Possible uses of the binary icosahedral group in grand unified theories

There are exactly three finite subgroups of SU(2) that act irreducibly in the spin 1 representation, namely the binary tetrahedral, binary octahedral and binary icosahedral groups. In previous papers I have shown how the binary tetrahedral group gives rise to all the necessary ingredients for a non-relativistic model of quantum mechanics and elementary particles, and how a modification of the binary octahedral group extends this to the ingredients of a relativistic model. Here I investigate the possibility that the binary icosahedral group might be related in a similar way to grand unified theories such as the Georgi--Glashow model, the Pati--Salam model, various $E_8$ models and perhaps even M-theory.

Comparison of group-theoretical strategies for unification of 3+1 structures in physics

One of the most important advances in our understanding of the physical world arose from the unification of 3-dimensional space with 1-dimensional time into a 4-dimensional spacetime. Many other physical concepts also arise in similar 3+1 relationships, and attempts have been made to unify some of these also. Examples in particle physics include the three intermediate vector bosons of the weak interaction, and the single photon of electromagnetism. The accepted unification in this case is the Glashow-Weinberg-Salam model of electro-weak interactions, which forms part of the standard model. Another example is the three colours of quarks and one of leptons. In this case, the Pati-Salam model attempts the unification, but is not currently part of the accepted standard model. I investigate these and other instances of 3+1=4 in fundamental physics, to see if a comparison between the successful and unsuccessful unifications can throw some light on why some succeed and others fail. In particular, I suggest that applying the group-theoretical methods of the more successful unifications to the less successful ones could potentially break the logjam in theoretical particle physics.

Options for a finite group model of quantum mechanics

There are four finite groups that could plausibly play the role of the spin group in a finite or discrete model of quantum mechanics, namely the four double covers of the three rotation groups of the Platonic solids. In an earlier paper I have considered in detail how the smallest of these groups, namely the binary tetrahedral group, of order 24, could give rise to a non-relativistic theory that contains much of the structure of the standard model of particle physics. In this paper I consider how one of the two double covers of the rotation group of the cube might extend this to a relativistic theory.

Finite symmetry groups in physics

Finite symmetries abound in particle physics, from the weak doublets and generation triplets to the baryon octet and many others. These are usually studied by starting from a Lie group, and breaking the symmetry by choosing a particular copy of the Weyl group. I investigate the possibility of instead taking the finite symmetries as fundamental, and building the Lie groups from them by means of a group algebra construction.

Elemental Abundances of Kepler Objects of Interest in APOGEE. I. Two Distinct Orbital Period Regimes Inferred from Host Star Iron Abundances

The Apache Point Observatory Galactic Evolution Experiment (APOGEE) has observed $sim$600 transiting exoplanets and exoplanet candidates from textit{Kepler} (Kepler Objects of Interest, KOIs), most with $geq$18 epochs. The combined multi-epoch spectra are of high signal-to-noise (typically $geq$100) and yield precise stellar parameters and chemical abundances. We first confirm the ability of the APOGEE abundance pipeline, ASPCAP, to derive reliable [Fe/H] and effective temperatures for FGK dwarf stars -- the primary textit{Kepler} host stellar type -- by comparing the ASPCAP-derived stellar parameters to those from independent high-resolution spectroscopic characterizations for 221 dwarf stars in the literature. With a sample of 282 close-in ($P<100$ days) KOIs observed in the APOGEE KOI goal program, we find a correlation between orbital period and host star [Fe/H] characterized by a critical period, $P_mathrm{crit}$= $8.3^{+0.1}_{-4.1}$ days, below which small exoplanets orbit statistically more metal-enriched host stars. This effect may trace a metallicity dependence of the protoplanetary disk inner-radius at the time of planet formation or may be a result of rocky planet ingestion driven by inward planetary migration. We also consider that this may trace a metallicity dependence of the dust sublimation radius, but find no statistically significant correlation with host $T_mathrm{eff}$ and orbital period to support such a claim.

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNEs scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.

The 2010 Interim Report of the Long-Baseline Neutrino Experiment Collaboration Physics Working Groups

In early 2010, the Long-Baseline Neutrino Experiment (LBNE) science collaboration initiated a study to investigate the physics potential of the experiment with a broad set of different beam, near- and far-detector configurations. Nine initial topics were identified as scientific areas that motivate construction of a long-baseline neutrino experiment with a very large far detector. We summarize the scientific justification for each topic and the estimated performance for a set of far detector reference configurations. We report also on a study of optimized beam parameters and the physics capability of proposed Near Detector configurations. This document was presented to the collaboration in fall 2010 and updated with minor modifications in early 2011.