Fermion masses, neutrino oscillations, and proton decay in the light of superKamiokande

Abstract

Within the framework of unified gauge models, interactions responsible for neutrino masses can also provide mechanisms for nucleon instability. We discuss their implications concretely in the light of recent results on neutrino oscillation from the SuperKamiokande collaboration. We construct a predictive SO(10)-based framework that describes the masses and mixing of all quarks and leptons. An overconstrained global fit is obtained, that makes five successful predictions for quarks and charged leptons. The same description provides agreement with the SuperK results on atmospheric neutrinos and typically supports a small-angle MSW mechanism. We find that current limits on nucleon stability put significant stress on the framework. Further, a distinctive feature of the SO(10) model developed here is the likely prominence of the μ⁺K⁰ mode in addition to the $\text{ν}\text{K}{}^{\mathrm{+}}$ mode of proton decay. Thus improved searches in these channels for proton decay will either turn up events, or force us outside this circle of ideas.

Introduction

Recent SuperKamiokande observations on atmospheric neutrinos [1] establish the oscillation of ν_μ to ν_τ with a mass splitting $\text{δm}{}^2\text{∼(10}{}^{\mathrm{-2}}\text{to}\text{10}{}^{\mathrm{-3}}\text{)}$ eV² and an oscillation angle sin²2θ_μτ^osc=(0.82−1.0). To be more precise, the observations do not directly exclude oscillation into some other ν_X, as long as it is not to ν_e, but Occam's razor and the framework adopted in this paper suggest X=τ, and we shall assume that in what follows, without further comment. These observations clearly require new physics beyond what is usually contemplated in the Standard Model.

As we shall presently discuss, a tau neutrino mass consistent with the observed oscillations fits extremely naturally into the framework supplied by unified gauge theories of the strong, weak, and electromagnetic interactions [2], [3], [4] that includes the symmetry structure G₂₂₄=SU(2)_L×SU(2)_R×SU(4)_C [2], [3], the minimal such symmetry being SO(10) [5], [6]. In this framework, the low-energy degrees of freedom need be no larger than the Standard Model. Neutrino masses appear as effective non-renormalizable (dimension 5) operators.

Unified gauge theories were already very impressive on other grounds. They combine the scattered multiplets of the Standard Model (five per family) into a significantly smaller number (two for SU(5), one for SO(10)). They rationalize the otherwise bizarre-looking hypercharge assignments in the Standard Model [2], [3], [4]. Finally, especially in their supersymmetric version [7], they account quantitatively for the relative values of the strong, weak, and electromagnetic couplings [8], [9].

This last feat is accomplished by renormalizing the separate couplings down from a single common value at a unification scale, taking into account the effects of vacuum polarization due to virtual particles, down to the much lower mass scales at which they are observed experimentally. A by-product of this overconstrained, and singularly successful, calculation, is to identify the mass scale at which the unified symmetry is broken, to be M_U∼2×10¹⁶ GeV [9].

This value is interesting in several respects. First, from data and concepts purely internal to gauge theories of particle interactions, it brings us to the threshold of the fundamental scale of quantum gravity, namely the Planck mass 2×10¹⁸ GeV (in rational units). Reading it the other way, by demanding unification, allowing for both the classical power-law running of the gravitational coupling and the quantum logarithmic running of gauge couplings, we obtain a roughly accurate calculation of the observed strength of gravity.

Second, it sets the scale for phenomena directly associated with unification but forbidden in the Standard Model, notably nucleon decay and neutrino masses. Prior to the SuperKamiokande observations, the main phenomenological virtues of the large value of the unification mass scale were its negative implications. It explained why nucleon decay is rare, and neutrino masses are small, although both are almost inevitable consequences of unification. Now the scale can also be positively identified, at least semi-quantitatively.

Indeed, any unification based on G₂₂₄ [2], [3] requires the existence of right-handed neutrinos ν^R. When G₂₂₄ is embedded in SO(10), ν^R fills out, together with the 15 left-handed quark and lepton fields in each Standard Model family, the 16-dimensional spinor representation of SO(10). The ν^R are Standard Model singlets, so that they can, and generically will, acquire large Majorana masses at the scale where unified SO(10) symmetry breaks to the Standard Model SU(3)×SU(2)×U(1). The ordinary, left-handed neutrinos couple to these ν^R much as ordinary quarks and leptons couple to their right-handed partners, through SU(2)×U(1) non-singlet Higgs fields. For the quarks and leptons, condensation of those Higgs fields transforms such interactions directly into mass terms. For neutrinos the effect of this condensation is slightly more involved. As mentioned, the ν^R have an independent, and much larger, source of mass. As a result, through the “see-saw” mechanism [10], [11], [12], the effective masses for the left-handed neutrinos, acquired through their virtual transitions into ν^R and back, are predictably tiny.

