Non-renormalizable Operators Research Articles

Lorentz Violation: Motivation and New Constraints

We review the main theoretical motivations and observational constraints on Planck scale–suppressed violations of Lorentz invariance. After introducing the problems related to the phenomenological study of quantum gravitational effects, we discuss the main theoretical frameworks within which possible departures from Lorentz invariance can be described. In particular, we focus on the framework of effective field theory, describing several possible ways of including Lorentz violation therein and discussing their theoretical viability. We review the main low-energy effects that are expected in this framework. We discuss the current observational constraints on such a framework, focusing on those achievable through high-energy astrophysics observations. In this context, we present a summary of the most recent and strongest constraints on quantum electrodynamics with Lorentz-violating nonrenormalizable operators. Finally, we discuss the status of the field and its future perspectives.

Bs mixing phase and lepton flavor violation in supersymmetric SU(5)

The connection between Bs mixing phase and lepton flavor violation is studied in a supersymmetric SU(5) theory, in the light of the latest measurements thereof. The \U0001d4aa(1) phase, preferring a non-vanishing squark mixing, generically implies r→ (e + μ) γ and μ → eγ. In addition to the facts already well-known, stresses are put on the role of gaugino to scalar mass ratio at the GUT scale and the possible modifications due to Planck-suppressed non-renormalizable operators.

Electroweak vacua, collider phenomenology, and possible connection with dark energy

Higher dimensional non-renormalizable operators may modify the Standard Model Higgs potential in many interesting ways. Here, we consider the appearance of a second vacuum which may play an important role in cosmology. For the certain range of parameters, the usual second order electroweak phase transition is followed by a first order phase transition that may drive the late time accelerated expansion of the universe. Such a potential contains kink-like solutions which in turn can play a crucial role in reconstructing the global shape of the potential in colliders, as we explicitly demonstrate.

Theoretical framework forR-parity violation

We propose a theoretical framework for $R$-parity violation. It is realized by a class of Calabi-Yau compactification of heterotic string theory. Trilinear $R$-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to nonrenormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear $R$-parity violation is generated, but there are good reasons why it is small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All $R$-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear $R$-parity violating operators. $B\ensuremath{-}L$ breaking neutron decay is predicted.

Fermion masses and mixing in models withSO(10)×A4symmetry

We study the flavor sector in models where the three families of matter are unified in a (16, 3) representation of the SO(10)×A4 group. The necessary ingredients to realize tribimaximal mixing in the lepton sector are identified systematically. The nonrenormalizable operators contributing to the fermion mass matrices play an important role. We also present a mechanism to explain the interfamily mass hierarchy of quarks and charged leptons, which relies on a universal seesaw mechanism and is compatible with tribimaximal mixing. © 2008 The American Physical Society.

Flavor physics in SO(10) GUTs with suppressed proton decay due to gauged discrete symmetry

Generic SO(10) grand unified theory models suffer from the problem that Planck scale induced nonrenormalizable proton-decay operators require extreme suppression of their couplings to be compatible with present experimental upper limits. One way to resolve this problem is to supplement SO(10) by simple gauged discrete symmetries which can also simultaneously suppress the renormalizable R-parity violating ones when they occur and make the theory ''more natural.'' Here we discuss the phenomenological viability of such models. We first show that for both classes of models, e.g the ones that use 16{sub H} or 126{sub H} to break B-L (baryon minus lepton number) symmetry, the minimal Higgs content which is sufficient for proton-decay suppression is inadequate for explaining fermion masses despite the presence of all apparently needed couplings. We then present an extended 16{sub H} model, with three 10 and three 45 Higgs field, where is free of this problem. We propose this as a realistic and natural model for fermion unification and discuss the phenomenology of this model e.g. its predictions for neutrino mixings and lepton flavor violation.

Metastable gauged O'Raifeartaigh

We study the possibility of obtaining metastable supersymmetry breaking vacua in a perturbative gauge theory without singlet fields, thus allowing for scenarios where a grand unified symmetry and supersymmetry are broken by the same sector. We show some explicit SU(5) examples. The minimal renormalizable example requires the use of two adjoints, but it is shown to inevitably lead to unwanted light states. We suggest various alternatives, and show that the viable possibilities consist of allowing for non-renormalizable operators, of employing four adjoints or of adding at least one field in a different representation.

Lorentz-Violating Electrodynamics and the Cosmic Microwave Background

Possible Lorentz-violating effects in the cosmic microwave background are studied. We provide a systematic classification of renormalizable and nonrenormalizable operators for Lorentz violation in electrodynamics and use polarimetric observations to search for the associated violations.

