Session H12: New Ideas and Directions

Sub-GUT mSUGRA

In this talk I will discuss the phenomenology of minimal supergravity (mSUGRA) models in which the supersymmetry-breaking parameters are universal at a scale below the scale at which the Standard Model gauge couplings unify, known as the GUT scale. We find that these so-called sub-GUT mSUGRA models can accommodate a $\sim$125 GeV Standard Model-like Higgs boson while at the same time providing a viable explanation for the observed dark matter in the universe. I will introduce the sub-GUT mSUGRA parameter space and present a brief exploration, focusing on cosmologically-favored regions where the dark matter abundance is in agreement with the measured value.   

Higher-dimensional oscillations of quantum particles

A theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions, based on an extension of the Schr\"{o}dinger equation to include 4$^{th}$ and 5$^{th}$ spatial components [E. R. Hedin, Physics Essays \textbf{25}, 2 (2012)]. A higher-dimensional harmonic oscillator confining potential localizes particles into 3-d space (characterizing the ``brane tension'' which confines Standard Model particles to the sub-manifold). Several consistency checks of this model are: a match with the quantum phenomenon of ``\textit{zitterbewegung}''; the predicted intrinsic spin angular momentum is of order h/2$\pi $; the magnetic moment of the electron is determined (with a gyromagnetic ratio of 2); the nuclear force ``hard core'' radius is accurately predicted; the ratio of quark masses (of the up and down quarks) is found to be consistent with QCD theory; and possible explanations of the Planck mass and Planck length. An application of higher-dimensional particle effects to the astrophysics of stars shows that radical physical inconsistencies are not evident. Finally, this model suggests a possible explanation of dark matter as the fractional probability manifestations of a ladder of the higher-dimensional symmetric excited states of ordinary particles.   

Scalar theories and symmetry breaking in the light-front coupled-cluster method

The light-front coupled-cluster method is a nonperturbative technique for solving Hamiltonian eigenvalue problems in light-front-quantized field theories. Its primary purpose is to provide a systematic sequence of solvable approximations to the original eigenvalue problem without the truncation of Fock space. Here we apply the method to various two-dimensional scalar theories to illustrate the incorporation of zero modes and symmetry breaking. In particular, we compute nontrivial light-front vacuum structure in such theories.   

E.Cartan's Spinor and the infrared QCD

In `The Theory of Spinor (Dover 1966)' of Erie Cartan, 8 spinors possessing odd number of indices, 8 spinors possessing even number of indices, 4 vectors X and X' make trilinear form F$=\varphi $CX$\psi $ which is invariant under super symmetric transformations G(23),G(12),G(13),G(123) and G(132). Since mixing of spinors and vectors occur by these transformations except G(23), the electro-magnetic(EM) wave emitted from the transformed world would be undetectable in our detector, and they would appear as dark matter. One of the 2-component spinors transformed by G(23) is the complex conjugate of the original, and the main part would be undetectable. There is an observation that the mass ratio of the dark matter to normal matter is almost exactly 5:1. I assume that the vertex of vector particle coupling to quarks and coupling to leptons have qualitative differences, i.e. EM interaction of a lepton is sensitive to the triality but that of a quark is blind. Roles of triality in the infrared QCD, in the axial vector anomaly, in the astrophysical observations, and a conjecture on making neutrino massive through triality without invoking right-handed neutrinos will be discussed.   

Knot Theory and Topologically Massive Yang-Mills Theory

In 2+1 dimensions, we study Yang-Mills(YM) + Chern-Simons(CS) theory also known as topologically massive Yang-Mills(TMYM) theory. Using geometric quantization method we calculate the Wilson Loop expectation values of TMYM theory. At large distances, where only the topological theory survives, we obtain a condition that makes skein relations of knot theory useful to calculate Wilson loop expectation values of TMYM theory. These link invariants may lead to a better understanding of mass gap in 2+1 dimensions.   

An Alternative Approach to the Klein-Gordon-Dirac Equations for Classical and Quantum Mechanics

This is an ongoing development to propose an encompassing solution to Klein-Gordon-Dirac equation which is treated as a factorable quadratic differential equation. The proposed solutions consist of both real and periodic components, defining a collection of particles, and their electromagnetic interactions. The real constituents generally define the classical particle interactions, and the periodic constituents define the quantum aspects. This should not be taken as a re-formulation of quantum mechanics, but as an alternate view and solution to the complex differential equation. The solutions are consistent with both classical, and quantum mechanics. The underlying mechanism defining the equation and the particle properties is presumed to be QFT, but physical interpretations are not the standard probability interpretation of QM. Located at http://www.arxdtf.org/css/system.pdf   

Unified Field Theory and Force Formulas of Interactions

The main objective of this talk is to drive a unified field model coupling four interactions, based on the principle of interaction dynamics (PID) and the principle of representation invariance (PID). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint. PRI requires that physical laws be independent of representations of the gauge groups. One important outcome of this unified field model is a natural duality between the interacting fields $(g, A, W^a, S^k)$, corresponding to graviton, photon, intermediate vector bosons $W^\pm$ and $Z$ and gluons, and the adjoint bosonic fields $(\Phi_\mu, \phi^0, \phi^a_w, \phi^k_s)$. This duality predicts two Higgs particles of similar mass with one due to weak interaction and the other due to strong interaction. PID and PRI can be applied directly to individual interactions, leading to 1) modified Einstein equations, giving rise to a unified theory for dark matter and dark energy, 2) three levels of strong interaction potentials for quark, nucleon/hadron, and atom respectively, and 3) a weak interaction potential. These potential/force formulas offer a clear mechanism for both quark confinement and asymptotic freedom.   

Using dispersion relations to look for new physics in pp elastic scattering at the LHC

The presence of new particles at the TeV+ scale is common to many new physics models. We provide a novel way for possibly probing the existence of a broad class of such models. The usage of integral dispersion relations (IDRs) is a well established technique for examining properties of $pp$ scattering at all energies. IDRs rely on Cauchy's integral formula and the analyticity of the scattering amplitude. In this talk, we analyze the possibility to extend to energy reach of colliders. We find that IDRs do allow the inference of new physics beyond the reach of direct production. However, the extended reach seems to be small. We explain why.   

Lorentz violation in positronium decay from the Standard Model Extension

Positronium is an attractive system for the study of fundamental symmetries and interactions because of its relative simplicity and its accessibility to precision measurements. As such, it can be (and has been) used as a laboratory in the search for beyond-the-standard-model physics. One approach to parametrizing such new physics is through the standard model extension (SME). The SME effective Lagrangian involves a number of new interactions not present in the standard model, many of which violate fundamental symmetries such as Lorentz invariance and CPT. We have calculated the leading-order effects of the SME on the decay rates or para- and orthopositronium and on correlations involving the initial orthopositronium polarization, finding effects that are measureable in principle.