Abstract
We study the effects of custodial symmetry violation in the Georgi-Machacek (GM) model. The GM model adds isospin-triplet scalars to the Standard Model in a way that preserves custodial symmetry at tree level; however, this custodial symmetry has long been known to be violated at the one-loop level by hypercharge interactions. We consider the custodial-symmetric GM model to arise at some high scale as a result of an unspecified ultraviolet completion, and quantify the custodial symmetry violation induced as the model is run down to the weak scale. The measured value of the eletroweak rho parameter (along with unitarity considerations) lets us constrain the scale of the ultraviolet completion to lie below tens to hundreds of TeV. Subject to this constraint, we quantify the size of other custodial-symmetry-violating effects at the weak scale, including custodial symmetry violation in the couplings of the 125 GeV Higgs boson to W and Z boson pairs and mixings and mass splittings among the additional Higgs bosons in the theory. We find that these effects are small enough that they are unlikely to be probed by the Large Hadron Collider, but may be detectable at a future $e^+e^-$ collider.
Highlights
With the discovery of a Standard Model (SM)–like Higgs boson at the CERN Large Hadron Collider (LHC) in 2012 [1], we have the first direct access to the dynamics of electroweak symmetry breaking
We consider the custodial-symmetric GM model to arise at some high scale as a result of an unspecified ultraviolet completion and quantify the custodial symmetry violation induced as the model is run down to the weak scale
We find that these effects are small enough that they are unlikely to be probed by the Large Hadron Collider (LHC), but may be detectable at a future eþe− collider
Summary
With the discovery of a Standard Model (SM)–like Higgs boson at the CERN Large Hadron Collider (LHC) in 2012 [1], we have the first direct access to the dynamics of electroweak symmetry breaking. Weak-scale measurements of the ρ parameter can be used to constrain how high the custodial-symmetric scale can be Subject to this constraint, we can quantify the physical effects of custodial symmetry violation in Higgs-sector observables, such as the ratio of the SM-like Higgs boson couplings to WW and ZZ and custodial-violating mixings and mass splittings among the additional scalars in the GM model. Larger custodial-violating effects arise when scalar masses in the custodial-symmetric theory are tuned to be nearly degenerate, so that custodial symmetry violation induces resonant mixing among mass eigenstates We handle these situations by exactly diagonalizing the resulting mass matrices; in the small regions of parameter space around these resonances our perturbative calculation remains unstable. In Appendix C we give some details of our calculation method for the RGEs
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