Natural suppression of proton decay in supersymmetric type III seesaw models

Supersymmetric Standard Model (MSSM) has two sources of rapid proton decay: (i) R-parity breaking terms and (ii) higher dimensional Planck induced B-violating terms; its extensions to include neutrino masses via the type I seesaw mechanism need not have the first of these problems due to the existence of B−L as a gauge symmetry but for sure always have the second one. If instead, neutrino masses are explained in a type III seesaw extension of standard model, an anomaly free gauge symmetry different from B−L is known to exist. In this note, it is shown that a realistic supersymmetric versions of this model can be constructed (MSSM as well as SUSY left–right with type III seesaw) which eliminate R-parity violating couplings and suppress Planck scale contributions to proton decay. The degree of suppression of the latter depends on the weak gauge group. For the left–right case, the suppression to the desired level is easily achieved.     

Phenomenology of the SU(3)_c\otimes SU(3)_L\otimes U(1)_X model with right-handed neutrinos

A phenomenological analysis of the three-family model based on the local gauge group with right-handed neutrinos is carried out. Instead of using the minimal scalar sector able to break the symmetry in a proper way, we introduce an alternative set of four Higgs scalar triplets, which combined with an anomaly-free discrete symmetry, produces a quark mass spectrum without hierarchies in the Yukawa coupling constants. We also embed the structure into a simple gauge group and show some conditions for achieving a low energy gauge coupling unification, avoiding possible conflict with proton decay bounds. By using experimental results from the CERN-LEP, SLAC linear collider, and atomic parity violation data, we update constraints on several parameters of the model. PACS 12.60.Cn, 12.15.Ff, 12.15.Mm     

Neutrino masses in the supersymmetric SU(3)C⊗SU(3)L⊗U(1)X model with right-handed neutrinos

The R-symmetry formalism is applied for the supersymmetric SU(3)_C⊗SU(3)_L⊗U(1)_X (3-3-1) model with right-handed neutrinos. For this kind of models, we study the generalization of the MSSM relation among R-parity, spin and matter parity. Discrete symmetries for the proton stable in this model are imposed, and we show that in such a case it is able to give leptons masses at only the tree level contributions required. A simple mechanism for the mass generation of the neutrinos is explored. We show that at the low-energy effective theory, the neutrino spectrum contains three Dirac fermions, one massless and two degenerate in mass. At the energy level where the mixing among them with the neutralinos is turned on, neutrinos obtain Majorana masses and correct the low-energy effective result which naturally gives rise to an inverted hierarchy mass pattern. This mass spectrum can fit the current data with minor fine-tuning. Consistent values for masses of the charged leptons are also given. In this model, the MSSM neutralinos and charginos can be explicitly identified in terms of the new constraints on masses which is not as in a supersymmetric version of the minimal 3-3-1 model. PACS 11.30.Er; 14.60.Pq; 14.60.-z; 12.60.Jv     

A novel string-derived $Z^\prime$ with stable proton,light neutrinos and R-parity violation

The standard model indicates the realization of grand unified structures in nature, and it can only be viewed as an effective theory below a higher energy cutoff. While the renormalizable standard model forbids proton decay mediating operators due to accidental global symmetries, many extensions of the standard model introduce such dimension 4, 5 and 6 operators. Furthermore, quantum gravity effects are expected to induce proton instability, indicating that the higher energy cutoff scale must be above 10¹⁶ GeV. Quasi-realistic heterotic string models provide the arena to explore how perturbative quantum gravity affects the particle physics phenomenology. An appealing explanation for the proton longevity is provided by the existence of an Abelian gauge symmetry that suppresses the proton decay mediating operators. Additionally, such a low scale U(1) symmetry should feature the following: it should allow for the suppression of the left-handed neutrino masses by a seesaw mechanism; allow for fermion Yukawa couplings to the electroweak Higgs doublets; be anomaly free; and finally be family universal. These requirements render the existence of such U(1) symmetries in quasi-realistic heterotic string models highly non-trivial. We demonstrate the existence of a U(1) symmetry that satisfies all of the above requirements in a class of left–right symmetric heterotic string models in the free fermionic formulation. The existence of the extra in the energy range accessible to future experiments is motivated by the requirement of adequate suppression of proton decay mediation. We further show that, while the extra U(1) forbids dimension 4 baryon number violating operators, it allows dimension 4 lepton number violating operators and R-parity violation.     

