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D. G. C. McKeon

Publications and source records attributed to D. G. C. McKeon.

At least 127 records · Page 7Linked to original sources
arXiv2005

A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime Dimensions

The canonical structure of the Einstein-Hilbert Lagrange density $L=\sqrt{-g}R$ is examined in two spacetime dimensions, using the metric density $h^{μν}\equiv \sqrt{-g}g^{μν}$ and symmetric affine connection $Γ_{σβ}^λ$ as dynamical variables. The Hamiltonian reduces to a linear combination of three first class constraints with a local SO(2,1) algebra. The first class constraints are used to find a generator of gauge transformations that has a closed off-shell algebra and which leaves the Lagrangian and $\det (h^{μν})$ invariant. These transformations are distinct from diffeomorphism invariance, and are gauge transformations characterized by a symmetric matrix $ζ_{μν}$.

hep-th↗
arXiv2005

Radiative Corrections to the Inflaton Potential as an Explanation of Suppressed Large Scale Power in Density Perturbations and the Cosmic Microwave Background

The Wilkinson Microwave Anisotropy Probe microwave background data suggest that the primordial spectrum of scalar curvature fluctuations is suppressed at small wavenumbers. We propose a UV/IR mixing effect in small-field inflationary models that can explain the observable deviation in WMAP data from the concordance model. Specifically, in inflationary models where the inflaton couples to an asymptotically free gauge theory, the radiative corrections to the effective inflaton potential can be anomalously large. This occurs for small values of the inflaton field which are of the order of the gauge theory strong coupling scale. Radiative corrections cause the inflaton potential to blow up at small values of the inflaton field. As a result, these corrections can violate the slow-roll condition at the initial stage of the inflation and suppress the production of scalar density perturbations.

hep-ph↗
arXiv2004

The Bargmann-Wigner Equations in Spherical Space

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of parameters characterizing them. For spheres embedded in three, four and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two point function shown to vanish at one loop order.

hep-th↗
arXiv2004

Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories

In the absence of a tree-level scalar-field mass, renormalization-group (RG) methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series for the effective-potential functions utilized in radiative symmetry breaking. For scalar-field electrodynamics, such a summation of leading logarithm contributions leads to upper bounds on the magnitudes of both gauge and scalar-field coupling constants, and suggests the possibility of an additional phase of spontaneous symmetry breaking characterized by a scalar-field mass comparable to that of the theory's gauge boson. For radiatively-broken electroweak symmetry, the all-orders summation of leading logarithm terms involving the dominant three couplings (quartic scalar-field, t-quark Yukawa, and QCD) contributing to standard-model radiative corrections leads to an RG-improved potential characterized by a 216 GeV Higgs boson mass. Upon incorporation of electroweak gauge couplants we find that the predicted Higgs mass increases to 218 GeV. The potential is also characterized by a quartic scalar-field coupling over five times larger than that anticipated for an equivalent Higgs mass obtained via conventional spontaneous symmetry breaking, leading to a concomitant enhancement of processes (such as $W^+ W^- \to ZZ$) sensitive to this coupling. Moreover, if the QCD coupling constant is taken to be sufficiently strong, the tree potential's local minimum at $ϕ= 0$ is shown to be restored for the summation of leading logarithm corrections. Thus if QCD exhibits a two-phase structure similar to that of $N = 1$ supersymmetric Yang-Mills theory, the weaker asymptotically-free phase of QCD may be selected by the large logarithm behaviour of the RG-improved effective potential for radiatively broken electroweak symmetry.

hep-ph↗
arXiv2004

Summation of Higher Order Effects using the Renormalization Group Equation

The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on these higher order effects determined by the RG. Particular attention is payed to the relationship between bare and renormalized quantities. Application of the method of characteristics to the RG equation to determine higher order effects is discussed, and is used to examine the free energy in thermal field theory, the relationship between the bare and renormalized coupling and the effective potential in massless scalar electrodynamics.

hep-th↗
arXiv2004

Supersymmetry on AdS3 and AdS4

We consider a supersymmetric extension of the algebra associated with three and four dimensional Anti de Sitter space. A representation of the supersymmetry operators in superspace is given. Supersymmetry invariant models are constructed for the superspace associated with AdS3.

hep-th↗
arXiv2003

Transmutation of Scale Dependence into Truncation Uncertainty via RG-Improvement of the $R(s)$ Series

The arbitrariness in how the logarithm is defined within the QCD series for the inclusive electroproduction cross-section is shown to affect the summation to all orders in $α_s$ of leading and successively-subleading logarithms within that perturbative series, even though such summations largely eliminate the residual dependence of the original series on the arbitrary renormalization scale $μ$. However, given that the original (unimproved) series is known to third-order in $α_s(μ)$, this logarithm ambiguity is shown not to enter the optimally improved summation-of-logarithms series until the term fourth-order in $α_s(s)$, where $s$ is the physical center-of-mass energy squared. Consequently, the ambiguity in how the logarithm is defined is absorbable in the uncertainty associated with truncating the original perturbative series after its calculationally known terms.

