Golden Probe of Electroweak Symmetry Breaking.

The ratio of the Higgs couplings to WW and ZZ pairs, λ_{WZ}, is a fundamental parameter in electroweak symmetry breaking as well as a measure of the (approximate) custodial symmetry possessed by the gauge boson mass matrix. We show that Higgs decays to four leptons are sensitive, via tree level or one-loop interference effects, to both the magnitude and, in particular, overall sign of λ_{WZ}. Determining this sign requires interference effects, as it is nearly impossible to measure with rate information. Furthermore, simply determining the sign effectively establishes the custodial representation of the Higgs boson. We find that h→4ℓ (4ℓ≡2e2μ, 4e, 4μ) decays have excellent prospects of directly establishing the overall sign at a high luminosity 13 TeV LHC. We also examine the ultimate LHC sensitivity in h→4ℓ to the magnitude of λ_{WZ}. Our results are independent of other measurements of the Higgs boson couplings and, in particular, largely free of assumptions about the top quark Yukawa couplings which also enter at one loop. This makes h→4ℓ a unique and independent probe of electroweak symmetry breaking and custodial symmetry.