Little Higgs and Custodial SU(2)
3/3/2003
209 citations (202 excluding self-citations). Extended the Minimal Moose by incorporating custodial symmetry, the key ingredient for compatibility with precision electroweak data.
The Problem
The original Little Higgs models generated contributions to the T parameter (the oblique correction measuring custodial SU(2) violation) that were in tension with precision electroweak measurements unless the symmetry-breaking scale f was pushed above 2-3 TeV. At those scales, the fine-tuning the models were designed to eliminate begins to reappear. The question was whether a Little Higgs model could be built with custodial SU(2) as an approximate symmetry, suppressing the T parameter and allowing a lower breaking scale with accessible new particles.
The Key Idea
The paper modifies the Minimal Moose construction by replacing the SU(3) gauge symmetries with SO(5), which contains custodial SU(2) as a subgroup. In a simple limit, the heavy W’ and B’ make small contributions to precision observables. The result: the breaking scale can be as low as 700 GeV, with a top partner at 2 TeV, W’ and B’ at 2.5 TeV, and heavy Higgs partners at 2 TeV — all accessible at the LHC. The model predicts two Higgs doublets at low energies and favors a light Higgs from precision constraints, though for different structural reasons than in the Standard Model.
Recollections
This was one of my first papers where I initiated the research. Spencer Chang was a younger graduate student at Harvard working under Howard Georgi. Between Nima Arkani-Hamed, Andy Cohen, Howard Georgi, myself, Thomas Gregoire, Ann Nelson, and Ami Katz, we had written a bunch of papers on Little Higgs. But some people had published papers claiming these theories were already effectively excluded by precision electroweak measurements.
I had never properly learned precision electroweak science, and when I sat down to read those papers I was pretty confused. There were all these complex observables. But I knew it couldn’t possibly be that complicated. These were decoupling theories: you could integrate out the heavy particles and end up with modifications to the ordinary Standard Model described by higher-dimensional operators. Michael Peskin had distilled the key constraints into his famous S, T, and U parameters, which were better, but still not entirely clear in my mind. Spencer and I worked out the limits on the operators directly. The most important was the T parameter, which was protected by custodial SU(2), a remnant of an accidental SO(4) symmetry in the Higgs potential that breaks to SU(2)diagonal during electroweak symmetry breaking. Our initial Little Higgs theories didn’t respect this symmetry and had severe limits as a result.
During a visit to UW Madison, Graham Kribs, who was a postdoc there, told me it was basically impossible to have a Little Higgs model preserve custodial SU(2) symmetry. I knew immediately that wasn’t true. The simplest approach was to make the symmetries at the moose nodes be SO(4) rather than SU(3). So that’s what I did. Spencer and I wrote the paper and worked out the limits. We found the S parameter was more generic and basically impossible to avoid, but the constraint from S alone wasn’t as tight. The whole thing took only a few weeks from idea to article. I remember thinking “it can’t be this easy,” and it was.