Golden Probe of Electroweak Symmetry Breaking

The ratio of the Higgs couplings to $WW$ and $ZZ$ pairs, ${\lambda }_{WZ}$, 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 ${\lambda }_{WZ}$. 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 $h\to 4\ell$ ($4\ell \equiv 2e2\mu$, $4e$, $4\mu$) 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 $h\to 4\ell$ to the magnitude of ${\lambda }_{WZ}$. 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 $h\to 4\ell$ a unique and independent probe of electroweak symmetry breaking and custodial symmetry.

Figure 1

Example of the posterior likelihood for one pseudo-data-set containing $\mathcal{O}(2000)$ signal events and generated for the SM case with ${\lambda }_{WZ}=1$. The shaded turquoise region is translated into a probability (see Fig. 2) that the sign of ${\lambda }_{WZ}$ is negative. See text for more details.

Figure 2

Probability, in units of effective $\sigma$’s, that the sign of ${\lambda }_{WZ}$ is negative as a function of luminosity. See text for more information.

Figure 3

Probability of mistaking a standard model Higgs boson (custodial singlet) for a custodial fiveplet or vice versa in terms of $p$ value. See text for more information.

Figure 4

$\sigma ({\lambda }_{WZ})$ or average error (as defined in Refs. [36, 39, 40, 44]) versus the number of signal events (bottom) and luminosity $\times$ efficiency (top). See text for more information.