Limitations and Opportunities of Off-Shell Coupling Measurements

Indirect constraints on the total Higgs width $\Gamma_h$ from correlating Higgs signal strengths with cross section measurements in the off-shell region for $p(g)p(g)\to 4\ell$ production have received considerable attention recently, and the CMS collaboration have published a first measurement. We revisit this analysis from a new physics and unitarity constraints perspective and conclude that limits on $\Gamma_h$ obtained in this fashion are not reliable unless we make model-specific assumptions, which cannot be justified at the current stage of the LHC programme. Relaxing the $\Gamma_h$ interpretation, we discuss the merits of high invariant mass cross section measurements in the context of Higgs CP analyses, higher dimensional operator testing, and resolved new physics in the light of electroweak precision constraints beyond effective theory limitations. Furthermore, we show that a rather model-independent LHC constraint can be obtained from adapting the $gg\to 4\ell$ analysis to the weak boson fusion channels at lower statistical yield.