Model-independent predictions for n and dn/d lnk from a broad class of inflationary models

We explore a well-motivated class of inflationary models from the particle physics point of view: those with a flat tree-level potential, where the radiative corrections cause the slow rolling of the inflaton and the running of the spectral index n. This includes typical SUSY inflation models (e.g. D-hybrid inflation). In the small-coupling regime the predictions for the size and running of n are remarkably neat and model independent, e.g. −dn/d ln k = (n − 1)2 ≪ 1. The fit to WMAP data gives the number of e-folds, Ne, as an output: Ne = 26+30−8, which is very encouraging. On the other hand, to account for the WMAP preliminary indication of a running n crossing n = 1, we find it extremely natural to incorporate non-renormalizable operators (only the dominant one is relevant), which automatically increase the running as demanded. The analysis is still very model independent and predicts a rapidly changing n at the initial scales, which then gets stabilized below n = 1.

NEUTRINO MASSES AND SUSY SU(5) GUT FLAVOR PREDICTIONS

The patterns of the flavor violating effects which are radiatively induced via the neutrino Yukawa couplings are analysed in realistic "minimal" SUSY SU (5) models, obtained by adding nonrenormalizable operators to the minimal one, in order to fix the fermion spectrum and suppress proton decay. We compare results for the three possible implementations of the seesaw mechanisms, i.e. of Type I, II and III.

Low intermediate scales for leptogenesis in supersymmetricSO(10)grand unified theories

A low intermediate scale within minimal supersymmetric $SO(10)$ GUTs is a desirable feature to accommodate leptogenesis. We explore this possibility in models where the intermediate gauge symmetry breaks spontaneously by (a) doublet Higgs scalars and also (b) by triplets. In both scenarios, gauge coupling unification requires the scale of left-right symmetry breaking (${M}_{R}$) to be close to the unification scale. This will entail unnaturally small neutrino Yukawa couplings to avoid the gravitino problem and allow successful leptogenesis. We point out that any one of three options---threshold corrections due to the mass spectrum near the unification scale, gravity induced nonrenormalizable operators near the Planck scale, or presence of additional light Higgs multiplets---can permit unification along with much lower values of ${M}_{R}$ as required for leptogenesis. In the triplet model, independent of these corrections, we find a lower bound on the intermediate scale, ${M}_{R}>{10}^{9}\text{ }\text{ }\mathrm{GeV}$, arising from the requirement that the theory must remain perturbative at least up to the GUT scale. We show that in the doublet model ${M}_{R}$ can even be in the TeV region which, apart from permitting resonant leptogenesis, can be tested at LHC and ILC.

Orbifold reduction of the quark-lepton symmetric model

We investigate the quark-lepton symmetric gauge group in five dimensions, with the gauge symmetry broken by a combination of orbifold compactification of the extra dimension and the Higgs mechanism. The gauge sector of the model is investigated and contrasted with the four dimensional case. We obtain lower bounds on the mass of the exotic gauge bosons, the inverse compactification scale and the exotic leptons. Light neutrinos are obtained without requiring any scale larger than a TeV. However an ultraviolet cutoff of order ${10}^{11}\text{ }\text{ }\mathrm{GeV}$ is required to suppress proton decay inducing nonrenormalizable operators.

Nonthermal production of dark matter from a late-decaying scalar field at an intermediate scale

We examine non-thermal dark matter production from a late-decaying scalar field, with a particular attention on non-renormalizable operators of D=5 through which the scalar field decays into the standard model particles and their superpartners. We show that almost the same number of superparticles as that of particles are generally produced from the decay. To avoid the gravitino overproduction problem, the decay is favored to proceed via interactions with an intermediate cut-off scale M << M_P. This should be contrasted to the conventional scenario using the modulus decay. The bosonic supersymmetry partner of the axion, i.e., saxion, is proposed as a natural candidate for such late-decaying scalar fields. We find that a right amount of the wino/higgsino dark matter with a mass of O(100) GeV is obtained for the saxion mass around the weak scale and axion decay constant, F_A = O(10^{9-12}) GeV.

The running spectral index as a probe of physics at high scales

The WMAP results on the scalar spectral indexn and its running with scale, though preliminary, open a very interesting window to physicsat very high energies. We address the problem of finding inflaton potentials well motivatedby particle physics which can accommodate WMAP data. We make a model independentanalysis of a large class of models: those with flat tree-level potentials lifted byradiative corrections, which cause the slow rolling of the inflaton and the running ofn. Thisincludes typical hybrid inflation models. In the small coupling regime the predictions for the size andrunning of n are remarkably neat, e.g. , and n doesnot cross n = 1, contrary to WMAP indications. On the other hand,n can run significantly if the couplings are stronger, but at the price of having a small number of e-folds,Ne. We also examine the effect of mass thresholds crossed during inflation. Finally, we showthat the presence of non-renormalizable operators for the inflaton, suppressed by a massscale above the inflationary range, is able to give both and Ne∼50.

