R-parity Research Articles

Gauge origin of baryon number conservation and suppressed neutrino masses from five dimensions

We consider a 5D SUSY $SU(3)_c\times SU(2)_L\times U(1)_Y\times {\cal U}(1)$ model compactified on an $S^{(1)}/Z_2$ orbifold. To cancel anomalies arising from the presence of ${\cal U}(1)$, we employ a Chern-Simons term and also chiral fields which could reside on the brane or in the bulk depending on the model. The presence of ${\cal U}(1)$ symmetry leads to baryon number conservation, gives rise to matter parity, and permits satisfactory neutrino masses and mixings even for a low fundamental scale. The brane Fayet-Iliopoulos D-terms naturally break ${\cal U}(1)$, leaving N=1 SUSY unbroken in 4 dimensions.

Rsymmetry in the minimal supersymmetric standard model and beyond with several consequences

The supersymmetric sector of the minimal supersymmetric standard model possesses a $U(1)$ $R$ symmetry which contains ${Z}_{2}$ matter parity. Nonzero neutrino masses, consistent with a ``redefined'' $R$ symmetry, are possible through the seesaw mechanism and/or a pair of superheavy (mass $M)$ ${\mathrm{SU}(2)}_{L}$ triplets with a $\mathrm{VEV}\ensuremath{\sim}{M}_{W}^{2}/M.$ If this $R$ symmetry is respected by the higher order terms, then baryon number conservation follows as an immediate consequence. In the presence of right-handed neutrinos, the observed baryon asymmetry of the universe arises via leptogenesis. An interplay of $R$ and Peccei-Quinn symmetry simultaneously resolves the strong $\mathrm{CP}$ and \ensuremath{\mu} problems.

On proton stability and the gauge hierarchy problem

We display an intimate relationship between proton stability and the gauge hierarchy (and μ) problems within minimal supersymmetric trinification based on the grand unified symmetry SU(3) c × SU(3) L × SU(3) R . A straightforward resolution of the hierarchy problem, achieved through discrete symmetries that contain matter parity, also transforms the problematic dimension-five proton decay process into a dimension six process. The proton is predicted to be essentially stable with a lifetime in excess of 10 50 years.

Role of the AnomalousU(1)Afor the Solution of the Doublet–Triplet Splitting Problem via the Pseudo-Goldstone Mechanism

The anomalous U(1)_A symmetry provides a generic method of getting accidental symmetries. Therefore, it can play a crucial role in solving the doublet-triplet splitting and the \mu-problems via the `pseudo-Goldstone' mechanism: U(1)_A can naturally uncorrelate the two grand unified Higgs sectors in the superpotential and simultaneously induce the desired expectation values through the Fayet-Iliopoulos D-term. The zero modes of the resulting compact vacuum degeneracy can be identified with the massless electroweak Higgs doublets. This automatically solves the doublet-triplet splitting and the \mu-problems to all orders in M_P^{-1}. No additional discrete or global symmetries are needed. U(1)_A can also play the role of the `matter parity' and suppress the baryon number violating operators. We present the simplest SU(6) gauge model with a minimal Higgs sector and no doublet-triplet splitting problem. This model also relates the fermion mass hierarchy to the hierarchy of scales and predicts, for the generic non-minimal Kahler potential, approximately universal values for the tree-level electroweak Higgs mass parameters.

Natural R parity conservation with horizontal symmetries: A four generation model.

