Neutral exotica at FASERν and SND@LHC

The (g − 2)$_{μ}$ anomaly indicates that the second generation of leptons should have new interactions beyond the standard model. The high flux of ν$_{μ}$ and $ \overline{\nu} _{μ}$ at the forward experiments such as FASERν and SND@LHC makes them suitable setups to search for new interactions of the second generation leptons. In this paper, we build a model in which the second generation left-handed leptons couple to a new right-handed neutrino, N and a new Higgs doublet which also couples to the quarks. The scattering of high energy ν$_{μ}$ off nuclei can produce N. We investigate how forward experiments can test this model by looking for the N production vertex followed by the displaced vertex of the N decay. Discovering even a single such event can be a harbinger to look for the spectacular signals of the new Higgs doublet production at the LHC. We discuss the possibility of explaining the (g − 2)$_{μ}$ anomaly by adding more generations of N which will lead to chain decays of N and multiple leptons with distinct signals both at forward experiments and at the CMS and ATLAS detectors. Finally, we show that by adding a new light singlet scalar mixed with the neutral component of the new Higgs doublet (i.e., 2HDM+S model), the statistics of the data sample can be dramatically increased.