Volume 143B, number 1, 2, 3 PHYSICSLETTERS 9 August 1984 CALCULATION OF THE COMPOSITE HIGGS MASS Howard GEORGI, David B. KAPLAN Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA and Peter GALISON Department of Physics, Stanford University, Stanford, CA 94305, USA Received 20 April 1984 In an interesting class of composite Higgs models, the composite Higgs mass can be calculated to be m H= 1.7 MwV~-/N where the confiningultracolor group which binds the Higgsis SU(N), N >/3. Thus mH~< 1.7 Mw. In these models, there is an additional gauged U(1) coupled to ordinary matter and broken at the ultracolor scale. Introduction. One of the most irksome features of the standard model is that the mass of the Higgs boson is undetermined. The reason for this is that the vacuum expectation value (VEV) and the mass of the Higgs are functions of two unre- lated parameters - the negative mass squared, and the quartic coupling. In this letter we point out that in composite Higgs models [1-3] the VEV and self-coupling of the scalar doublet may be related so as to render the Higgs mass calculable. We have calculated the Higgs mass in the SU(3)x SU(3) ultracolor model and found it to be m H --1.7 Mw~/N. The factor of N refers to the size of the ultracolor SU(N) group which binds together the constituents of the Higgs (" ultrafermions"), N >~ 3. This model also contains a heavy U(1) gauge boson which couples to ordinary matter and has a mass of the order Arc, the ultracolor confining scale. These results are of particular interest now that experimentalists are probing energies at and above M w. They are also of general interest be- cause, to our knowledge, this is only the second class of models which can predict the Higgs mass, the first being Coleman-Weinberg type theories [4]. In the next section we provide a brief review of the composite Higgs mechanism and discuss the resulting Higgs potential in the SU(3) x SU(3) ul- trafermion models of the sort discussed in ref. [3]. The effects on this potential of nonrenormalizable interactions characterized by an extended ultra- color scale AEU c (necessary for generating quark and lepton masses) will be assumed small com- pared to the effect of the renormalizable weak gauge interactions. Because of this we can make a prediction for the Higgs mass in terms of the ~r+-Tr ° mass difference without specifying the na- ture of the extended ultracolor theory. The SU(3) x SU(3) ultrafermion scenario. We postulate a strong SU(N)u c gauge group and consider ultrafermions transforming under SU(N)u c X SU(2) X U(1) X U(1)A as: QL = (N, 2)~j+c, QR = (N, 2)o_1+ c, (1) QL=(N, 1)b.-z+a, QR=(N, 1)b.2+a" For the time being we will not gauge the U(1)A. This theory possesses an approximate SU(3)x SU(3) symmetry which is spontaneously broken to SU(3) by the ultrafermion condensate at the scale Auc. Note that the U(1)A breaks at this scale. 152 0370-2693/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)