arXiv subjects
Publications and source records attributed to P. Ramond.
After a review of the early history of neutrinos and their detection, we analyze the different types of models that extend the standard model to massive neutrinos. We emphasize the generic nature of maximal mixing between muon and tau neutrinos, given simple assumptions based on grand unification.
A gauged phase symmetry with its anomalies cancelled by a Green-Schwarz mechanism, broken at a large scale by an induced Fayet-Iliopoulos term, is a generic feature of a large class of superstring theories. It induces many desirable phenomenological features: Yukawa coupling hierarchy, the emergence of a small Cabibbo-like expansion parameter, relating the Weinberg angle to $b-τ$ unification, and the linking of R-parity conservation to neutrino masses. Some are discussed in the context of a three-family model which reproduces all quark and lepton mass hierarchies as well as the solar and atmospheric neutrino oscillations.
We present a model which contains three Abelian symmetries beyond the standard model. One is anomalous {\it \` a la} Green-Schwarz, and family-independent; the other two are family symmetries. All are broken at a large scale by stringy effects. The model is predictive in the neutrino sector: large mixing between $ν_μ-ν_τ$, and {\cal O}$(λ^3)$ $ν_e-ν_μ$ mixings. Its natural cut-off is the gauge unification scale, orders of magnitude below the perturbative string cut-off.
The light-cone little group, SO(9), classifies the massless degrees of freedom of eleven-dimensional supergravity, with a triplet of representations. We observe that this triplet generalizes to four-fold infinite families with the quantum numbers of massless higher spin states. Their mathematical structure stems from the three equivalent ways of embedding SO(9) into the exceptional group $F_4$.
Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_λ$ of F we assign a multiplet of irreducible representations of B with m elements in each multiplet, where m is the index of the Weyl group of B in the Weyl group of F. We obtain a generalization of the Weyl character formula; our formula gives the character of $V_λ$ as a quotient whose numerator is an alternating sum of the characters in the multiplet associated to $V_λ$ and whose denominator is an alternating sum of the characters of the multiplet associated to the trivial representation of F.
We discuss, in the context of the strongly coupled E_8 \times E_8 heterotic string proposed by Horava and Witten, the appearance of anomalous U(1)_X symmetries of a nonperturbative origin, related to the presence, after compactification, of five-branes in the five-dimensional bulk of the theory. We compute the gauge anomalies and the induced Fayet-Iliopoulos terms on each boundary, which we find to be lower than the universal one induced in the weakly coupled case.
In models with an anomalous abelian symmetry broken at a very large scale, we study which requirements to impose on the anomalous charges in order to prevent standard model fields from acquiring large vacuum expectation values. The use of holomorphic invariants to study D-flat directions for the anomalous symmetry, proves to be a very powerful tool. We find that in order to forbid unphysical vacuum configurations at that scale, the superpotential must contain many interaction terms, including the usual Yukawa terms. Our analysis suggests that the anomalous charge of the μ-term is zero. It is remarkable that, together with the seesaw mechanism, and mass hierarchies, this implies a natural conservation of R-parity.
We show that models with an abelian family symmetry which accounts for the observed hierarchies of masses and mixings in the quark sector may also accomodate quasi-degeneracies in the neutrino mass spectrum. Such approximate degeneracies are, in this context, associated with large mixing angles. The parameters of this class of models are constrained. We discuss their phenomenological implications for present and foreseen neutrino experiments.
$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the gauge group is $SO(n_c)$, with vector matter, it is a W-algebra, and the primary invariants form one of its representation. The same superalgebra exists in the dual theory, but its construction in terms of the dual fields suggests that duality may be understood in terms of a charge conjugation within the algebra. We extend the analysis to the gauge group $E_6$.
