Curing the Ills of Higgsless Models: the S Parameter and Unitarity

Abstract

We consider various constraints on Higgsless models of electroweak symmetry breaking based on a bulk SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group in warped space. First we show that the S parameter which is positive if fermions are localized on the Planck brane can be lowered (or made vanishing) by changing the localization of the light fermions. If the wave function of the light fermions is almost flat their coupling to the gauge boson KK modes will be close to vanishing, and therefore contributions to the S parameter will be suppressed. At the same time the experimental bounds on such Z' and W' gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV. The biggest difficulty of these models is to incorporate a heavy top quark mass without violating any of the experimental bounds on bottom quark gauge couplings. In the simplest models of fermion masses a sufficiently heavy top quark also implies an unacceptably large correction to the Zb\bar{b} vertex and a large splitting between the KK modes of the top and bottom quarks, yielding large loop corrections to the T-parameter. We present possible directions for model building where perhaps these constraints could be obeyed as well.

Figures (5)

• Figure 1: Combined plots of the experimental constraints on Higgsless models for different values of the $g_{5R}/g_{5L}$ ratio, in the parameter space $\tau$--$\tau'$ (normalized by $R \log R'/R$). The solid contours for $S$ (red) and $T$ (blue) are at $0.25$; the dashed contours at $0.5$. The black solid (dashed) line corresponds to a deviation in the differential cross section of $3\%$ ($2\%$) at LEP2. The shaded region is excluded by a deviation larger that $3\%$ at LEP and/or direct search at Run1 at Tevatron.
• Figure 2: Plots of the oblique parameters as function of the bulk mass of the reference fermion. The values on the right correspond to localization on the Planck brane. $S$ vanishes for $c=0.487$.
• Figure 3: Contour plots of $\Lambda_{\rm NDA}$ (solid blue lines) and $M_{Z^{(1)}}$ (dashed red lines) in the parameter space $c_L$--$R$. The shaded region is excluded by direct searches of light $Z^\prime$ at LEP.
• Figure 4: On the left, contours of $S$ (red), for $|S|=0.25$ (solid) and $0.5$ (dashed) and $T$ (blue), for $|T|=0.1$ (dotted), $0.3$ (solid) and $0.5$ (dashed), as function of $c_L$ and $R$. On the right, contours for the generic suppression of fermion couplings to the first resonance with respect to the SM value. In particular we plotted the couplings of a lh down--type massless quark with the $Z'$. The region for $c_L$, allowed by $S$, is between $0.43\div 0.5$, where the couplings are suppressed at least by a factor of 10.
• Figure 5: Plots of the percentage deviation of the $Zb_L\bar{b}_L$ coupling with respect to the SM value as function of the scale $1/R'$ (left, with $c_L=0.46$ and $c_R=-0.05$) and as function of the bulk masses $c_L$ and $c_R$ for $1/R'=1750$ GeV (right). The contours are at $1\,\%$ and $1.5\,\%$. Different values of $1/R'$ are obtained varying the ratio $g_R/g_L$ between 1 and 6; the plot on the right assumes $g_R/g_L=5$.