arXiv subjects

V. Elias

Publications and source records attributed to V. Elias.

At least 19 recordsLinked to original sources

arXiv2006

On the Standard Approach to Renormalization Group Improvement

Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing N^{n}LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless $λϕ^{4}$ model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.

hep-th↗

arXiv2006

Trailing Edge Unification via an Intermediate Pati-Salam Group

We demonstrate to two-loop order that an intermediate symmetrically embedded Pati-Salam $SU(2)_L \times SU(2)_R \times SU(4)$ level of symmetry is all that is necessary to accommodate empirical values of $α(M_z), α_s(M_z)$ and $\sin^2θ_w(M_z)$ within a grand unification context but with a high (10^{14} GeV) intermediate mass scale and with a concomitant higher GUT scale.

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arXiv2006

Stability of Subsequent-to-Leading-Logarithm Corrections to the Effective Potential for Radiative Electroweak Symmetry Breaking

We demonstrate the stability under subsequent-to-leading logarithm corrections of the quartic scalar-field coupling constant $λ$ and the running Higgs boson mass obtained from the (initially massless) effective potential for radiatively broken electroweak symmetry in the single-Higgs-Doublet Standard Model. Such subsequent-to-leading logarithm contributions are systematically extracted from the renormalization group equation considered beyond one-loop order. We show $λ$ to be the dominant coupling constant of the effective potential for the radiatively broken case of electroweak symmetry. We demonstrate the stability of $λ$ and the running Higgs boson mass through five orders of successively subleading logarithmic corrections to the scalar-field-theory projection of the effective potential for which all coupling constants except the dominant coupling constant $λ$ are disregarded. We present a full next-to-leading logarithm potential in the three dominant Standard Model coupling constants ($t$-quark-Yukawa, $α_s$, and $λ$) from these coupling constants' contribution to two loop $β$- and $γ$-functions. Finally, we demonstrate the manifest order-by-order stability of the physical Higgs boson mass in the 220-231 GeV range. In particular, we obtain a 231 GeV physical Higgs boson mass inclusive of the $t$-quark-Yukawa and $α_s$ coupling constants to next-to-leading logarithm order, and inclusive of the smaller $SU(2)\times U(1)$ gauge coupling constants to leading logarithm order.

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arXiv2006

Improvement of Renormalization-Scale Uncertainties Within Empirical Determinations of the b-Quark Mass

Accurate determinations of the MS-bar b-quark mass $m_b(m_b)$ from $σ(e^+e^-\to{\rm hadrons})$ experimental data currently contain three comparable sources of uncertainty; the experimental uncertainty from moments of this cross-section, the uncertainty associated with $α_s(M_z)$, and the theoretical uncertainty associated with the renormalization scale. Through resummation of all logarithmic terms explicitly determined in the perturbative series by the renormalization-group (RG) equation, it is shown that the renormalization-scale dependence is virtually eliminated as a source of theoretical uncertainty in $m_b(m_b)$. This resummation also reduces the estimated effect of higher-loop perturbative contributions, further reducing the theoretical uncertainties in $m_b(m_b)$. Furthermore, such resummation techniques improve the agreement between the values of the MS-bar b-quark mass extracted from the various moments of $R(s)=σ(e^+e^-\to{\rm hadrons})/σ_{pt}$ [$σ_{pt}=4πα^2/(3s)$], obviating the need to choose an optimummoment for determining $m_b(m_b)$. Resummation techniques are also shown to reduce renormalization-scale dependence in the relation between b-quark MS-bar and pole mass and in the relation between the pole and $1S$ mass.

hep-ph↗

arXiv2006

Massless Scalar Field Propagator in a Quantized Space-Time

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H.S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex $p^2$ plane and goes like $1/p^2$ as $p^2\to 0$ from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as $p^2$ increases to the discretization scale $1/a^2$ and remains zero for $p^2>1/a^2$. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-production branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when $1/a^2<p^2<\infty$. Finally, we argue that the spectral function for the multiparticle states appears to saturate as $p^2$ probes just beyond the $1/a^2$ discretization scale. We speculate on the cosmological consequences of such a spectral function.

