• GUT
• Minimal Dark Matter

The main objective of this work is to study the possibility of incorporating an accidentally stable SU(2) 5-plet (the candidate minimum DM (mDM)) into the GUT theory. Specifically, I first completed the preliminary part by confirming that the mass of the colourless 5-plet of SU(2) with zero hypercharges is about 14 TeV and then began a more specialised one with the aim of incorporating the mDM candidate into SU(5). First, I discovered that the smallest representation containing the 5-plet is the 200. Then I gave mass to the new particles in the 200 by spontaneously breaking SU(5) and analysed the conditions under which the couplings are unified at high energies. In the last part of the thesis, I studied the rich phenomenology of the UV completion of mDM. In particular: i) I analysed the problem of giving mass to neutrinos by constructing an effective operator capable of reproducing the Weinberg operator in the low-energy limit; ii) I calculated the decay of the new particles induced by a limited set of dim-6 operators in such a way as to be consistent with the BBN limits; iii) I analysed the gamma-ray and neutrino signals from the decay of the lightest particle of the 200 (the 5-plet of mDM) induced by the same dim-6 operators. After analysing the parameter space, we can conclude that once the 5-plet and other (predicted) fundamental particles are included, we can achieve unification and a coherent theory not excluded by any experimental searches.