Triplet-doublet Splitting, Proton Stability and Extra Dimension

TL;DR

The paper addresses the challenge of achieving gauge coupling unification together with triplet-doublet Higgs splitting in SU(5) grand unification by embedding the theory in five dimensions on the orbifold $S^1/(Z_2 × Z_2')$. A 5D SUSY SU(5) model is constructed with a bulk vector multiplet and two hypermultiplets, placing the three SM families on a 4D wall so that the MSSM emerges after compactification. A non-universal parity assignment breaks SU(5) to the SM and projects out the triplet Higgs zero modes, realizing triplet-doublet splitting and yielding unification relations $g_3 = g_2 = g_1 = g_U$ and $f_d = f_e = f_D$ at the unification scale, with the compactification scale $M_C = 1/R$ near $M_X \approx 2.1 × 10^{16}$ GeV. Proton stability is discussed, with possible exponential suppression from brane recoil reducing KK-mode couplings, though several model-building challenges remain, including the $\mu$ term, SUSY breaking, and brane dynamics.

Abstract

We propose a new possibility to reconcile the coupling unification scenario with the triplet-doublet mass splitting based on a 5-dimensional supersymmetric model with SU(5) gauge symmetry. It is shown that the minimal supersymmetric standard model is derived on a 4-dimensional wall through compactification on $S^1/(Z_2 \times Z_2')$.