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It was shown recently that the original SU(5) theory of Georgi and Glashow,augmented with an adjoint fermionic multiplet 24_F, can be made compatible bothwith neutrino masses and gauge coupling unification. In particular, the modelpredicts that either electroweak-triplet states are light, within the reach ofthe Large Hadron Collider (LHC), or proton decay will become accessible at thenext generation of megaton-scale facilities. In this paper, we present thecomputation of the correlation function between the electroweak-triplet massesand the unification scale at the next-to-next-to-leading-order (NNLO). Such anaccuracy on the theory side is necessary in order to settle the convergence ofthe perturbative expansion and to match the experimental precision on thedetermination of the electroweak gauge couplings at the Z-boson mass scale.

Unification scale vs. electroweak-triplet mass in the SU(5) + 24_F model at three loops