In most supersymmetric models the stability of the proton is ensured by invoking R-parity. A necessary ingredient to enforce R-parity is the possibility of distinguishing the lepton superfields from the Higgs ones. This is generally achieved either by assuming different charges under some matter parity, or by assigning the superfields to different representations of a unified gauge group. We want to put forward the idea that the replica of the fermion generations, which constitute an intrinsic difference between the fermions and the Higgs superfields, can give a clue to understand R-parity as an accidental symmetry. More ambitiously, we suggest a possible relation between proton stability and the actual number of fermion generations. We carry out our investigation in the framework of non-Abelian horizontal gauge symmetries. We identify $SU(4)_H$ as the only acceptable horizontal gauge group whichcan naturally ensure the absence of R parity violating operators, without conflicting with other theoretical and phenomenological constraints. We analyze a version of the supersymmetric standard model equipped with a gauged horizontal $SU(4)_H$, in which R-parity is accidental. The model predicts four families of fermions, it allows for the dynamical generation of a realistic hierarchy of fermion masseswithout any ad hoc choice of small Yukawa couplings, it ensures in a natural way the heaviness of all the fourth family fermions (including the neutrino) and it predicts a {\it lower} limit for the $\tau$-neutrino mass of a few eV. The scale of the breaking of the horizontal symmetry can be constrained rather precisely in a narrow window around $\sim 10^{11}$ GeV. Some interesting astrophysical and cosmological implications of the model are addressed as well.

Elements of finite order in Lie groups and discrete gauge symmetries

We apply Kac's theory of elements of finite order (EFO) in Lie groups to the description of discrete gauge symmetries in various supersymmetric grand unified models. Taking into account the discrete anomaly cancellation conditions, we identify the EFO which generate certain matter parities in the context of the supersymmetric SO(10) and E 6 models.

Patterns of quark mass matrices in a class of Calabi-Yau models

We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete E 6-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all leptoquarks heavy while preserving light Higgs fields. Then we classify the patterns of ordinary quark mass matrices and show that (without invoking effects due to nonrenormalizable terms) only one structure can accommodate the observed value of fermion masses and mixing angles. The model, which unifies perturbatively and predicts a realistic structure of quark mass matrices with texture zeros, is one of the many possible string vacua. However, in contrast with what is often assumed in the search for realistic unified scenarios, it is highly nonminimal near the unification scale, and the predicted mass matrices have no simple symmetry properties.

Gauge hierarchy, Planck scale corrections and the origin of GUT scale in supersymmetric ( SU (3)) 3

Within a supersymmetric unified framework we explore the resolution of the gauge hierarchy problem taking account of the non-renormalizable terms in the superpotential. For [ SU(3)] 3 supplemented by a discrete R-parity, we find the remarkable property that the vacuum configuration corresponding to the correct gauge symmetry breaking remains flat (in the supersymmetric limit) to all orders in M −1 Planck. The grand unification scale arises from an interplay of the Planck and supersymmetry breaking scales. An ‘internal’ Z 3 ⊗ Z 4 symmetry protects a pair of electroweak doublets from becoming superheavy, yielding at the same time the supersymmetric ‘μ term’ with the right order of magnitude. The Z 4 symmetry also acts as matter parity and eliminates the dangerous baryon number violating couplings.

Large tan β from SU(2)R gauge symmetry

Sufficient conditions for the relation tan β⋍mt/mb to hold in supersymmetric grand unified theories are formulated. Essential ingredients are the SU(2)R gauge symmetry and a discrete matter parity. The applicability of our conditions is illustrated by specific examples. Implications for neutrino masses are discussed.

A Susy SO(10) model with large tan β

We construct a supersymmetric SO(10) model with the asymptotic relation tan β ⋍mt/mb automatically arising from its structure. The model retains the significant minimal supersymmetric standard model predictions for sin2θw and αs and contains an automatic Z2 matter parity. Proton decay through d = 5 operators is sufficiently suppressed. It is remarkable that no global symmetries need to be imposed on the model.

Discrete gauge symmetries in supersymmetric grand unified models.

We investigate the presence of discrete gauge symmetries in grand unification models based on SO(10) and ${\mathrm{E}}_{6}$. These models include flipped and unflipped SU(5), $\mathrm{SU}(4)\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}$, ${\mathrm{SU}(3)}_{C}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{R}$, and SU(6)\ifmmode\times\else\texttimes\fi{}SU(2). Using the Dynkin formalism we find the U(1) subalgebras contained in the unified groups, give an expression for the Higgs fields that preserves each discrete symmetry, and determine the low-energy matter content implied by chirality. We discuss two ${Z}_{2}$ and three ${Z}_{3}$ non-equivalent cases. Among the possibilities found, only the usual ${Z}_{2}$ matter parity ($R$ parity) of supersymmetric extensions is consistent with a minimal matter content with no right-handed neutrinos, extra Higgs doublets, or nonstandard down-type quarks.

