Probing the desert with fermion masses.

The standard SU(3) S SU(2) S U(1) model provides a very successful description of the strong, weak, and electromagnetic interactions. It is, however, in no sense a fundamental theory. The SU(3) II SU(2) S U(1) model contains at least eighteen parameters, each of which must be adjusted by hand to account for low-energy phenomenology. What lies beyond the standard model? A variety of extensions have been discussed in recent years. Most of these proposals predict new physics above a characteristic scale M&. This threshold ranges from a few hundred gigaelectronvolts, in hypercolor scenarios, to about 10'o GeV, in axion models, and all the way up to 10's GeV, in typical grand unified theories. It is very important to constrain the scale M&. Experiments place lower limits on M& that are typically of the order of a few hundred gigaelectronvolts. The precise bounds depend on the model under consideration and on the values of various free parameters. In this Letter we describe a new upper bound of the scale Mz. %'e shall show that heavy quarks provide a model independent p-robe of the SU(3) SU(2) S U(1) desert. Our idea is based on the following two observations: (1) Heavy fermions have large Yukawa couplings at the weak scale M~. The structure of the SU(3) S SU(2) S U(1) renormalization-group equations implies that such couplings blow up at a relatively low energy Mz. (2) At the scale Mtt, where the Yukawa couplings diverge, new physics should be found. For example, large Yukawa couplings induce strong couplings in the Higgs sector. Such a strongly coupled Higgs sector should give rise to a new spectrum of bound states and to new effective interactions. Of course, it is always possible that the gauge group might change at an energy M~ (Mz. In this case, new gauge bosons of mass M~ should then be found. No matter what happens, new physics must emerge before the Yukawa couplings diverge. The idea that diverging couplings imply new physics is not new. In quantum electrodynamics, it is associated with the presence of "Landau ghosts. " In QED, the electromagnetic coupling blows up at an astronomically high energy, about Mtt & e'3 GeV. If QED were a fundamental theory, it would —at the very least —become strongly coupled at the scale Mz. New physics would arise, and quantum electrodynamics as we know it would break down. Of course, we can never see this new physics because QED is only an effective theory. At the scale Miv = 80 GeV, QED loses its separate identity and becomes absorbed into the standard electroweak theory. ' In what follows we apply these ideas to the standard SU(3) S SU(2) S U(1) model. For ease of presentation, we first examine a three-family model with a heavy top quark (and a single Higgs doublet). We denote the top Yukawa coupling by g, . Its evolution with energy is given by dg, /d r = —, ' g, (9g,' —2 G ), (1)