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. (von Buddenbrock et al., J Phys G 45(11):115003, arXiv:1711.07874 [hep-ph], 2018; Buddenbrock et al., JHEP 1910:157, arXiv:1901.05300 [hep-ph], 2019). 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. (von Buddenbrock et al., J Phys G 45(11):115003, arXiv:1711.07874 [hep-ph], 2018; von Buddenbrock et al., Eur Phys J C 76(10):580, arXiv:1606.01674 [hep-ph], 2016) 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.