Scale Ratios in the Standard Model

We review the present knowledge of the Standard Model that is relevant in formulating its possible short distance extensions. We present different scenarios in terms of the Higgs mass, the only unknown parameter of the model. We concentrate on the many small numbers in the model and suggest generic methods to reproduce these numbers in terms of scale ratios, applying see-saw like ideas to the breaking of chiral symmetries. ∗ Invited Lecture at the 1994 Moriond Conference, Méribel, March 1994 ∗∗ Research supported in part by the US Department of Energy under grant DE-FG05-86-ER-40272 The Standard Model is described in terms of a mere twenty parameters, counting Newton’s constant. The challenge to theorists is to devise the extension of the Standard Model which explain not only the number of parameters but their values as well. Any extension will predict many new phenomena at shorter distances. There are many candidates for extending the Standard Model, but none have so far distinguished themselves by reproducing the values of the parameters, not even their multiplicity. Thus it is timely to review the types of extensions which might generically explain the observed patterns, before plunging in detailed models. The Standard Model is described by three dimensionless gauge couplings α1 for the hypercharge U(1), α2 for the weak isospin SU(2), and α3 for QCD. QCD itself predicts strong CP violation, parametrized by a fourth dimensionless parameter θ. The Higgs sector yields two parameters, a dimensionless Higgs self-coupling, and the Higgs mass. The self coupling is expressed in terms of the scale of electroweak breaking, which is directly “measured” as the Fermi coupling. The value of the Higgs mass is the only parameter that has not yet been determined from experiment. The Yukawa sector of the model yields the nine masses of the elementary fermions, which are in turn expressed as nine dimensionless Yukawa couplings multiplied by the electroweak order parameter. This sector also contains three mixing angles which account for interfamily decays, and one phase which describes CP violation in these decays. Let us start by discussing the dimensionful parameters. The most important is Newton’s constant which sets the scale. All fundamental questions concerning dimensionful parameters should be posed in terms of the Planck scale (10−33 cm, or 1019 GeV). Together with the other two fundamental constants, it sets a truly natural system of units. The second most striking one is the value of the electroweak order parameter, the inverse square root of the Fermi constant, in terms of the Planck mass G −1/2 F MPl ∼ 10−17 . There is no satisfactory explanation for this small parameter. All proposed extensions have strived to explain the value of this number. One class of theories, generically called technicolor, has proposed the existence of strong new forces just beyond electroweak scales; 2 this yields a natural explanation of this parameter, but fails to explain the values of the fermion masses. Another class of theories postulates the existence of another type of symmetry, supersymmetry(1). There, the electroweak order parameter is related to another small parameter, the order parameter of supersymmetry breaking. This may not seem very economical, but it is remarkable that supersymmetry breaking automatically generates electroweak breaking(2) in a wide class of theories. Thus it appears that there is nothing gained nor lost. The ideas of technicolor can then be successfully applied to supersymmetry breaking, by means of gaugino condensation, without the problem of fermion masses. Thus many believe that supersymmetry provides the best hope for explaining both the electroweak breaking scale and the value of the fermion masses. All quark and charged lepton masses break weak isospin by half a unit, along ∆IW = 1 2 , with the same quantum numbers as the electroweak order parameter, which gives the Wboson its mass. It is thus natural to form the dimensionless ratio