The Flavour Puzzle from an Orbifold GUT Perspective

Neutrino masses and mixings are very different from quark masses and mixings. This puzzle is a crucial hint in the search for the mechanism which determines fermion masses in grand unified theories. We study the flavour problem in an SO(10) GUT model in six dimensions compactified on an orbifold. Three sequential families are localized at three branes where SO(10) is broken to its three GUT subgroups. Their mixing with bulk fields leads to large neutrino mixings as well as small mixings among left-handed quarks. The small hierarchy of neutrino masses is due to the mismatch between up-quark and down-quark mass hierarchies. Talk given at the Fujihara Seminar Neutrino Mass and Seesaw Mechanism, KEK, Japan, February 2004 1 Gauge unification in six dimensions The symmetries and the particle content of the standard model (SM) point towards grand unified theories (GUTs) as the next step in the unification of all forces. Leftand right-handed quarks and leptons can be grouped in three SU(5) multiplets [1], 10 = (qL, u c R, e c R) , 5 ∗ = (dcR, lL) , 1 = ν c R , (1) or, alternatively, in two SU(4)× SU(2)× SU(2) multiplets [2], (4, 2, 1) = (qL, lL) , (4 , 1, 2) = (ucR, d c R, ν c R, e c R) . (2) All quarks and leptons of one generation are unified in a single multiplet in the GUT group SO(10) [3], 16 = 10+ 5 + 1 = (4, 2, 1) + (4, 1, 2) . (3) The group SO(10) contains two different SU(5)×U(1) subgroups, corresponding to ordinary and ‘flipped’ SU(5) [4], where right-handed upand down-quarks are interchanged, yielding another viable GUT group. Together with the seesaw mechanism [5], whose twenty-fifth anniversery is celebrated at this symposium, grand unified theories provide an attractive extension of the standard model, which can also account for the observed smallness of neutrino masses. In ordinary four-dimensional (4D) grand unified models, the breaking of the GUT symmetry groups to the standard model group GSM = SU(3)×SU(2)×U(1) requires a complicated Higgs sector, and considerable effort is needed to achieve the wanted gauge symmetry breaking together with a description of fermion masses and mixings that is consistent with experimental data. Higher-dimensional theories offer new possibilities for gauge symmetry breaking in connection with the compactification to four dimensions. A simple and elegant scheme, leading to chiral fermions in four dimensions, is the compactification on orbifolds, first considered in string theories [6, 7], and recently revived in the context of effective field theories in higher dimensions [8]. Orbifold compactifications lead generically to ‘split multiplets’, i.e. incomplete representations of the underlying GUT symmetry, which provides a natural mechanism to split the light weak doublet from the heavy colour triplet Higgs fields. In the following we shall consider a supersymmetric SO(10) model in 6D 1 and discuss its flavour structure [11]. Consider now the gauge theory with symmetry group SO(10) in 6D with N = 2 supersymmetry. The gauge fields VM(x, y, z), with M = μ, 5, 6, x 5 = y, x = z, and the For SO(10) models in 5D see Refs. [10]. 2