Probing grand unification with fermion masses,neutrino oscillations and proton decay

It is noted that a set of facts points to the relevance in four dimensions of conventional supersymmetric unification based on minimally a string-unifiedG(224) symmetry, or maximallySO(10). These include: (i) the observed family structure, (ii) quantization of electric charge, (iii) meeting of the three gauge couplings, (iv) neutrino oscillations (in particular the value of δm ²(νμ−δ _τ), suggested by SuperK), (v) the intricate pattern of the masses and mixings of the fermions, including the smallness ofV _cb and the largeness ofθ _μνμτ ^osc , and (vi) the need for B-L as a generator to implement baryogenesis (via leptogenesis). A concrete proposal is presented within a predictiveSO(10)/G(224) framework that successfully describes the masses and mixings of all fermions, including the neutrinos — with eight predictions, all in agreement with observation. Within this framework, a systematic study of proton decay is carried out, which (a) pays special attention to its dependence on the fermion masses, (b) limits the threshold corrections so as to preserve natural coupling unification, and (c) uses recently improved values of the matrix element and renormalization effects. Allowing for both minimal supersymmetric standard model (MSSM) and its proposed variant, the so-called extended supersymmetric standard model (ESSM), as effective low-energy the ories, the study shows that a conservative upper limit on the proton lifetime is about (l–2)× 10³⁴ years, with ·⁻K⁺ being the dominant decay mode, and quite possibly μ⁺ K ⁰ ande ⁺π⁰ being prominent. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten ought to reveal proton decay. For comparison, some alternatives to the conventional approach to unification pursued here are mentioned at the end. Invited paper presented at the International Summer School held at ICTP, Trieste (June, 2001) and at WHEPP-7 Conference, Allahabad, India (January, 2002). This is an updated version of the paper presented at the Erice School (September, 2000), hep-ph/0106082.     

Hierarchical fermion masses from grand unification

A mechanism is presented for generating fermion masses as a reflection of the superheavy fermions existing in a class of grand unified theories. By means of it we propose a way of understanding how, giving a driving mass term for the top-generation, the charm-generation mass results as a relative first-order perturbation in the unified gauge coupling g²/4π ≈ 10^?2, and the up-generation mass as a second-order perturbation. An illustrative calculation of the charm-generation mass is described in a model based on E₆.     

Links between neutrino oscillations,leptogenesis, and proton decay within supersymmetric grand unification

Evidence in favor of supersymmetric grand unification including that based on the observed family multiplet-structure, gauge coupling unification, neutrino oscillations, baryogenesis, and certain intriguing features of quark-lepton masses and mixings is noted. It is argued that attempts to understand (a) the tiny neutrino masses (especially Δm ²(v ₂ – v₃)), (b) the baryon asymmetry of the Universe (which seems to need leptogenesis), and (c) the observed features of fermion masses such as the ratiom _b/m_τ, the smallness ofV _cb and the maximality of seem to select out the route to higher unification based on an effective string-unifiedG(224) =SU(2)_L ×SU(2)_R ×SU(2)^c orSO(10)-symmetry that should be operative in 4D, as opposed to other alternatives. A predictiveSO(10)/G(224)-framework possessing supersymmetry is presented that successfully describes the masses and mixings of all fermions including neutrinos. It also accounts for the observed baryon asymmetry of the Universe by utilizing the process of leptogenesis, which is natural to this framework. It is argued that a conservative upper limit on the proton lifetime within thisSO(10)/G(224)-framework, which is so far most successful, is given by x 10³⁴ years. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten (compared to SuperK) ought to reveal proton decay. Implications of this prediction for the next-generation nucleon decay and neutrino-detector are noted.     

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists a simple relation between the quark and lepton mixings, which supports the idea of grand unification and probes the underlying robust bimaximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bimaximal, predicting theta(sol)+theta(C)=pi/4, where theta(C) is the Cabibbo angle, theta(atm)+theta(CKM)(23)=pi/4 and theta(MNS)(13) approximately theta(CKM)(13) approximately O(lambda(3)), in perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable of explaining this flavor mixing pattern and inducing the measured quark and lepton masses is outlined.     