Proton and neutron decay rates in conventional and supersymmetric guts

We present a general calculation of the two-body decay rates of the nucleon, for the most general form of four-fermion ΔB = ΔL operators, in the framework of the SU(6) non-relativistic quark model. We have applied our general formulas to Higgs mediated decays in conventional and in supersymmetric SU(5) models. Lower bounds upon the exchanged particles masses are given. We point out that the hierarchies of branching ratios in decays mediated by Higgs bosons are different from those of gauge boson decay modes (in the former case, neutrinos modes are dominant). We give, in conclusion, an experimental way to distinguish non-supersymmetric GUTs from supersymmetric ones, if the nucleon decays via Higgs bosons.     

Gauge-Higgs unification in the left–right model

We construct a supersymmetric left–right model in four dimension with gauge-Higgs unification starting from a SU(3)_c×SU(4)_w×U(1)_B−L gauge symmetry in five dimension. The model has several interesting features, such as, the CKM mixings in the quark sector are naturally small while for the neutrino sector it is not, light neutrino masses can be generated via the seesaw mechanism in the usual way, and the model has a U(1)_R symmetry which naturally forbid dimension five proton decay operators. We also discuss the grand unification of our model in SO(12) in five dimensions.     

Dirac neutrino masses from generalized supersymmetry breaking

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the standard model with a generalized supersymmetry breaking sector. If the superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order.     

Grand unified theories without the desert

We present a grand unified theory (GUT) that has GUT fields with masses of the order of a TeV, but at the same time preserves (at the one-loop level) the success of gauge-coupling unification of the minimal supersymmetric standard model (MSSM) and the smallness of proton decay operators. This scenario is based on a five-dimensional theory with the extra dimension compactified as in the Randall-Sundrum model. The MSSM gauge sector and its GUT extension live in the 5D bulk, while the matter sector is localized on a 4D boundary.the is a test again     

Orbifold compactifications with three families of Su(3) ×Su(2) ×U(1)n

We construct several N = 1 supersymmetric three-generation models with SU(3)×SU(2)×U(1)ⁿ gauge symmetry, obtained from orbifold compactification of the heterotic string in the presence of constant gauge-background fields. This Wilson-line mechanism also allows us to eliminate extra colour triplets which could mediate fast proton decay.     

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.     

Minimal grand unification model in an anthropic landscape

It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lifetime is long enough to avoid the experimental bounds. These models are the truly minimal fine-tuned extensions of the standard model in the sense proposed by Davoudiasl et al.Received: 3 September 2004, Published online: 23 March 2005     

Neutrino masses in an extended gauge model with E6 particle content

Naturally light singlet neutrinos which mix with the usual doublet neutrinos are possible if the supersymmetric standard gauge model is extended to include a specific additional U(1) factor derivable from an E₆ decomposition. The low-energy particle content of the model is limited to the fundamental 27 representations of E₆.     

Sneutrino dark matter in gauged inverse seesaw models for neutrinos

Extending the minimal supersymmetric standard model to explain small neutrino masses via the inverse seesaw mechanism can lead to a new light supersymmetric scalar partner which can play the role of inelastic dark matter (IDM). It is a linear combination of the superpartners of the neutral fermions in the theory (the light left-handed neutrino and two heavy standard model singlet neutrinos) which can be very light with mass in ~5-20 GeV range, as suggested by some current direct detection experiments. The IDM in this class of models has keV-scale mass splitting, which is intimately connected to the small Majorana masses of neutrinos. We predict the differential scattering rate and annual modulation of the IDM signal which can be testable at future germanium- and xenon-based detectors.     

Proposal for a supersymmetric standard model

The fact that neutrinos are massive suggests that the minimal supersymmetric standard model (MSSM) might be extended in order to include three gauge-singlet neutrino superfields with Yukawa couplings of the type H2Lnuc. We propose to use these superfields to solve the mu problem of the MSSM without having to introduce an extra singlet superfield as in the case of the next-to-MSSM (NMSSM). In particular, terms of the type nuc H1H2 in the superpotential may carry out this task spontaneously through neutrino vacuum expectation values. In addition, terms of the type (nuc)3 avoid the presence of axions and generate effective Majorana masses for neutrinos at the electroweak scale. On the other hand, these terms break lepton number and R parity explicitly. For Dirac masses of the neutrinos of order 10(-4) GeV, eigenvalues reproducing the correct scale of neutrino masses are obtained.     

