Proton Stability in Six Dimensions

Abstract

We show that Lorentz and gauge invariance explain the long proton lifetime within the standard model in six dimensions. The baryon-number violating operators have mass dimension 15 or higher. Upon TeV-scale compactification of the two universal extra dimensions on a square T 2 /Z2 orbifold, a discrete subgroup of the 6-dimensional Lorentz group continues to forbid dangerous operators.

Chiral Compactification on a Square

“…In Ref. [1], it has been shown that for the standard model in six dimensions the Z 8 symmetry ensures a lifetime for the proton longer than the current experimental bounds, even in the presence of baryon number violation at the TeV scale. Another implication is that Majorana masses are forbidden (the implications for neutrino masses are discussed in Ref.…”

“…This is a consequence of the sixdimensional Lorentz symmetry, or more precisely of the invariance under rotations by π/2 in the (x 4 , x 5 ) plane. In the context of the T 2 /Z 4 orbifold [1], the Z 8 symmetry is the group of rotations by π/2 around the center of T 2 . From the point of view of the folded square, Z 8 is an internal symmetry, with fermions carrying discrete charge q = Σ 45 /2 + n, where Σ 45 has eigenvalue ∓1 for the ± L chiralities, and ±1 for the ± R chiralities.…”

“…The field decomposition in Kaluza-Klein (KK) modes is given in [16] for the case where the parallelogram is a rectangle. The T 2 /Z 4 orbifold, which is a compactification on a square, has the merit of automatically preserving a Z 8 subgroup of the six-dimensional Lorentz symmetry [1] which ensures a long proton lifetime, and forces the neutrino masses to be of the Dirac type [17]. In a different context, the T 2 /Z 4 orbifold was shown to allow the Higgs doublet be part of a G 2 gauge field [4].…”

“…Quantum field theory in six dimensions has been studied in connection to various alternatives for physics beyond the standard model, and was shown to provide explanations for proton stability [1], the origin of electroweak symmetry breaking [2,3,4,5], the number of fermion generations [6,7,8,9,10,11], and the breaking of grand unified gauge groups [12,13,14].…”

“…(2.35), but the integers n i = 0, 1, 2, 3 and l i = 0, 1 that determine the boundary conditions may differ for different fields, and are therefore labeled by a flavor index i. 1 The most general interactions involving these fields which do not involve derivatives are of the type…”