arXiv subjects
Publications and source records attributed to Pierre Ramond.
The recent neutrino data seem to favor two large and one small mixing angles and a hierarchy of their squared mass differences. We discuss these within the context of hierarchical neutrino masses. We show that this scheme suggests a specific neutrino mass matrix with mild fine-tuning. We then present a Froggatt-Nielsen model that reproduces this matrix.
We investigate symmetry breaking patterns from replicated gauge groups which generate anomaly-free and family-dependent U(1) symmetries. We discuss the extent to which these symmetries can explain the observed hierarchies of fermion masses and mixings.
Quarks and leptons charges and interactions are derived from gauge theories associated with symmetries. Their space-time labels come from representations of the non-compact algebra of Special Relativity. Common to these descriptions are the Lie groups stemming from their invariances. Does Nature use Exceptional Groups, the most distinctive among them? We examine the case for and against their use. They do indeed appear in charge space, as the Standard Model fits naturally inside the exceptional group $E_6$. Further, the advent of the $E_8\times E_8$ Heterotic Superstring theory adds credibility to this venue. On the other hand, their use as space-time labels has not been as evident as they link spinors and tensors under space rotations, which flies in the face of the spin-statistics connection. We discuss a way to circumvent this difficulty in trying to generalize eleven-dimensional supergravity.
We construct Wigner's continuous spin representations of the Poincaré algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the {\it short little group} $SO(d-3)$, where $d$ is the space-time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincaré algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry algebra contains a central charge in four dimensions.
Nature's attraction to unique mathematical structures provides powerful hints for unraveling her mysteries. None is at present as intriguing as eleven-dimensional M-theory. The search for exceptional structures specific to eleven dimensions leads us to exceptional groups in the description of space-time. One specific connection, through the coset $F_4/SO(9)$, may provide a generalization of eleven-dimensional supergravity. Since this coset happens to be the projective space of the Exceptional Jordan Algebra, its charge space may be linked to the fundamental degrees of freedom underlying M-theory.
Reminiscences on the String origins of Supersymmetry are followed by a discussion of the importance of confusing bosons with fermions in building superstring theories in 9+1 dimensions. In eleven dimensions, the kinship between bosons and fermions is more subtle, and may involve the exceptional group $F_4$.
We present a comprehensive study of five-dimensional brane-world models for neutrino physics based on flat compactifications. Particular emphasis is put on the inclusion of bulk mass terms. We derive a number of general results for such brane-world models with bulk mass terms. In particular, in the limit of small brane-bulk couplings, the electroweak eigenstates are predominantly given as a superposition of three light states with non-trivial small admixtures of bulk states. As a consequence, neutrinos can undergo standard oscillations as well as oscillation into bulk Kaluza-Klein states. We use this structure to construct a specific model based on Z_2 orbifolding and bulk Majorana masses which is compatible with all observed oscillation phenomena. The solar neutrino deficit is explained by oscillations into sterile bulk states while the atmospheric neutrino deficit is due to mu - tau oscillations with naturally maximal mixing. In addition, the model can accommodate the LSND result and a significant neutrino dark matter component. We also analyze the constraints from supernova energy loss on neutrino brane-world theories and show that our specific model is consistent with these constraints.
A plausible explanation for the existence of additional light sterile neutrinos is that they correspond to modulini, fermionic partners of moduli, which propagate in new large dimensions. We discuss the phenomenological implications of such states and show that solar neutrino oscillation is well described by small angle MSW oscillation to the tower of Kaluza Klein states associated with the modulini. In the optimal case the recoil electron energy spectrum agrees precisely with the measured one, in contrast to the single sterile neutrino case which is disfavoured. We also consider how all oscillation phenomena can be explained in a model including bulk neutrino states. In particular, we show that a naturally maximal mixing for atmospheric neutrinos can be easily obtained.
Certain static soliton configurations of gauge fields in 4+1 dimensions correspond to the instanton in 4-Euclidean dimensions ``turned on its side,'' becoming a monopole in 4+1. The periodic instanton solution can be used with the method of images to construct solutions satisfying D-brane boundary conditions. The $θ$-term on the brane becomes a topological current source, yielding an emission amplitude for monopoles into the bulk. Instantons have a novel reinterpretation in terms of monopole exchange between branes.