Discrete flavor symmetry, dynamical mass textures, and grand unification

Discrete flavor symmetry is explored for an intrinsic property of mass matrix forms of quarks and leptons. In this paper we investigate the S3 permutation symmetry and derive the general forms of mass matrices in various types of S3 theories. We also exhibit particular realizations of previous ansatze of mass matrices, which have often been applied in the literature to the standard model Yukawa sector. Discrete flavor symmetry is also advantageous for vanishing matrix elements being dynamically generated in the vacuum of scalar potential. This is due to the fact that group operations are discrete. While zero elements themselves do not explain mass hierarchies, we introduce an Abelian flavor symmetry. A non-trivial issue is whether successful quantum numbers can be assigned so that they are compatible with other (non-Abelian) flavor symmetries. We show typical examples of charge assignments which not only produce hierarchical orders of mass eigenvalues but also prohibit non-renormalizable operators which disturb the hierarchies in first-order estimation. As an explicit application, a flavor model is constructed in grand unification scheme with S3 and U(1) (or ZN) flavor symmetries.

Quark and lepton masses from deconstruction

We propose a supersymmetric SU ( 5 ) ′ × SU ( 5 ) ″ model, where the quarks and leptons live in a U ( 1 ) product group theory space that is compactified on the real projective plane RP 2 . The fermion generations are placed on different points in the deconstructed manifold by assigning them SO ( 10 ) compatible U ( 1 ) charges. The observed masses and mixing angles of quarks and leptons emerge from non-renormalizable operators involving the chiral link fields. The link fields introduce a large atmospheric neutrino mixing angle θ 23 ∼ 1 via a dynamical realization of the seesaw mechanism, which sets the deconstruction scale to a value of the order the usual B – L breaking scale ∼10 14 GeV. Supersymmetry breaking can be achieved through topological effects due to a nontrivial first homology group Z 2 . The mixed anomalies of the link fields are canceled by Wess–Zumino terms, which are local polynomials in the gauge and link fields only. We also comment on the construction of Chern–Simons couplings from these fields.

Operator analysis for proton decay in supersymmetric SO(10) GUT models

Nonrenormalizable operators both account for the failure of down quark and charged lepton Yukawa couplings to unify and reduce the proton decay rate via dimension-five operators in minimal SUSY SU(5) GUT. We extend the analysis to SUSY SO(10) GUT models.

Coupling quintessence to inflation in supergravity

The evolution of the quintessence field during a phase of chaotic inflation is studied. The inflaton {phi} and the quintesssence field Q are described in a supergravity framework where the coupling between the inflaton and quintessence is induced by nonrenormalizable operators suppressed by the Planck mass. We show that the resulting quintessence potential during inflation possesses a time-dependent minimum playing the role of an attractor. The presence of this attractor forces the quintessence field to be small during inflation. These initial conditions are such that the quintessence field is on track now.

Flipped cryptons and ultrahigh energy cosmic rays

Cryptons are metastable bound states of fractionally-charged particles that arise generically in the hidden sectors of models derived from heterotic string. We study their properties and decay modes in a specific flipped SU(5) model with long-lived four-particle spin-zero bound states called {\it tetrons}. We show that the neutral tetrons are metastable, and exhibit the tenth-order non-renormalizable superpotential operators responsible for their dominant decays. By analogy with QCD, we expect charged tetrons to be somewhat heavier, and to decay relatively rapidly via lower-order interactions that we also exhibit. The expected masses and lifetimes of the neutral tetrons make them good candidates for cold dark matter (CDM), and a potential source of the ultra-high energy cosmic rays (UHECRs) which have been observed, whereas the charged tetrons would have decayed in the early Universe.

Light grand unified theory triplets and Yukawa splitting

Triplet-mediated proton decay in Grand Unified Theories (GUTs) is usually suppressed by arranging a large triplet mass. Here we explore instead a mechanism for suppressing the couplings of the triplets to the first and second generations compared to the Yukawa couplings, so that the triplets' mass can be below the GUT scale. This mechanism is based on a ``triplet symmetry'' in the context of product-group GUTs. We study two possibilities. One, which requires the top Yukawa to arise from a non-renormalizable operator at the GUT scale, is that all triplet couplings to matter are negligible, so that the triplets can be at the weak scale. The second is that some triplet couplings, and in particular $T t b$ and $T \bar{t} \bar{l}$, are equal to the corresponding Yukawa couplings. This would give a distinct signature of grand unification if the triplets were sufficiently light. However, we derive a model-independent bound on the triplet mass in this case, which is at least 10$^6$GeV. Finally, we construct a GUT model based on Yukawa splitting, with the triplets at 10$^{14}$GeV, as required for coupling unification to work.