and 1014 GeV are:
  1. 1.

    Electroweak and strong interactions are described by gauge theories. There is good evidence that all these forces are mediated by spin 1 particles, coupled to “weak isospin” and colour respectively, and gauge theories are the only sensible field theories of elementary vector bosons coupled to such non-commuting charges.

  2. 2.

    The gauge theory is SU(3)c × SU(2)L × U(1), which is the simplest model compatible with the data.

  3. 3.

    This theory is not complete. It does not explain charge quantization, and it does not really unify electro-weak interactions. It contains far too many parameters — mainly associated with the Higgs system, which supplies one parameter for every mass and mixing angle. It does not explain the existence of different “generations” of quarks and leptons.

  4. 4.

    In the conventional gauge theory framework the obvious way to improve the theory is to enlarge the gauge group, thereby reducing the number of forces and perhaps combining more fermions in common multiplets. The simplest step of unifying SU(2) × U(1) turns out to be surprisingly difficult; in particular it is hard to get sin2θw < 3/8. However, if the unification scale is very large (~ 1014 GeV), allowing αs to have decreased to 0(α2,1), it is relatively easy to Grand Unify all three forces. This is tremendously attractive and allows us also to combine quarks and leptons into common multiplets, thus unifying the two different forms of matter.

  5. 5.

    Economy and simplicity lead us to the minimal group SU(5).1 Models based on larger groups are more complex and do not have overwhelming compensating advantages. In the minimal version of SU(5) only the W, Z, t and Higgs boson remain to be discovered at low energy and there will then be a desert extending to Mx ~ 4 × 1014 GeV.



Gauge Theory Higgs Boson Gauge Boson Spectral Function SUSY Breaking 
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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • C. H. Llewellyn Smith
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of OxfordOxfordEngland

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