Minimality Condition and Atmospheric Neutrino Oscillations

Abstract

A structure is proposed for the mass matrices of the quarks and leptons that arises in a natural way from the assumption that the breaking of SO͑10͒ gauge symmetry is achieved by the smallest possible set of vacuum expectation values. This structure explains well many features of the observed spectrum of quarks and leptons. It reproduces the Georgi-Jarlskog mass relations and leads to a charm quark mass in reasonable agreement with data. It also predicts a large mixing angle between n m and n t , as suggested by atmospheric neutrino data. The mixing angles of the electron neutrino are predicted to be small. [S0031-9007(98)06830-6] PACS numbers: 12.15.Ff, 12.10.Dm, 12.60.Jv, 14.60.Pq In this Letter we propose a structure for the quark and lepton mass matrices that arises naturally in supersymmetric SO͑10͒ from the simple assumption that SO͑10͒ is broken to the standard model by the smallest possible set of vacuum expectation values (VEVs). This structure reproduces many of the features of the known fermion mass spectrum. It also predicts a large value for the n m 2 n t mixing angle, as is suggested by the atmospheric neutrino data [1]. Usually this angle is small (or not predicted) in grand unified models, but in the present model its large value has a simple group-theoretical explanation.The smallest set of vacuum expectation values that can break SO͑10͒ to the standard model consists of one adjoint (45) and one pair of spinors (16 1 16) [2]. The spinor pair breaks the rank of the group from 5 to 4 and provides superlarge masses for the right-handed neutrinos. The adjoint completes the breaking of SO͑10͒ to the standard model (SM) group SU͑3͒ 3 SU͑2͒ 3 U͑1͒ and produces the "doublet-triplet splitting"-that is, gives superlarge mass to the color-triplet partners of the SM Higgs doublets, while leaving those doublets light.Our assumption of minimality requires that there is only one adjoint Higgs. It has recently been shown that this is enough to break SO͑10͒ with no fine-tuning, while preserving gauge-coupling unification [3]. Besides its economy, having only one adjoint seems to be desirable in the context of perturbative heterotic string theory where there are limitations on multiple adjoints [4]. If there is only one adjoint, its VEV is fixed to be in the B-L direction, as required by the Dimopoulos-Wilczek mechanism for doublet-triplet splitting [3,5]. This severely constrains the possibilities for constructing realistic quark and lepton masses. (For other approaches that generate mass matrix textures in SO͑10͒ utilizing an extended Higgs sector see [6].) In "minimal SO͑10͒" the quark and lepton masses come from the operators 16 i 16 j 10 H , where i and j are family indices and subscript H denotes a Higgs field. This leads to the "naive SO͑10͒ relations": N U~D L. Here U, D, L, and N denote, respectively, the Dirac mass matrices for the up quarks, down quarks, charged leptons, and neutrinos. U~D would imply vanishing Cabibbo-Kobayashi-Maskawa angles and m 0 c ͞m 0 t m 0 s ͞m 0 b , which is off by 1 order o...

Order and anarchy hand in hand in 5D SO(10)

“…There are several SO(10) models, in both renormalizable [25][26][27][28][29][30][31][32][33][34][35][36][37][38] and nonrenormalizable [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] versions (see [56,57] for reviews), where new ingredients are added either to reduce the number of free parameters or to reduce their relevant range. In the first case the predictability of the model is increased, while in the second case the model becomes more natural.…”

Precision test of a Fermion mass texture

“…In such models, a large leptonic mixing angle accounting for the atmospheric neutrino anomaly originates from a sizeable (2,3) entry in the charged lepton mass matrix. The GUT symmetry then forces the (3,2) element in the down quark matrix to be of the same order of magnitude [4]. However we note that the original symmetric structure can also lead, very naturally, to a large neutrino mixing angle [5].…”

Neutrino mass and New physics

“…Large lepton mixing in these models follows from the charged lepton mass matrix in the symmetry basis which should be left-right non-symmetric [120]. This does not contradict the grand unification since in GUT models such as SU (5) is nearly diagonal, one obtains the large 2-3 lepton mixing.…”