The observed quark hierarchies suggest a simple family symmetry. Generalized to leptons through grand-unified quantum numbers, it produces a neutrino mixing matrix with order-one ν_μ - ν_τ mixing, and order-λ^3 ν_e - ν_μ and ν_e - ν_τ mixings. The intrafamily hierarchy and observed neutrino mass differences together require this symmetry to be anomalous, suggesting through the Green-Schwarz mechanism a string or M-theory origin for the symmetry.
We present a supersymmetric standard model with three gauged Abelian symmetries, of a type commonly found in superstrings. One is anomalous, the other two are $E_6$ family symmetries. It has a vacuum in which only these symmetries are broken by stringy effects. It reproduces all observed quark and charged lepton Yukawa hierarchies, and the value of the Weinberg angle. It predicts three massive neutrinos, with mixing that can explain both the small angle MSW effect, and the atmospheric neutrino anomaly. The Cabibbo angle is expressed in terms of the gauge couplings at unification. It conserves R-parity, and proton decay is close to experimental bounds.
We present a model for the observed hierarchies among the Yukawa couplings of the standard model in the context of an effective low energy theory with an anomalous U(1) symmetry. This symmetry, a generic feature of superstring compactification, is a remnant of the Green-Schwarz anomaly cancellation mechanism. The gauge group is that of the standard model, augmented by X, the anomalous U(1), and two family-dependent phase symmetries $Y^{(1)}$ and $Y^{(2)}$. The correct hierarchies are reproduced only when $sin^2θ_w=3/8$ at the cut-off. To cancel anomalies, right-handed neutrinos and other standard model singlets must be introduced. Independently of the charges of the right-handed neutrinos, this model produces the same neutrino mixing matrix and an inverted hierarchy of neutrino masses. The heaviest is the electron neutrino with a mass $\sim 1$ meV, and mixing of the order of $λ_c^3$ with each of the other two neutrinos.
The addition of an Abelian family symmetry to the Minimal Supersymmetric Standard Model reproduces the observed hierarchies of quark and lepton masses and quark mixing angles, only if it is anomalous. Green-Schwarz compensation of its anomalies requires the electroweak mixing angle to be $\sin^2θ_w=3/8$ at the string scale, without any assumed GUT structure, suggesting a superstring origin for the standard model. The analysis is extended to neutrino masses and the lepton mixing matrix.
We review the present knowledge of the Standard Model that is relevant in formulating its possible short distance extensions. We present different scenarios in terms of the Higgs mass, the only unknown parameter of the model. We concentrate on the many small numbers in the model and suggest generic methods to reproduce these numbers in terms of scale ratios, applying see-saw like ideas to the breaking of chiral symmetries.
In the minimal supersymmetric standard model, the three gauge couplings appear to unify at a mass scale near $2 \times 10^{16}$ GeV. We investigate the possibility that intermediate scale particle thresholds modify the running couplings so as to increase the unification scale. By requiring consistency of this scenario, we derive some constraints on the particle content and locations of the intermediate thresholds. There are remarkably few acceptable solutions with a single cleanly defined intermediate scale far below the unification scale.
We augment the Minimal Supersymmetric Standard Model with a gauged family-dependent $U(1)$ to reproduce Yukawa textures compatible with experiment. In the simplest model with one extra chiral electroweak singlet field, acceptable textures require this $U(1)$ to be anomalous. The cancellation of its anomalies by a generic Green-Schwarz mechanism requires $\sin^2θ_w=3/8$ at the string scale, suggesting a superstring origin for the standard model.
We present partial numerical results in the Minimal Supersymmetric Standard Model with soft breaking of supersymmetry, and radiative breaking of the electroweak symmetry. We impose the additional relation, bottom mass = tau mass at the GUT scale. For the special case of the strict no-scale model, in which global supersymmetry breaking arises solely from soft gaugino masses, we find that the top mass is expected to be lighter than about 128 GeV. A higher upper bound for the top mass of about 138 GeV is predicted, if the mass of the bottom is at the lower end of its experimental uncertainty.
The supersymmetric standard model with supergravity-inspired soft breaking terms predicts a rich pectrum of sparticles to be discovered at the SSC, LHC and NLC. Because there are more supersymmetric particles than unknown parameters, one can write down sum rules relating their masses. We discuss the pectrum of sparticles from this point of view. Some of the sum rules do not depend on the input parameters and can be used to test the consistency of the model, while others are useful in determining the input parameters of the theory. If supersymmetry is discovered but the sum rules turn out to be violated, it will be evidence of new physics beyond the minimal supersymmetric standard model with universal soft supersymmetry-breaking terms.