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...

The conclusions of the Physics Working Group of the International Scoping Study of a future Neutrino Factory and super-beam facility (the ISS) are presented. The ISS was carried out by the international community between NuFact05, (the 7th International Workshop on Neutrino Factories and Super-beams, Laboratori Nazionali di Frascati, Rome, 21-26 June 2005) and NuFact06 (Ivine, CA, 24-30 August 2006). The physics case for an extensive experimental programme to understand the properties of the neutrino is presented and the role of high-precision measurements of neutrino oscillations within this programme is discussed in detail. The performance of second-generation super-beam experiments, beta-beam facilities and the Neutrino Factory are evaluated and a quantitative comparison of the discovery potential of the three classes of facility is presented. High-precision studies of the properties of the muon are complementary to the study of neutrino oscillations. The Neutrino Factory has the potential to provide extremely intense muon beams and the physics potential of such beams is discussed in the final section of the report.

Possible alternatives to tri-bimaximal mixing are presented based on other symmetry principles, and their predictions for |U e3 |, sin 2 θ 12 and sin 2 θ 23 are compared to the present neutrino mixing data. In some cases perturbations are required to give better agreement with the data, and the use of a minimal approach is illustrated. Precise experimental determinations of the mixing parameters will be required to decipher the correct mixing pattern and to pin down the appropriate flavor symmetry. *

We analyze in detail the predictions of "trimaximal" neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually can have the same forms as for tri-bimaximal mixing. The phenomenology of these alternative scenarios and their mixing angle and CP phase correlations are studied. We emphasize how trimaximal mixing scenarios can be distinguished experimentally from broken tri-bimaximal mixing.

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It has recently been shown how to break SO(10) down to the standard model in a realistic way with only one adjoint Higgs field. The expectation value of this adjoint must point in the BϪL direction. This has consequences for the possible form of the quark and lepton mass matrices. These consequences are explored in this paper, and it is found that one is naturally led to consider a particular form for the masses of the heavier generations. This form implies typically that there should be large ͑nearly maximal͒ mixing of the and neutrinos. An explanation that does not involve large tan␤ also emerges for the fact that b and are light compared to the top quark. ͓S0556-2821͑98͒01413-1͔

A complete set of fermion and Higgs superfields is introduced with well-defined SO(10) properties and U(1)xZ2xZ2 family charges from which the Higgs and Yukawa superpotentials are constructed. The structures derived for the four Dirac fermion and right-handed Majorana neutrino mass matrices coincide with those previously obtained from an effective operator approach. Ten mass matrix input parameters accurately yield the twenty masses and mixings of the quarks and leptons with the bimaximal atmospheric and solar neutrino vacuum solutions favored in this simplest version.

We have surveyed leptonic and grand unified models of neutrino masses and mixings in the literature which are still viable and give numerical predictions for the reactor angle,