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The Type-I seesaw model is a common extension to the Standard Model thatdescribes neutrino masses. The Type-I seesaw introduces heavy right-handedneutrinos with Majorana mass that transform as Standard Model electroweak gaugesinglets. We initially study a case with two right-handed neutrinos called the3-2 model. At an energy scale above the right-handed neutrinos, the effectiveneutrino mass matrix is rank degenerate implying the lightest neutrino ismassless. After considering renormalization effects below the two right-handedneutrinos, the effective neutrino mass matrix remains rank degenerate. Next, westudy a model with three right-handed neutrinos called the 3-3 model. Above theenergy scale of the three right-handed neutrinos, we construct the effectiveneutrino mass matrix to be rank degenerate. After solving for therenormalization effects to energies below the three right-handed neutrinos, wefind the rank of the effective neutrino mass matrix depends on the kernelsolutions of the renormalization group equations. We prove for the simplestkernel solutions the effective neutrino mass matrix remains rank degenerate.

Renormalization group effects for a rank degenerate Yukawa matrix and the fate of the massless neutrino