In this paper we do two things. First, we flesh out with quantitative detail the rough picture just sketched. Its most straightforward embodiment leads to the hierarchical pattern m_νe≪m_νμ≪m_ντ, and to a value of m_ντ very consistent with the SuperK observations, interpreted as ν_μ–ν_τ oscillations. We demonstrate that the large mixing angle observed does not force us to swerve from this straightforward direction. Indeed, it can arise rather plausibly in the context of ideas which have been applied successfully to understanding quark masses and mixings. Motivated by the success of the circle of ideas mentioned above, we insist that the pattern of neutrino masses and mixings should be discussed together with those of the quarks and charged leptons, and not in isolation. A simple and predictive SO(10)-based mass structure that describes the observed masses and mixings of all fermions including those of the neutrinos will be presented and analyzed. We thus demonstrate by example how the large ν_μ–ν_τ oscillation angle can be obtained quite naturally along with a large hierarchy in the ν_μ–ν_τ masses. (This is in contrast to several recent attempts where such a large oscillation angle is explained as a consequence of the near degeneracy of the ν_μ–ν_τ system. The bulk of the papers in Refs. [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54] belong to this category.)¹ In this scheme, ν_e–ν_μ oscillation drives the small angle MSW explanation [55], [56] of the solar neutrino puzzle.

Second, we revisit a previously noted link between neutrino masses and nucleon decay, in the framework of supersymmetric SO(10) unified models [57]. Previously, motivated in part by possible cosmological indications for a hot dark matter component, we used numerical estimates for m_ντ∼1 eV, considerably larger than are now favored by the SuperK result (∼1/20 eV). This amounts to an increase in the Majorana mass of ν^R_τ compared to previous work, and correspondingly an increase in the strength of the neutrino mass related d=5 proton decay rate. Another important change is caused by the large ν_μ–ν_τ oscillation angle suggested by the SuperK result. With hierarchical neutrino masses, we will argue, their result strongly suggests substantial mixing in the charged lepton (μ–τ) sector. That, in turn, affects the strength and the flavor structure not only of the neutrino related, but also of the standard d=5 proton decay operators induced by the exchange of color triplet partners of the electroweak Higgs doublets [58], [59]. These adjustments in our expectations for proton decay turn out to be quite significant quantitatively. They considerably heighten the tension around nucleon decay: either it is accessible, or the framework fails.

As an accompanying major result, we observe that, in contrast to the minimal supersymmetric SU(5) model for which the charged lepton mode p→μ⁺K⁰ has a negligible branching ratio (∼10⁻³, see text), for the SO(10) model developed here the corresponding branching ratio should typically lie in the range of 20 to even 50%, if the relevant hadronic matrix elements have comparable magnitudes. This becomes possible because of the presence of the new d=5 proton decay operators mentioned above, which are related to neutrino masses. Thus the μ⁺K⁰ mode, if observed, would provide an indication in favor of an SO(10) model of the masses and mixings of all fermions including neutrinos, as developed here.

This paper is organized as follows. In Section 2, we discuss the scale of new physics implied by the SuperK observations. In Section 3 we describe a caricature model that accommodates large neutrino oscillation angle as suggested by SuperK without assuming neutrino mass degeneracy. Section 4 is devoted to a more ambitious SO(10) model that accounts for the masses of second and third generation quarks and leptons including the large neutrino oscillation angle. In Section 5 we suggest, by way of example, a predictive way to incorporate the first family fermions into the SO(10) scheme that retains the success of Section 4, leading to a total of eight successful predictions for the masses and the mixings of the fermions including the neutrinos, and supports a small angle MSW mechanism. In Section 6 we discuss the issue of proton decay in the context of neutrino masses. Four appendices contain relevant technical details of our proton decay calculations including unification scale threshold corrections to α₃(m_Z). Finally, a summary of our results and some concluding remarks are given in Section 7².