LAUSR

We explore the parameter space of lepton flavor violating (LFV) neutral Higgs Yukawa couplings with the muon and tau leptons that can be probed at the high-luminosity Large Hadron Collider (HL-LHC) via the vector boson fusion~(VBF) Higgs production process. Our projected sensitivities for the Standard Model Higgs ($h$) LFV branching ratio ${\rm Br}(h \to \mu\tau)$ in the $pp \to h j j \to (h \to \mu \tau) jj$ channel at the HL-LHC are contrasted with the current and future low-energy constraints from the anomalous magnetic moment and electric dipole moment of the muon, as well as with other LFV observables, such as $\tau\to 3\mu$ and $\tau\to \mu\gamma$. We also study the LFV prospects of a generic beyond the Standard Model neutral Higgs boson ($H$) with a mass in the range of $m_{H}\in [20,800]~$GeV and give the projected model-independent upper limits on the VBF production cross-section of $Hjj$ times the branching ratio of $H\to \mu\tau$ at the HL-LHC. We interpret these results in the context of a two-Higgs doublet model as a case study.