Nuclear Physics B176 (1980) 449465 @ North-Holland Publishing Company PROBLEMS AND VIRTUES OF SCALARLESS THEORIES OF ELECTROWEAK INTERACTIONS S. DIMOPOULOS’ and S. RABY* zyxwvutsrqponmlkjihgfedcbaZYXWVU Institute of Theoretical Physics, Dept. of Physics, Stanford University, Standford, CA 94305, USA P. SIKIVIE Theory Division, CERN, 1211 Geneva 23, Switzerland Received 27 May 1980 We discuss several of the issues involved in the construction of a realistic theory of electroweak interactions. We illustrate these issues within the context of a Mickey Mouse model which bears some resemblance to the real world. 1. Introduction During the last several years, the standard SU(2)L X U( 1) x SU(3)o gauge theory [l] of the weak, electromagnetic, and strong interactions has established itself as the best available description of low-energy (~100 GeV) particle physics. A serious flaw of this model is the existence of elementary scalar Higgs fields. Scalar fields are undesirable for the following reasons. (i) They introduce a large number of arbitrary parameters (Yukawa couplings and vacuum expectation values). This limits the predictive power of the theory. (ii) They cannot account for the huge difference between the electroweak (-300 GeV) and the grand unified scale a10i5 GeV [2]. This would require an unnatural fine tuning of parameters [3]. These problems first led to the introduction of technicolor (TC) [4, 31 as a mechanism for giving mass to the W’ and Z” bosons. A serious flaw of TC theories, however, is that quarks and leptons remain massless. To solve this problem the concept of extended technicolor (ETC) was introduced [5]. Finally it was realized that the concept of tumbling gauge theories [6] can naturally lead to an explanation of the mass hierarchy of quarks and leptons. In this paper we wish to discuss several of the issues that arise when one attempts to construct realistic models making use of the above concepts. 2. Issues In this section we wish to enumerate the many constraints that have to be satisfied by any credible candidate model of extended technicolor (ETC). The scenario that ’ Supported in part by NSF grant PHY 78-26847. ’ Supported in part by NSF grant PHY 79-18046. 449