Combining LEP and LHC to bound the Higgs Width

The correlation of on- and off-shell Higgs boson production at the LHC in $gg \to h^* \to ZZ$ to bound the Higgs width, under specific model-dependent assumptions, has recently received a lot of attention. As off-shell cross section measurements in this channel suffer from a small signal yield, large backgrounds, and theoretical uncertainties, we propose an alternative complementary constraint which is only possible through the combination of LEP and LHC measurements. Previous precision electroweak measurements at LEP allow for the determination of indirect constraints on Higgs couplings to vector bosons by considering one-loop processes involving virtual Higgs exchange. As the Higgs is off-shell in these diagrams we venture that LEP can be interpreted as an off-shell `Higgs Factory'. By combining these LEP constraints with current LHC 8 TeV Higgs measurements a stronger limit on the Higgs width can be achieved than with LHC data alone for models with rescaled Higgs couplings. Looking to the future, avoiding ambiguities arising due to new physics modifications of the $hGG$ coupling, a theoretically more robust constraint can be achieved by correlating LEP measurements with WBF Higgs production followed by Higgs decays to $WW$ and $ZZ$. This method for indirectly constraining the Higgs width is very effective for specific BSM scenarios and is highly complementary to other proposed methods. The limits we obtain particularly highlight the power of a concrete LEP+LHC combination, not only limited to Higgs width measurements.