Generalized 2HDM with wrong-sign lepton Yukawa coupling, in light of $g_{mu}-2$ and lepton flavor violation at the future LHC

To explain the observed muon anomaly and simultaneously evade bounds from lepton flavor violation in the same model parameter space is a long cherished dream. In view of a generalized Two Higgs Doublet Model, with a Yukawa structure as a perturbation of Type-X, we are able to get substantial parameter space satisfying this criteria. We are focusing on a region with {bf wrong-sign} lepton-Yukawa coupling which gives rise to an interesting phenomenological consequences. We found that in the wrong-sign region, it is possible to probe the low-mass pseudoscalar in flavor-violating decay mode with considerably better significance compared to the right-sign region. Performing a simple cut-based analysis we show that at 14 TeV run of the LHC with $300 fb^{-1}$ integrated luminosity, part of the model parameter space can be probed with significance $geq 5sigma$ which further improves with Artificial Neural Network analysis.