The Friedberg–Lee symmetry and minimal seesaw model

The Friedberg–Lee (FL) symmetry is generated by a transformation of a fermionic field q to q+ξz. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to N fermionic fields, we find that the number of independent fields is reduced to N−1 if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero.     

The supersymmetric Standard Models with decaying and stable dark matters

We propose two supersymmetric Standard Models (SMs) with decaying and stable dark matter (DM) particles. To explain the SM fermion masses and mixings and have a heavy decay DM particle S, we consider the Froggatt–Nielsen mechanism by introducing an anomalous U(1) _X gauge symmetry. Around the string scale, the U(1) _X gauge symmetry is broken down to a Z ₂ symmetry under which S is odd while all the SM particles are even. S obtains a vacuum expectation value around the TeV scale, and then it can three-body decay dominantly to the second/third family of the SM leptons in Model I and to the first family of the SM leptons in Model II. Choosing a benchmark point in the constrained minimal supersymmetric SM with exact R parity, we show that the lightest neutralino DM is consistent with the CDMS II experiment. Considering S three-body decay and choosing suitable parameters, we show that the PAMELA and Fermi-LAT experiments and the PAMELA and ATIC experiments can be explained in Model I and Model II, respectively.     

Massive and massless neutrinos on unbalanced seesaws

The observation of neutrino oscillations requires new physics beyond the standard model (SM).A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L x U(1)y gauge symmetry.The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix.Given p＞q,the rank of M is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues.The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model,independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M,and the q x q heavy Majorana neutrino mass matrix MR.In other words,the numbers of massive left- and right-handed neutrinos are fairly matched.A good example to illustrate this "seesaw fair play rule"is the minimal seesaw model with p ＝ 3 and q ＝ 2,in which one masslese neutrino sits on the unbalanced seesaw.     

Distinguishable RGE Running Effects Between Dirac Neutrinos and Majorana Neutrinos with Vanishing Majorana CP-Violating Phases

In a novel parametrization of neutrino mixing and in the approximation of τ-lepton dominance, we show that the one-loop renormalization-group equations （RGEs） of Dirac neutrinos are different from those of Majorana neutrinos even if two Majorana CP-violating phases vanish. As the latter can keep vanishing from the electroweak scale to the typical seesaw scale, it makes sense to distinguish between the RGE running effects of neutrino mixing parameters in Dirac and Majorana cases. The differences are found to be quite large in the minimal supersymmetric standard model with sizable tan β, provided the masses of three neutrinos are nearly degenerate or have an inverted hierarchy.     

Discrete gauge symmetry anomalies

It has been recently argued that quantum gravity effects strongly violate all non-gauge symmetries. This would suggest that all low energy discrete symmetries should be gauge symmetries, either continuous or discrete. Acceptable continuous gauge symmetries are constrained by the condition they should be anomaly free. We show here that any discrete gauge symmetry should also obey certain “discrete anomaly cancellation” conditions. These conditions strongly constrains the massles fermion content of the theory and follow from the “parent” cancellation of the usual continuous gauge anomalies. They have interesting applications in model building. As an example we consider the constraints on the Z_N “generalized matter parities” of the supersymmetric standard model. We show that only a few (including the standard R-parity) are “discrete anomaly free” unless the fermion content of the minimal supersymmetric standard model is enlarged.     

Baryogenesis,proton decay and fermion masses in supergravity guts

In realistic N = 1 supergravity theories with a gravitino mass of order 1 TeV, the reheat temperature after inflation is bounded to be no greater than 10⁸ GeV. We construct an N = 1 supergravity model with realistic fermion masses and mixings in which D = 5 operators are suppressed by a Peccei-Quinn symmetry. We compute the ensuing proton decay and show that the dominant modes involve strange particles in the final state. Efficient baryogenesis is induced by Higgs decay to massive right-handed neutrinos and we find an upper bound on the proton lifetime if the Higgs are light enough to be reheated.