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T. G. Steele

Publications and source records attributed to T. G. Steele.

At least 145 records · Page 8Linked to original sources
arXiv2000

Probing the Infrared Structure of Gauge Theories: A Pade-Approximant Approach

Pade-approximant treatments of the known terms of the QCD $β$-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop $β$-function contribution. Below this flavour threshold, Pade approximants based upon the QCD $β$-function manifest the same infrared attractor structure as that which characterizes the exact NSVZ $β$-function of supersymmetric gluodynamics. Such infrared attractor structure is also seen to characterize Pade-approximant treatments of vector SU(N) gauge theory in the large $N$ limit, suggesting common infrared dynamics for the strong and weak phases of this theory.

hep-ph↗
arXiv2000

Holder Inequalities and Bounds on the Masses of Light Quarks

QCD Laplace sum-rules must satisfy a fundamental (Holder) inequality if they are to consistently represent an integrated hadronic cross-section. After subtraction of the pion-pole, the Laplace sum-rule of pion currents is shown to violate this fundamental inequality unless the up and down quark masses are sufficiently large, placing a lower bound on the 1.0 GeV MS-bar running masses.

hep-ph↗
arXiv2000

Hoelder Inequalities and QCD Sum-Rule Bounds on the Masses of Light Quarks

QCD Laplace Sum-Rules must satisfy a fundamental Hoelder inequality if they are to consistently represent an integrated hadronic spectral function. The Laplace sum-rules of pion currents is shown to violate this inequality unless the $u$ and $d$ quark masses are sufficiently large, placing a lower bound on $m_u+m_d$, the SU(2)-invariant combination of the light-quark masses.

hep-ph↗
arXiv2000

Reducing the Theoretical Uncertainty in Extracting |V_{ub}| from the Inclusive Semileptonic b to u Decay Rate

Utilizing asymptotic Pade-approximant methods, we estimate the three-loop order MS-bar coefficients of alpha_s^3[\log(μ^2/m^2_b(μ)]^k terms [k = {0,1,2,3}] within the $b \to u\ell^-\barν_\ell$ decay rate. Except for the coefficient of the k = 0 term, all other coefficients may also be obtained via renormalization-group (RG) methods. The relative errors in asymptotic Pade-approximant estimates of the k = {1,2,3} terms are found to be 5.1% or less, thereby providing an estimate of the theoretical uncertainty in the asymptotic Pade-approximant estimate of the RG-inaccessible k = 0 term. By a judicious choice in the renormalization scale parameter, we are able to extract |V_{ub}| from the inclusive decay rate to within 7% theoretical uncertainty.

hep-ph↗
arXiv2000

Next-Order Estimate of Higgs to Two-Gluon Rate

Using asymptotic Pade approximant methods, we have calculated the O(alpha_s^5) contribution to the Standard-Model H to gg decay rate. This process is of particular interest because of the slow convergence evident from the known terms of its QCD series. The O(alpha_s^5) term is expressed as a 3rd degree polynomial in $L= log (\frac{μ^2}{m_t^2(μ)})$. We find that the asymptotic Pade predictions for the renormalization-group accessible coefficients of L, L^2 and L^3 are within 1%, 2% and 7% of their respective values. The inclusion of the O(alpha_s^5) contribution renders the full decay rate virtually scale independent over the entire 0.3 M_H < mu < M_t range of the renormalization scale mu.

hep-ph↗
arXiv2000

Gaussian Sum-Rules and Prediction of Resonance Properties

Techniques for using Gaussian QCD sum-rules to predict hadronic resonance properties are developed for single-resonance and two-resonance phenomenological models, and criteria are developed for determining which of these models is required for analyzing a particular hadronic channel. The vector current sum-rule coupled to the $ρ$ meson is shown to be consistent with a single resonance model, and the Gaussian sum-rule analysis results in an accurate $ρ$ mass prediction which exhibits excellent agreement between the theoretical prediction of the Gaussian sum-rule and the phenomenological model. A two-resonance model is shown to be necessary for the Gaussian sum-rule for the non-strange quark scalar ($\bar n n$) currents. The two-resonance Gaussian sum-rule analysis of the isoscalar and isovector ($I=0,1$) $\bar n n$ scalar mesons exhibits excellent agreement between the theoretical prediction and phenomenological model. The prediction of the resonance properties of the $I=0,1$ $\bar n n$ scalar mesons in this two-resonance model provides valuable information for the interpretation of the scalar mesons, including the X(1775).

