Strongly Interacting Higgs Effects On The Masses Of Gauge Bosons.

We study the radiative corrections to the W('(+OR-)) and Z masses in the large Higgs mass limit (m(,H) > 1 TeV). Since the unitarity limit of the standard SU(2) x U(1) electroweak model at the tree level is m(,H) (TURNEQ) 1 TeV, one must go beyond the perturbation theory. We study the SU(N) x U(1) model by the 1/N expansion, keeping the lowest order in the gauge couplings (g('2)N, g'('2)N) and summing up all orders of the Higgs self-coupling ((lamda)N). We show that the effects of the strong interaction on the vector boson mass shifts saturate and the mass shifts can be written as (delta)M('2)/M('2) = (1/N g('2)N/16(pi)('2) f((lamda)N)) + (0 1/N (g('2)N)('2)/(16(pi)('2))('2) ), where the function f((lamda)N) remains finite even in the limit of infinite Higgs self-coupling constant. The radiative corrections are determined by the electroweak scale v('2)/N. This cannot be inferred from the perturbation expansion which is a series in increasing powers of the Higgs mass. Also this shows the saturation effect which is stronger than Veltman's screening theorem in the perturbation expansion. We also argue that this saturation of the strong interaction effects is due to unitarity and is not peculiar to the 1/N expansion.Ph.D.High energy physicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/127913/2/8621308.pd