hep-ph↗
arXiv2003

Radiative Electroweak Symmetry-Breaking Revisited

In the absence of a tree-level scalar-field mass, renormalization-group methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series within the effective potential for $SU(2)\times U(1)$ electroweak symmetry. This improvement of the effective potential function is seen to reduce residual dependence on the renormalization mass scale. The all-orders summation of leading logarithm terms involving the dominant three couplings contributing to radiative corrections is suggestive of a potential characterized by a plausible Higgs boson mass of 216 GeV. However, the tree potential's local minimum at $ϕ=0$ is restored if QCD is sufficiently strong.

hep-ph↗
arXiv2003

Consequences of Leading-Logarithm Summation for the Radiative Breakdown of Standard-Model Electroweak Symmetry

In the empirically sensible limit in which QCD, t-quark Yukawa, and scalar-field-interaction coupling constants dominate all other Standard-Model coupling constants, we sum all leading-logarithm terms within the perturbative expansion for the effective potential that contribute to the extraction of the Higgs boson mass via radiative electroweak symmetry breaking. A Higgs boson mass of 216 GeV emerges from such terms, as well as a scalar-field-interaction coupling constant substantially larger than that anticipated from conventional spontaneous symmetry breaking. The sum of the effective potential's leading logarithms is shown to exhibit a local minimum in the limit $ϕ\to 0$ if the QCD coupling constant is sufficiently strong, suggesting (in a multiphase scenario) that electroweak physics may provide the mechanism for choosing the asymptotically-free phase of QCD.

hep-ph↗
arXiv2003

Antisymmetric Tensor Gauge Fields on S_4

Antisymmetric tensor gauge fields phi_{ab}(eta) are formulated on the surface of a sphere S_4t(eta^2 = a^2) embedded in five dimensions. The free field model is equivalent to a scalar model on this sphere. Interactions with gauge fields are discussed. It is feasable to formulate models for interactions with U(1) gauge fields A_a(eta) that are akin to those of Freedman and Townsend in flat space. In addition, it proves possible to have a novel interaction of phi_{ab}with A_a and a spinor field Psi(eta) on S_4 with both Abelian and non-Abelian gauge invariance. In these models, A_a plays the role of a Stueckelberg field.

hep-th↗
arXiv2003

Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics

We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron-positron annihilation cross-section. We demonstrate how one such renormalization-group improvement of this series is equivalent to a closed-form summation of the first four towers of renormalization-group accessible logarithms to all orders of perturbation theory.

hep-th↗
arXiv2003

Vanishing of the Bare Coupling in Four Dimensions

We examine two restructurings of the series relationship between the bare and renormalized coupling constant in dimensional regularization. In one of these restructurings, we are able to demonstrate via all-orders summation of leading and successive epsilon = 0 (dimensionality = 4) poles that the bare coupling vanishes in the dimension-4 limit.

hep-th↗
arXiv2003

Optimal Renormalization-Group Improvement of the Perturbative Series for the e^+ e^- -Annihilation Cross-Section

Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = sigma(e^+ e^- --> hadrons)/sigma(e^+ e^- --> mu^+ mu^-), as obtained from the imaginary part of the purely-perturbative vector-current correlation function. We present explicit solutions for the summation of leading and up to three subsequent subleading orders of logarithms. The summations accessible from the four-loop vector-correlator not only lead to a substantial reduction in sensitivity to the renormalization scale, but necessarily impose a common infrared bound on perturbative approximations to R(s), regardless of the infrared behaviour of the true QCD couplant.

hep-ph↗
arXiv2002

Supersymmetry on the Surface S_2

By using symplectic Majorana spinors as Grassmann coordinates in a superspace associated with the supersymmetric extension of the isometry group on the spherical surface S_2, it proves possible to formulate supersymmetric models on S_2 using superspace techniques.

hep-th↗
arXiv2002

Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms

Invariance of the effective action under changes of the renormalization scale $μ$ leads to relations between those (presumably calculated) terms independent of $μ$ at a given order of perturbation theory and those higher order terms dependent on logarithms of $μ$. This relationship leads to differential equations for a sequence of functions, the solutions of which give closed form expressions for the sum of all leading logs, next to leading logs and subsequent subleading logarithmic contributions to the effective action. The renormalization group is thus shown to provide information about a model beyond the scale dependence of the model's couplings and masses. This procedure is illustrated using the $ϕ_6^3$ model and Yang-Mills theory. In the latter instance, it is also shown by using a modified summation procedure that the $μ$ dependence of the effective action resides solely in a multiplicative factor of $g^2 (μ)$ (the running coupling). This approach is also shown to lead to a novel expansion for the running coupling in terms of the one-loop coupling that does not require an order-by-order redefinition of the scale factor $Λ_{QCD}$. Finally, logarithmic contributions of the instanton size to the effective action of an SU(2) gauge theory are summed, allowing a determination of the asymptotic dependence on the instanton size $ρ$ as $ρ$ goes to infinity to all orders in the SU(2) coupling constant.

hep-ph↗
arXiv2002

AdS2 Models in an Embedding Superspace

An embedding superspace, whose Bosonic part is the flat 2 + 1 dimensional embedding space for AdS2, is introduced. Superfields and several supersymmetric models are examined in the embedded AdS2 superspace.

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