Doublet-Triplet Splitting and Fat Branes

We consider the doublet-triplet splitting problem in supersymmetric SU(5) grand unified theory in five dimensions where the fifth dimension is non-compact. We point out that an unnatural fine-tuning of parameters in order to obtain the light Higgs doublets is not required due to the exponential suppression of the overlap of the wave functions. e-mail address: [email protected]; JSPS Research Fellow. The grand unified theory (GUT) [1] is one of the most elegant scenarios in particle physics because of its aesthetic point of view and various interesting physical features. In particular, the success of the gauge coupling unification with the minimal supersymmetric standard model (MSSM) [2] motivates us to consider the supersymmetric (SUSY) GUT seriously. In GUT, there is a serious problem called “the doublet-triplet splitting problem”. After GUT symmetry breaking, the Higgs triplets and the Higgs doublets in general obtain the GUT scale mass because these belong to the same multiplet. This requires an unnatural fine-tuning of parameters to obtain the light Higgs doublets [3]. In the minimal SU(5) GUT case, the mass term MHH̄ is tuned for the coupling H̄ΣH (Σ: the adjoint under SU(5)) to obtain the Higgs doublet with weak scale mass, while leaving the Higgs triplets with GUT scale mass to avoid a fast proton decay by dimension five operators [4]. Many people have tried to solve this problem from various points of view [5]-[16]. Arkani-Hamed and Schmaltz [17] have proposed an interesting mechanism to generate exponentially small coupling in the context of extra dimensions. They discussed that the hierarchies of Yukawa couplings can be explained by the slight displacement of the standard model field wave functions inside four dimensional domain wall in higher dimensional space-time. Even if there is a parameter of order one in the fundamental theory, it is highly suppressed in the effective theory due to the small overlap of wave functions. In this letter, we apply this mechanism to the doublet-triplet splitting problem. It is pointed out that an unnatural fine-tuning of parameters to obtain the light Higgs doublets is not required in this scenario, i.e. at most the tuning of O(1) orders of magnitude. For simplicity, we consider the SUSY GUT in five dimensions where the fifth dimension is non-compact. The action of the Higgs sector is S = ∫