The link between neutrino masses and proton decay in supersymmetric unification

Following recent joint works with K. Babu and F. Wilczek, I stress here that supersymmetric unification, based on symmetries like SO(10) or a string-derived G(224)=SU(2) _L ×SU(2) _R ×SU(4) ^C possesses some crucial features that are intimately linked to each other. They are (a) gauge-coupling unification; (b) the masses and mixings of all fermions, including especially the neutrinos; and last but not least (c) proton decay. In this context, it is noted that the value of $m_{v_L^\tau } \sim 1/20{\text{ }}eV$ , suggested by the Super-Kamiokande result, goes extremely well with the unification-hypothesis, based on the ideas of (i) SU(4)-color, (ii) left-right symmetry, and (iii) supersymmetry. A concrete proposal is presented within an economical SO(10)-framework that makes five successful predictions for the masses and mixings of the quarks and the charged leptons. The same framework explains why the ν_π?ν_τ oscillation angle is so large $(\sin ^2 2\theta _{\nu _\mu \nu _\tau }^{osc} \approx 0.82 - 0.96)$ and yet V _bc is so small (≈0.04), both in accord with observation. The influence of the masses of the neutrinos and of the charged fermions on proton decay is discussed concretely, within this framework. The $\bar \nu K^ + $ mode is expected to be dominant for SUSY SO(10) as well as SU(5). A distinctive feature of the SO(10) model, however, is the likely prominence of the μ⁺ K ⁰ mode, which, for SU(5), is highly suppressed. Our study shows that while current limits on the rate of proton decaying into $\bar \nu K^ + $ are compatible with theoretical expectations, improvements in these limits by a factor of 5–10 should either turn up events, or else the SO(10)-framework described here, which is otherwise so successful, will be in jeopardy. Prominence of theμ⁺ K ⁰ mode, if observed, will be most significant in that it will reveal the intriguing link that exists between neutrino masses and proton decay in the context of supersymmetric unification.     

New type of seesaw mechanism for neutrino masses

In a wide class of unified models there is an additional (and possibly dominant) term in the neutrino mass formula that under the simplest assumption takes the form M(nu)=(M(N)+M(T)(N))u/M(G), where M(N) is the neutrino Dirac mass matrix, and u=O(M(W)). This makes possible highly predictive models. A generalization of this form yields realistic neutrino masses and mixings more readily than the usual seesaw formula in some models. The conditions for resonant enhancement of leptogenesis can occur naturally in such models.     

Barygenesis without grand unification

A mechanism is pointed out to generate cosmological baryon number excess without resorting to grand unified theories. The lepton number excess originating from Majorana mass terms may transform into the number excess through the unsuppressed baryon number violation of electroweak processes at high temperatures.     

The geometry of grand unification

Arguments are presented which lead to the conclusion thatSU(3, 2) is the grand unification gauge group (GUGG). The gauge theory includes all known forces. We incorporated supersymmetry within the framework of the gauge theory and show how the theory may be quantized.     

F-theory grand unification at the colliders

We predict the exact gaugino mass relation near the electroweak scale at one loop for gravity mediated supersymmetry breaking in F-theory SU(5) and SO(10) models with UY(1) and U(1)_B−L fluxes, respectively. The gaugino mass relation introduced here differs from the typical gaugino mass relations studied thus far, and in general, should be preserved quite well at low energy. Therefore, these F-theory models can be tested at the Large Hadron Collider and future International Linear Collider. We present two typical scenarios that satisfy all the latest experimental constraints and are consistent with the CDMS II experiment. In particular, the gaugino mass relation is indeed satisfied at two-loop level with only a very small deviation around the electroweak scale.     

Local grand unification in the heterotic landscape

We consider the possibility that the unification of the electroweak interactions and the strong force arises from string theory, at energies significantly lower than the string scale. As a tool, an effective grand unified field theory in six dimensions is derived from an anisotropic orbifold compactification of the heterotic string. It is explicitly shown that all anomalies cancel in the model, though anomalous Abelian gauge symmetries are present locally at the boundary singularities. In the supersymmetric vacuum additional interactions arise from higher‐dimensional operators. We develop methods that relate the couplings of the effective theory to the location of the vacuum, and find that unbroken discrete symmetries play an important role for the phenomenology of orbifold models. An efficient algorithm for the calculation of the superpotential to arbitrary order is developed, based on symmetry arguments. We furthermore present a correspondence between bulk fields of the orbifold model in six dimensions, and the moduli fields that arise from compactifying four internal dimensions on a manifold with non‐trivial gauge background.     

Isotopic grand unification with the inclusion of gravity

We introduce a dual lifting of unified gauge theories, the first characterized by theisotopies, which are axiom-preserving maps into broader structures with positive-definite generalized units used for the representation of matter under the isotopies of the Poincaré symmetry, and the second characterized by theisodualities, which are anti-isomorphic maps with negative-definite generalized units used for the representation of antimatter under the isodualities of the Poincaré symmetry. We then submit, apparently for the first time, a novel grand unification with the inclusion of gravity for matter embedded in the generalized positive-definite units of unified gauge theories while gravity for antimatter is embedded in the isodual isounit. We then show that the proposed grand unification provides realistic possibilities for a resolution of the axiomatic incompatibilities between gravitation and electroweak interactions due to curvature, antimatter and the fundamental space-time symmetries.