Studies on the phenomenological analysis of rare processes at next-generation particle colliders focus on the search for anomalous interactions in experimental scenarios such as photon-induced collisions and muon colliders. In particular, cross-section calculations and event simulations of the relevant processes are performed within frameworks such as extended Higgs sectors, large extra dimensions, and flavor-changing neutral currents. Detailed analyses are conducted using particle physics software tools like MadGraph, CalcHEP, FeynRules, Pythia, and ROOT to evaluate the detectability of new physics signals. These studies offer original theoretical contributions that aim to interpret experimental observations through the lens of effective field theories.