Baryon and lepton number (non-)conservation in supersymmetric theories

We discuss the origin of baryon and lepton number (non-)conservation in supersymmetric versions of the standard model in which the Higgs mass term is generated via the vacuum expectation value of a singlet field and nucleon stability is guaranteed by a discrete symmetry. We determine the simplest examples satisfying the discrete anomaly cancellation conditions. With only one singlet field present anomaly cancellation can be achieved with nucleon conservation guaranteed at dimension 4 by a matter parity or a lepton parity (a symmetry that allows baryon number violating operators in the low energy lagrangian). If two singlet fields are present, a baryon parity (which allows lepton number violating terms) is also anomaly free. In some cases nucleon decay is further inhibited because all the dimension-five baryon number violating operators are forbidden eliminating the need for any small couplings. We show that such discrete symmetries may also allow a flavour subset of lepton number violating operators, allowing for primordial baryogenesis and non-standard SUSY phenomenology. A novel feature in the latter case is the simultaneous presence of both lepton and baryon number violating operators without disturbing the proton stability.

More about discrete gauge anomalies

I discuss and extend several results concerning the cancellation of discrete gauge anomalies. I show how heavy fermions do not decouple in the presence of discrete gauge anomalies. As a consequence, in general, cancellation of discrete gauge anomalies cannot be described merely in terms of low-energy operators involving only the light fermions. I also discuss cancellation of discrete gauge anomalies through a discrete version of the Green-Schwarz (GS) mechanism as well as the possibility of discrete gauge R-symmetries and their anomalies. Finally, some phenomenological applications are discussed. This includes symmetries guaranteeing absence of FCNC in two-Higgs models and generalized matter parities stabilizing the proton in the supersymmetric standard model. In the presence of a discrete GS mechanism or / and gauge R-symmetries, new possibilities for anomaly free such symmetries are found.

Massive neutrinos in a Calabi-Yau model.

We present an extension of the standard neutrino sector motivated by the heterotic string. Its basic ingredients are two nonweakly interacting neutrinos and a ${Z}_{3}$ discrete symmetry acting as a matter parity. Although this model represents a very minimal extension of the standard model, its flexibility to produce nonstandard effects in a way consistent with the constraints from cosmology, astrophysics, and particle physics phenomenology seems quite remarkable. In particular, we discuss the ability of the model to accommodate the various experimental anomalies ($\ensuremath{\tau}$ lifetime, 17 keV neutrino, and solar-neutrino deficit) which have been the object of recent controversy.

A SUPERSTRING MODEL WITH R SYMMETRIES AND LOW B−L BREAKING

The phenomenology of a three-generation superstring model arising from the compactification of the ten-dimensional heterotic superstring theory on the Tian-Yau manifold with a discrete Z2×Z3 symmetry is discussed. The Z2 is used to define a matter parity and the Z3 generates an R symmetry. Presence of the discrete R symmetry enforces the existence of exactly flat directions in the superpotential that motivate us to break the SU(3) 3 to SU(3) × SU(2) L× SU(2) R× U(1) B−L at a scale M X closely associated with the compactification scale MC~1018 GeV , since the R symmetry and B−L breaking need to arise from unknown string physics and for the successful suppression of proton decay rate due to certain dimension-five operators. When the R symmetry is broken at a scale MR~1014 GeV , the matter parity is broken spontaneously as well, guiding us to the scale of the breaking to the standard model, MB−L~103 GeV , making the additional Z boson accessible at accelerator energies. When the spectrum of particles is derived from the mass matrices, the model emerges as the first model with known particles having nonstandard Z2 matter-parity assignments. The transformation properties of the standard model fermions under the discrete symmetries of the theory give rise to an extremely interesting pattern for their mass generation. The model has acceptable properties vis à vis proton decay lifetime considerations and renormalization group considerations. This is a superstring model where the lightest supersymmetric particle, favored to be the photino, decays with a cosmologically interesting lifetime.