The masses of quarks and leptons suggest a strong hierarchical structure. We argue that their patterns can be reproduced through the introduction of a new Abelian symmetry. The data suggest that this symmetry is anomalous. We suggest that the cancellation of its anomalies occur through the Green-Schwarz mechanism. An important check of this idea is that it links the Weinberg angle to a mass ratio of the elementary fermions. The Green-Schwarz mechanism occurs naturally in many superstring compactifications, and produces a small parameter, which we use to determine the quark mass hierarchy. We show that hierarchy and mixings among the chiral fermions is a consequence of the Green-Schwarz mechanism. We present several models where this idea is realized.
The observed hierarchy of quark and lepton masses and mixings may be obtained by adding an abelian family symmetry to the Minimal Supersymmetric Model and coupling quarks and leptons to an electroweak singlet scalar field. In a large class of such models, this symmetry suffers from anomalies which must be compensated by the Green-Schwarz mechanism; this in turn fixes the electroweak mixing angle to be $\sin^2 θ_W = 3/8$ at the string scale, without any assumed GUT structure. The analysis is extended to two distinct generalisations of the Standard Model: neutrino masses and mixings and R-parity violating interactions.
The differences between the $N=0$ and $N=1$ standard models are emphasized in formulating their short distance extension. We sketch methods to reproduce many of the small numbers in the model in terms of scale ratios, applying see-saw like ideas to the breaking of chiral symmetries. We sketch how the $N=1$ standard model, outfitted with an extra family Abelian symmetry to reproduce the mass hierarchies, naturally fits superstring models, by making use of generic non-renormalizable operators.
We review the Standard Model in a form conducive to formulating its possible short distance extensions. This depends on the value of the Higgs mass, the only unknown parameter of the model. We suggest methods to reproduce many of the small numbers in the model in terms of scale ratios, applying see-saw like ideas to the breaking of chiral symmetries. We then investigate how the $N=1$ Standard Model extrapolated to or near the Planck scale can fit superstring models, emphasizing the use of some non-renormalizable operators generic to superstrings.
In this paper we summarize the minimal supersymmetric standard model as well as the renormalization group equations of its parameters. We proceed to examine the feasability of the model when the breaking of supersymmetry is parametrized by the soft terms suggested by supergravity theories. In such models, the electroweak symmetry is exact at tree level and is broken spontaneously at one loop order. We make the additional assumption that the GUT-inspired relation $m_b=m_τ$ be valid at the scale where the gauge coupling constants unify, which constrains the value of the top quark mass. For all types of soft breaking terms expected in supergravity theories, we present the results of numerical runs which yield electroweak breaking at the required scale. These yield not only the allowed ranges for the soft supersymmetry breaking parameters, but also the value of the supersymmetric partner' masses. For example in the strict no-scale model, in which global supersymmetry breaking arises solely from soft supersymmetry breaking parameters, but also the value of the supersymmetric partner' masses. For example in the strict no-scale model, in which global supersymmetry breaking arises solely from soft gaugino masses, we find that $M_t$ can be no heavier than $\sim 127$ GeV.
I present an algorithm in the search for symmetric textures in the quark Yukawa matrices. This is based on a talk at the Coral Gables conference in January 1993. I include the macro tables2.tex for making tables, and use the Santa Barbara jnl and reforder macros.
We develop a systematic analysis of quark mass matrices which, starting with the measured values of quark masses and mixing angles, allows for a model independent search for all possible (symmetric or hermitian) mass matrices having texture zeroes at the unification scale. A survey of all six and five texture zero structures yields a total of five possible solutions which may be distinguished by improved measurements of the CKM matrix elements and which may readily be extended to include lepton masses with the Georgi-Jarlskog texture. The solutions naturally suggest a parameterisation for the mass matrices based on a perturbative expansion and we present some speculations concerning the origin of such structure.
Using renormalization group techniques, we examine several interesting relations among masses and mixing angles of quarks and leptons in the Standard Model. We extend the analysis to the minimal supersymmetric extension to determine its effect on these mass relations. Remarkably Supersymmetry allows for these relations to be satisfied at a single grand unified scale.