A New Custodian for a Realistic Higgsless Model

TL;DR

The paper studies realistic Higgsless electroweak symmetry breaking in a warped extra dimension and shows that an enhanced custodial symmetry, realized via alternative $SU(2)_R$ assignments for the third generation, can suppress problematic $Z b_\ell\bar{b}_\ell$ couplings. By placing $t_L$ and $b_L$ in a bi-doublet and arranging $t_R$ as a singlet with $b_R$ in an $SU(2)_R$ triplet, the authors attain a large top mass while keeping custodial protection, but some residual corrections remain, especially for light fermions. For light fermions, the universal $Z d_\ell \bar{d}_\ell$ deviation is about $4\%$–$5\%$ and cannot be canceled by bulk mass tuning, making this particular realization unsuitable for them; however, for the third generation, tuning the bulk masses $c_L$, $c^t_R$, and $c^b_R$ (e.g., $c_L\approx0.1$, $c^t_R\approx0$, $c^b_R\approx-0.75$) yields a realistic spectrum with SM-like $Z b_\ell \bar{b}_\ell$ and a set of Kaluza-Klein resonances at the few hundred GeV to TeV scale. The construction provides a concrete benchmark with calculable gauge KK states near current collider bounds and predicts measurable deviations in triple gauge boson couplings, making it a useful test case for LHC and future colliders while encouraging search for more symmetry-based Higgsless models.

Abstract

We present an example of a realistic Higgsless model that makes use of alternative $SU(2)_R$ assignments for the top and bottom quarks recently proposed by Agashe et al. which results in an enhanced custodial symmetry. Using these new representat ions reduces the deviations in the $Zb_\ell\bar{b}_\ell$ coupling to $\sim 4%$ for a wide range of parameters, while this remaining correction can also be eliminated by varying the localization parameter (bulk mass) for $b_r$.

Figures (2)

• Figure 1: Deviations in the coupling of the down-type quarks as a function of the bulk mass $c_L$ using the alternative realization of custodial symmetry, where $\Psi_L=({\bf{2,2}}), \Psi_R = ({\bf{1,3}}), t_R=({\bf{1,1}})$ (continuous line) and the original case, where $\Psi_L=({\bf{2,1}}), \Psi_R = ({\bf{1,2}})$ (dashed line). In the left panel, we consider a light quark (first and second generation). In the right panel, we show the $b$ quark, with $c_R^t = 0$, while neglecting the $b$ mass.
• Figure 2: Deviations in the coupling $Z f_\ell \bar{f}_\ell$ as a function of the bulk mass $c^b_R$ of $SU(2)_R$ triplet containing the $b_R$ using the alternative realization of custodial symmetry. The other bulk masses have been set to $c_L=0.1, \; c^t_R=0$.