The anomalous production of multi-lepton and its impact on the measurement of $Wh$ production at the LHC

Anomalies in multi-lepton final states at the Large Hadron Collider (LHC) have been reported in Refs.~\cite{vonBuddenbrock:2017gvy,vonBuddenbrock:2019ajh}. These can be interpreted in terms of the production of a heavy boson, $H$, decaying into a Standard Model (SM) Higgs boson, $h$, and a singlet scalar, $S$, which is treated as a SM Higgs-like boson. This process would naturally affect the measurement of the $Wh$ signal strength at the LHC, where $h$ is produced in association with leptons and di-jets. Here, $h$ would be produced with lower transverse momentum, $p_{Th}$, compared to SM processes. Corners of the phase-space are fixed according to the model parameters derived in Refs.~\cite{vonBuddenbrock:2016rmr,vonBuddenbrock:2017gvy} without additional tuning, thus nullifying potential look-else-where effects or selection biases. Provided that no stringent requirements are made on $p_{Th}$ or related observables, the signal strength of $Wh$ is $\mu(Wh)=2.41 \pm 0.37$. This corresponds to a deviation from the SM of $3.8\sigma$. This result further strengthens the need to measure with precision the SM Higgs boson couplings in $e^+e^-$, and $e^-p$ collisions, in addition to $pp$ collisions.