Top condensation without fine-tuning

Abstract

Quadratic divergencies which lead to the usual fine-tuning or hierarchy problem are discussed in top condensation models. As in the Standard Model a cancellation of quadratic divergencies is not possible without the boson contributions in the radiative corrections which are absent in lowest order of an 1/N c -expansion. To deal with the cancellation of quadratic divergencies we propose therefore an expansion in the flavor degrees of freedom. In leading order we find the remarkable result that quadratic divergencies automatically disappear. *

Top-quark condensation

“…Suppression of ⌳ 2 terms in the composite Higgs self-energy Blumhofer (1994Blumhofer ( , 1995 investigated the question of whether radiative ⌳ 2 contributions that appear in the coefficient of the Higgs ⌽ † ⌽ term (Higgs self-energy) could be suppressed in tt condensation frameworks. The minimal standard model is plagued by such terms at the one-loop level, where ⌳ is a large UV cutoff of the theory.…”

“…The ⌳ 2 term in the composite Higgs self-energy in the quark-loop approximation is in fact still there and is ϰ4N c m t 2 ⌳ 2 /3, just as in the minimal standard model. Blumhofer (1994) noted the following interesting property: if we also include in the composite Higgs self-energy corrections from exchange of the composite scalars with leading-N c propagators (9.4), as depicted in Fig. 13, and set N c ϭ3, the ⌳ 2 terms cancel…”

Left-right symmetry breaking in NJL approach

“…We use the well known abbreviation NJL though the paper of Vaks and Larkin was received and published first 2. It has been claimed in[7] that taking into account the loops with composite Higgs scalars results in the automatic cancelation of quadratic divergences and solves the gauge hierarchy problem of the Standard Model in the BHL approach. We do not discuss this possibility here.…”

Exact cancellation of quadratic divergences in top condensation models

“…Instead of the color factor N c the second graph is enhanced by the number of the Higgs field components. Hence, in a recent paper [8], I have used a combined expansion in the color and flavor degrees, where both graphs are of the same order. In this paper we do not need any special expansion since we will calculate the quadratic divergences to all orders 1/N c .…”

“…In a recent paper [8] it was shown that a cancellation of quadratic divergences appears in such top condensation models in lowest order of a combined color-flavor-expansion. The reason is that like in supersymmetry the fermion and boson couplings, i. e. in top condensation the top Yukawa-coupling and the Higgs self-coupling, are related since the Higgs is att-boundstate.…”