Radiative $\mu -\tau$ Corrections and Renormalization of Neutrino Mass Operators in Type II Seesaw Models

We explore the impact of radiative $\mu -\tau$ corrections on the renormalization of neutrino mass operators in the Type II Seesaw framework, incorporating both dimension-five and dimension-six operators. Using renormalization group equations (RGE), we analyze the evolution of flavor coupling matrices and their deviations from $\mu -\tau$ symmetric configurations due to quantum corrections. Given the stringent constraints from the Large Hadron Collider (LHC) on the triplet scalar masses and couplings, we examine how these bounds influence the viability of $\mu -\tau$ symmetric seesaw models. Our analysis highlights the interplay between high-scale $\mu -\tau$ symmetry predictions and low-scale phenomenology, revealing whether radiative corrections remain within experimentally allowed limits.