arXiv subjects
Publications and source records attributed to Stuart Raby.
I discuss an evolution of SUSY GUT model building, starting with the construction of 4d GUTs, to orbifold GUTs and finally to orbifold GUTs within the heterotic string. This evolution is an attempt to obtain realistic string models, perhaps relevant for the LHC. This review is in memory of the sudden loss of Julius Wess, a leader in the field, who will be sorely missed.
We analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective 5 dimensional orbifold GUT field theories. Our analysis assumes three fundamental scales, the string scale, $\mstring$, a compactification scale, $\mc$, and a mass scale for some of the vector-like exotics, $\mex$; the other exotics are assumed to get mass at $\mstring$. In the particular models analyzed, we show that gauge coupling unification is not possible with $\mex = \mc$ and in fact we require $\mex \ll \mc \sim 3 \times 10^{16}$ GeV. We find that about 10% of the parameter space has a proton lifetime (from dimension 6 gauge exchange) $10^{33} {\rm yr} \lesssimτ(p\to π^0e^+) \lesssim 10^{36} {\rm yr}$. The other 80% of the parameter space gives proton lifetimes below Super-K bounds. The next generation of proton decay experiments should be sensitive to the remaining parameter space.
I review some of the latest directions in supersymmetric model building, focusing on SUSY breaking mechanisms in the minimal supersymmetric standard model [MSSM], the "little" hierarchy and $μ$ problems, etc. I then discuss SUSY GUTs and UV completions in string theory.
In a previous paper, referred to as a "Mini-Landscape" search, we explored a "fertile patch" of the heterotic landscape based on a Z6-II orbifold with SO(10) and E6 local GUT structures. In the present paper we extend this analysis. We find many models with the minimal supersymmetric standard model spectra and an exact R parity. In all of these models, the vector-like exotics decouple along D flat directions. We present two "benchmark" models which satisfy many of the constraints of a realistic supersymmetric model, including non-trivial Yukawa matrices for 3 families of quarks and leptons and Majorana neutrino masses for right-handed neutrinos with non-trivial See-Saw masses for the 3 light neutrinos. In an appendix we comment on the important issue of string selection rules and in particular the so-called "gamma-rule".
In this letter we consider the consequences for the LHC of light vector-like exotica with fractional electric charge. It is shown that such states are found in orbifold constructions of the heterotic string. Moreover, these exotica are consistent with gauge coupling unification at one loop, even though they do not come in complete multiplets of SU(5).
In this paper we show how some flavor symmetries may be derived from the heterotic string, when compactified on a 6D orbifold. In the body of the paper we focus on the $D_4$ family symmetry, recently obtained in $Z_3 \times Z_2$ orbifold constructions. We show how this flavor symmetry constrains fermion masses, as well as the soft SUSY breaking mass terms. Flavor symmetry breaking can generate the hierarchy of fermion masses and at the same time the flavor symmetry suppresses large flavor changing neutral current processes.
We study possible correlations between properties of the observable and hidden sectors in heterotic string theory. Specifically, we analyze the case of the Z6-II orbifold compactification which produces a significant number of models with the spectrum of the supersymmetric standard model. We find that requiring realistic features does affect the hidden sector such that hidden sector gauge group factors SU(4) and SO(8) are favoured. In the context of gaugino condensation, this implies low energy supersymmetry breaking.
We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D_4 and Delta(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Abelian flavor symmetries.
We explore a ``fertile patch'' of the heterotic landscape based on a Z_6-II orbifold with SO(10) and E_6 local GUT structures. We search for models allowing for the exact MSSM spectrum. Our result is that of order 100 out of a total 3\times 10^4 inequivalent models satisfy this requirement.
In this talk I briefly review the status of SUSY GUTs in 4, 5, 6 and 10 dimensions, focusing on the issue of gauge coupling unification and proton decay. I then discuss the predictions of the minimal SO(10) SUSY model [MSO$_{10}$SM].
In this talk I outline work done in collaboration with R.J. Zhang and T. Kobayashi. We show how to construct the equivalent of three family orbifold GUTs in five dimensions from the heterotic string. I focus on one particular model with E(6) gauge symmetry in 5D, the third family and Higgs doublet coming from the 5D bulk and the first two families living on 4D SO(10) branes. Note the E(6) gauge symmetry is broken to Pati-Salam in 4D which subsequently breaks to the Standard Model gauge symmetry via the Higgs mechanism. The model has two flaws, one fatal and one perhaps only unaesthetic. The model has a small set of vector-like exotics with fractional electromagnetic charge. Unfortunately not all of these states obtain mass at the compactification scale. This flaw is fatal. The second problem is R parity violating interactions. These problems may be avoidable in alternate orbifold compactification schemes. It is these problems which we discuss in this talk.
We construct a simple SO(10) SUSY GUT with $D_3$ family symmetry and low energy R parity. The model describes fermion mass matrices with 14 parameters and gives excellent fits to 20 observable masses and mixing angles in both quark and lepton sectors, giving 6 predictions. Bi-large neutrino mixing is obtained with hierarchical quark and lepton Yukawa matrices; thus avoiding the possibility of large lepton flavor violation. The model naturally predicts small 1-3 neutrino mixing, $\sin θ_{13} \simeq 0.05$, and a CP violating phase $δ$ close to $π/2$. Among other interesting predictions is a tiny effective Majorana mass for neutrinoless double-beta decay. Leptogenesis is also possible with the decay of the lightest right-handed neutrino giving an acceptable CP violating asymmetry $ε_1$ of order $10^{-6}$, {\em and with the correct sign for the resultant baryon asymmetry}. We also show how similar models with the non-abelian symmetry groups SU(2) or $D_4$, instead of $D_3$, can be constructed.
