Isospin Breaking and Fine Tuning in Top-Color Assisted Technicolor
R. S. Chivukula, B. A. Dobrescu, J. Terning
TL;DR
The paper analyzes isospin breaking in top-color assisted technicolor (TC^2) and shows that isospin-violating U(1) interactions, if they couple to technifermions, can markedly shift the electroweak parameter Δρ_* unless the new physics scale is high or couplings are finely tuned. It computes contributions to Δρ_* from technifermion loops and top-quark loops, highlighting that top-color exchange alone already pushes top-color boson masses above ~1.4 TeV to satisfy precision data. A global electroweak fit constrains the parameter space, revealing a trade-off between keeping the top quark light and avoiding large Δρ_* through small couplings or heavier top-color states, typically at the percent level of tuning. The results imply substantial fine-tuning or custodial-symmetry-preserving constructions are required for TC^2 to remain viable, and mirror similar tension in strong ETC scenarios.
Abstract
Recently, Hill has proposed a model in which new, potentially low-energy, top-color interactions produce a top-condensate ({\em a la} Nambu---Jona-Lasinio) and accommodate a heavy top quark, while technicolor is responsible for producing the $W$ and $Z$ masses. Here we argue that isospin breaking gauge interactions, which are necessary in order to split the top and bottom quark masses, are likely to couple to technifermions. In this case they produce a significant shift in the $W$ and $Z$ masses (i.e.~contribute to $Δρ_* = αT$) if the scale of the new interactions is near 1 TeV. In order to satisfy experimental constraints on $Δρ_*$, we find that either the effective top quark coupling or the top-color coupling must be adjusted to 1\%. Independent of the couplings of the technifermions, we show that the isospin-splitting of the top and bottom quarks implies that the top-color gauge bosons must have masses larger than about 1.4 TeV. Our analysis can also be applied to strong extended technicolor (ETC) models that produce the top-bottom splitting via isospin breaking ETC interactions.