hep-th↗

arXiv2005

Diminished Upper Bounds on the Unification Mass Scales for Heavy Higgs Boson Masses

We consider dominant 3-, 4-, and 5-loop contributions to $λ$, the quartic scalar coupling-constant's $β$-function in the Standard Model. We find that these terms accelerate the evolution of $λ$ to nonperturbative values, thereby lowering the unification bound for which scalar-couplings are still perturbative. We also find that these higher order contributions imply a substantial lowering of $λ$ itself before the anticipated onset of nonperturbative physics in the Higgs sector.

hep-th↗

arXiv2005

The Renormalization Group with Exact beta-Functions

The perturbative $β$-function is known exactly in a number of supersymmetric theories and in the 't Hooft renormalization scheme in the $ϕ_4^4$ model. It is shown how this allows one to compute the effective action exactly for certain background field configurations and to relate bare and renormalized couplings. The relationship between the MS and SUSY subtraction schemes in $N = 1$ super Yang-Mills theory is discussed.

hep-th↗

arXiv2005

Higher Order Stability of a Radiatively Induced 220 GeV Higgs Mass

The effective potential for radiatively broken electroweak symmetry in the single Higgs doublet Standard Model is explored to four sequentially subleading logarithm-summation levels (5-loops) in the dominant Higgs self-interaction couplant $λ$. We augment these results with all contributing leading logarithms in the remaining large but sub-dominant Standard Model couplants (t-quark, QCD and $SU(2)\otimes U(1)$ gauge couplants) as well as next to leading logarithm contributions from the largest of these, the t-quark and QCD couplants. Order-by-order stability is demonstrated for earlier leading logarithm predictions of an order 220 GeV Higgs boson mass in conjunction with fivefold enhancement of the value for $λ$ over that anticipated from conventional spontaneous symmetry breaking.

hep-ph↗

arXiv2005

Radiative Electroweak Symmetry Breaking Beyond Leading Logarithms

The top-quark Yukawa coupling is too large to permit radiative electroweak symmetry breaking to occur for small values of y, the Higgs self-coupling, to leading-logarithm order. However, a large y solution leading to a viable Higgs mass of approximately 220 GeV does exist, and differs from conventional symmetry breaking by an approximately five-fold enhancement of the Higgs self-coupling. This scenario for radiative symmetry breaking is reviewed, and the order-by-order perturbative stability of this scenario is studied within the scalar field theory projection of the standard model in which the Higgs self-coupling y represents the dominant standard-model coupling.

hep-ph↗

arXiv2005

Startling Equivalences in the Higgs-Goldstone Sector between Radiative and Lowest-Order Conventional Electroweak Symmetry Breaking

For the Higgs boson mass of $\sim 220$ GeV expected to arise from radiative electroweak symmetry breaking, we find the same lowest-order expressions as would be obtained from conventional electroweak symmetry breaking, given the same Higgs boson mass, for Higgs-Goldstone sector scattering processes identified with $W_L^ + W_L^- \to W_L^+ W_L^-$, $W_L^+ W_L^- \to Z_L Z_L$, as well as for Higgs boson decay widths $H \to W_L^+ W_L^-$, $H \to Z_L Z_L$. The radiatively broken case, however, leads to an order of magnitude enhancement over lowest-order conventional symmetry breaking for scattering processes $W_L^+ W_L^+ \to H H$, $Z_L Z_L \to H H$, as well as a factor of $\sim 30$ enhancement for $H H \to H H$.

hep-ph↗

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

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↗

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

Optimal RG-Improvement of Perturbative Calculations in QCD

Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation functions. For a QCD perturbative series known to four orders, such as the e+ e- annihilation cross-section, explicit solutions to these equations are obtained for the summation to all orders in alpha_s of the leading set and the subsequent two non-leading sets of logarithms. Such summations are shown for a number of processes to lead to a substantial reduction in sensitivity to the renormalization scale parameter. Surprisingly, such summations are also shown to lower the infrared singularity within the perturbative expression for the e+ e- annihilation cross-section to coincide with the Landau pole of the naive one-loop running QCD couplant.

hep-ph↗

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.

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