We construct a five dimensional supersymmetric SO(10)$\times$D$_3$ grand unified model with an $S^1/(Z_2 \times Z^\prime_2)$ orbifold as the extra dimension. The orbifold breaks half of the supersymmetry and breaks the SO(10) gauge symmetry down to ${\rm SU(4)}_C \times {\rm SU(2)}_L \times {\rm SU(2)}_R$. The Higgs mechanism is used to break the remaining gauge symmetry the rest of the way to the Standard Model. We place matter fields variously in the bulk and on the orbifold fixed points and the resulting massless fields are mixtures between these brane and bulk fields. A chiral adjoint field in the bulk gets a U(1)$_X$ vacuum expectation value, resulting in an $X$-dependent localization of the bulk matter fields and the Standard Model Higgs field. This Higgs field localization allows us to simultaneously explain the hierarchies $m_u < m_d$ and $m_t \gg m_b$. The model uses 11 parameters to fit the 13 independent low energy observables of the quark and charged lepton Yukawa matrices. The model predicts the values of two quark mass combinations, $\f{m_u}{m_c}$ and $m_d m_s m_b$, each of which are predicted to be approximately $1 σ$ above their experimental values. The remaining observables are successfully fit at the 5% level.
Motivated by orbifold grand unified theories, we construct a class of three-family Pati-Salam models in a Z6 abelian symmetric orbifold with two discrete Wilson lines. These models have marked differences from previously-constructed three-family models in prime-order orbifolds. In the limit where one of the six compactified dimensions (which lies in a Z2 sub-orbifold) is large compared to the string length scale, our models reproduce the supersymmetry and gauge symmetry breaking pattern of 5d orbifold grand unified theories on an S1/Z2 orbicircle. We find a horizontal 2+1 splitting in the chiral matter spectra -- 2 families of matter are localized on the Z2 orbifold fixed points, and 1 family propagates in the 5d bulk -- and identify them as the first-two and third families. Remarkably, the first two families enjoy a non-abelian dihedral D4 family symmetry, due to the geometric setup of the compactified space. In all our models there are always some color triplets, i.e. (6,1,1) representations of the Pati-Salam group, survive orbifold projections. They could be utilized to spontaneously break the Pati-Salam symmetry to that of the Standard Model. One model, with a 5d E6 symmetry, may give rise to interesting low energy phenomenology. We study gauge coupling unification, allowed Yukawa couplings and some of their phenomenological consequences. The E6 model has a renormalizable Yukawa coupling only for the third family. It predicts a gauge-Yukawa unification relation at the 5d compactification scale, and is capable of generating reasonable quark/lepton masses and mixings. Potential problems are also addressed, they may point to the direction for refining our models.
In this talk I describe a natural framework for bi-large neutrino mixing within the context of two models -- 1) a simple generalization of the MSSM and 2) an SO(10) model. Our starting point is the Frampton, Glashow, Yanagida [FGY] neutrino mass ansatz which can easily accomodate bi-large neutrino mixing. The main point of FGY, however, is to obtain a theory of neutrino masses with only one possible CP violating angle. They argue that the sign of the baryon asymmetry of the universe (assuming leptogenesis) is then correlated with CP asymmetries possibly observable in accelerator experiments. Unfortunately, there is a fly in the ointment. It was later shown by Raidal and Strumia [RS] that there is a sign ambiguity which frustrates the above correlation. We note that the Raidal-Strumia ambiguity is resolved in our models.
In this article we try to clarify why supersymmetry [SUSY] and supersymmetric grand unified theories [SUSY GUTs] are the new standard model of particle physics, i.e. the standard by which all other theories and experiments are measured.
A three-generation Pati-Salam model is constructed by compactifying the heterotic string on a particular T^6/Z_6 Abelian symmetric orbifold with two discrete Wilson lines. The compactified space is taken to be the Lie algebra lattice G_2+SU(3)+SO(4). When one dimension of the SO(4) lattice is large compared to the string scale, this model reproduces many features of a 5d SO(10) grand unified theory compactified on an S^1/Z_2 orbifold. (Of course, with two large extra dimensions we can obtain a 6d SO(10) grand unified theory.) We identify the orbifold parities and other ingredients of the orbifold grand unified theories in the string model. Our construction provides a UV completion of orbifold grand unified theories, and gives new insights into both field theoretical and string theoretical constructions.
Recent precise measurements of sin 2 beta from the B-factories (BABAR and BELLE) and a better known strange quark mass from lattice QCD make precision tests of predictive texture models possible. The models tested include those hierarchical N-zero textures classified by Ramond, Roberts and Ross, as well as any other hierarchical matrix Ansatz with non-zero 12 = 21 and vanishing 11 and 13 elements. We calculate the maximally allowed value for sin 2 beta in these models and show that all the aforementioned models with vanishing 11 and 13 elements are ruled out at the 3 sigma level. While at present sin 2 beta and |Vub/Vcb| are equally good for testing N-zero texture models, in the near future the former will surpass the latter in constraining power.