Discrete gauge symmetries and the origin of baryon and lepton number conservation in supersymmetric versions of the standard model

In the supersymmetric standard model operators of dimension 4 and 5 generically violate B and L number. One usually assumes the presence of some discrete symmetry (“matter parities”) in order to forbid dangerous operators which may lead otherwise to unacceptable violations of B and L. We give a general classification of such discrete Z N symmetries (and R-symmetries) and show that the number of independent possibilities is substantially reduced by equivalences. We argue that normal discrete symmetries may be expected to be violated by quantum gravity effects and hence are not enough to inhibit nucleon decay. On the other hand, gauge (either discrete or continuous) symmetries are stable under quantum gravity effects and we discuss how such symmetries may eliminate the dangerous B- or L-violating operators. We find that the massless fermion content of modeld with discrete “gauge” symmetries is strongly constrained by the cancellation of “discrete gauge anomalies”. We show that there are two preferred Z N symmetries which are discrete anomaly free with the minimal light matter content. One of them is the standard R-parity whereas the other is a unique Z 3 symmetry allowing for lepton number violation. We argue that from the point of view of arranging for proton stability without fine-tuning the second option should be preferred. The differences in the phenomenology of the various sypersymmetric models dictated by the different symmetries are discussed.

Cosmology of three-generation Calabi-Yau superstring models

The cosmology of three-generation Calabi-Yau (CY) superstring models is discussed. A model independent lower bound ∼ 10 14 GeV on the largest intermediate scale in models with SU(3) 3 gauge group is derived by requiring that the magnetic monopole flux in the Galaxy does not exceed the Parker bound. Using this bound we argue that the baryon asymmetry in three-generation CY models should necessarily be created at temperatures of ∼ 1 GeV at most. A late baryogenesis scenario is presented in the context of a model with naturally suppressed proton decay which is generalizable to others with Z 3 matter parity and low U(1) B-L breaking scale.

Light Higgs bosons in three-generation Calabi-Yau superstring theory.

An analysis of the Higgs sector is given in three-generation superstring models which arise via Calabi-Yau compactifications where the flux breaking at the compactification scale reduces the ${\mathrm{E}}_{6}$ grand unified group to ${[\mathrm{S}\mathrm{U}(3)]}^{3}$ and a further spontaneous breaking at an intermediate scale ${M}_{I}$ reduces this symmetry down to the standard-model gauge group symmetry $\mathrm{SU}{(3)}_{C}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$. The analysis is carried out within the framework of matter parity invariance which is needed for proton stability and the assumption that spontaneous breaking at the intermediate scale is triggered by supersymmetry breaking. Conditions for the existence of a pair of light Higgs doublets needed for the further breaking of the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$ electroweak symmetry are obtained. These conditions act as constraints on the moduli space of the theory in order that the ${(27)}^{3}$ interactions accommodate light Higgs bosons below the intermediate mass scale.

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.

Predictions from three-generation Calabi-Yau string theory.

Superstring models are considered where there is ${\mathrm{E}}_{6}$ flux breaking to [SU(3)${]}^{3}$ at compactification and dynamical breaking of [SU(3)${]}^{3}$ to SU(3${)}_{\mathit{C}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathit{L}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathit{Y}}$ at an intermediate scale ${\mathit{M}}_{\mathit{I}}$. If the intermediate scale breaking preserves matter parity (to stabilize the proton) and is triggered by supersymmetry breaking, then it is shown that there will always be at least two, and often four, new light SU(3${)}_{\mathit{C}}$\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}U(1) neutral chiral multiplets (in addition to the usual standard-model states). The interactions of these new particles with the standard-model particles are deduced and are expected to produce \ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma} decay and, in some cases, neutrino masses and oscillations in a range that may be accessible to experiment.