Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 305 / 2 / f / Solution

The leptons consist ofwith charged-lepton Yukawa coupling $-{\overline{L}}_L{Y}_{e}H{e}_R+h.c.$

Adding gauge-singlet right-handed neutrinos ${\nu }_R\sim (1,1{)}_0$ permits the Dirac Yukawa couplingwhich gives $M_D=v{Y}_{\nu }/\sqrt{2}$. Because ${\nu }_R$ carries no Standard Model gauge charge, a Majorana mass term ${\nu }_R^{\mathsf{T}}C{M}_R{\nu }_R/2$ is also allowed. For $M_R\gg M_D$, the seesaw mechanism produces light neutrino masses of order $M_D{M}_R^{-1}{M}_D^{\mathsf{T}}$.