Triviality and the Precision Bound on the Higgs Mass

Abstract

The triviality of the scalar sector of the standard one-doublet Higgs model implies that this model is only an effective low-energy theory valid below some cut-off scale Lambda. For a heavy higgs this scale must be relatively low (10 TeV or less). Additional interactions coming from the underlying theory, and suppressed by the scale Lambda, give rise to model-dependent corrections to precisely measured electroweak quantities. Dimension six operators arising from the underlying physics naturally contribute to the S and T parameters, and their effects should be included in a global fit to the precision data that determines any limit on the Higgs mass. Using dimensional analysis, we estimate the expected size of these corrections in a custodially-symmetric strongly-interacting underlying theory. Taking these operators' coefficients to be of natural size gives sufficiently large contributions to the T parameter to reconcile Higgs masses as large as 400-500 GeV with the precision data.

Figures (3)

• Figure 1: The triviality and precision bounds in the $\Lambda$-$m_h$ plane. The regions above the corresponding curves are excluded.
• Figure 2: The oval demarks the area of the S-T plane compatible with the precision electroweak measurements at the $95 \%$ confidence level. The line is the trajectory of Higgs mass in the standard model from 76 GeV to 1 TeV. The black rectangles show the natural size of corrections from the underlying physics for different scales $\Lambda$ and varying $a$ and $b \kappa$ between $\pm 1$ (they should be centered on the point on the Higgs line corresponding to the Higgs mass of interest).
• Figure 3: The value of $b \kappa$ compatible with the precision bounds as a function of $\Lambda$ for different values of $m_h$. The blocked off area in the last plot is forbidden by triviality. The values of cut off on the x axis varies logarithmically between 2500 -- 25000 GeV.