Unification through extra dimensions at two loops

The presence of an extra dimension of size R ≡ M−1 c introduces corrections of order (μ/Mc)α to the gauge and Yukawa couplings and accelerates their running at scales μ larger than Mc. This could result in a grand unification scale MX ≈ 20Mc. We study the corrections at the two-loop level. We find corrections of order (μ/Mc)α 2 for the gauge couplings and of order (μ/Mc) 2α2 for the Yukawa couplings. Therefore, in the Yukawa sector one and two-loop contributions can be of the same order below MX . We show that in the usual scenarios the dominant gauge and Yukawa couplings are decreasing functions of the scale, in such a way that (μ/Mc)α becomes approximately constant and two-loop contributions introduce just a 30% correction which does not increase with the scale.