hep-ph↗
arXiv2000

Pade-Summation Approach to QCD Beta-Function Infrared Properties

We address whether Padé-summations of the $\bar{MS}$ QCD $β$-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and Shifman for the case of supersymmetric gluodynamics. Below an approximant-dependent flavour threshold $(6 \leq n_f \leq 8)$, we find that Padé-summation $β$-functions incorporating $[2|1], [1|2], [2|2], [1|3]$, and $[3|1]$ approximants always exhibit a positive pole prior to the occurrence of their first positive zero, precluding any identification of this first positive zero as an infrared-stable fixed point of the $β$- function. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop $β$-function contribution. Moreover, the pole in question suggests the occurrence of dynamics in which both a strong and an asymptotically-free phase share a common infrared attractor. We briefly discuss the possible relevance of infrared-attractor dynamics to the success of recent calculations of the glueball mass spectra in QCD with $N_c \to \infty$ via supergravity. As $n_f$ increases above an approximant-dependent flavour threshold, Padé-summation $β$-functions incorporating $[2|2], [1|3]$, and $[3|1]$ approximants exhibit dynamics controlled by an infrared-stable fixed point over a widening domain of the five-loop $\bar{MS}$ $β$-function parameter $(β_4/β_0)$. Above this threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number.

hep-ph↗
arXiv2000

Extended BRS Symmetry and Gauge Independence in On-Shell Renormalization Schemes

Extended BRS symmetry is used to prove gauge independence of the fermion renormalization constant $Z_2$ in on-shell QED renormalization schemes. A necessary condition for gauge independence of $Z_2$ in on-shell QCD renormalization schemes is formulated. Satisfying this necessary condition appears to be problematic at the three-loop level in QCD.

hep-th↗
arXiv2000

Pade-Improved Estimates of Hadronic Higgs Decay Rates

Asymptotic Pade-approximant methods are utilized to estimate the order $α_s^5$ contribution to the $H\to gg$ rate and the order $α_s^4$ contribution to the $H \to b \bar{b}$ rate. The former process is of particular interest because of the slow convergence evident from the three known terms of its QCD series, which begins with an order $α_s^2$ leading-order term. The order $α_s^5$ contribution to the $H \to gg$ rate is expressed as a degree-3 polynomial in $L \equiv ln (μ^2 / m_t^2 (μ))$. We find that asymptotic Pade-approximant predictions for the coefficients of $L$, $L^2$, and $L^3$ are respectively within 1%, 2%, and 7% of true values extracted via renormalization-group methods. Upon including the full set of next-order coefficients, the $H \to gg$ rate is found to be virtually scale-independent over the 0.3 $M_{H} < μ< M_t$ range of the renormalization scale-parameter $μ$. We conclude by discussing the small order $α_s^4$ contribution to the $H \to b \bar{b}$ rate, which is obtained from a prior asymptotic Pade-approximant estimate of the order $α_s^4$ contribution to the quark-antiquark scalar-current correlation function.

hep-ph↗
arXiv2000

Estimate of the Three-Loop Perturbative Contribution to Inclusive Semileptonic b to u Decays

We utilize asymptotic Pade-approximant methods to estimate the three-loop order MS bar-scheme coefficients within the inclusive semileptonic b to u decay rate for four and five active quark flavours. The estimates we obtain for the three renormalization-group-accessible coefficients within the three-loop contribution are all found to be within 5.1% of their true values, using a least-squares procedure in conjunction with an asymptotic Pade-approximant estimate of the three-loop term over the entire $μ\ge m_b$ domain. Given the input values $α_s(M_Z) = 0.118 \pm 0.004$ and $m_b(m_b) =4.17 \pm 0.05 GeV$, the three-loop expression for the purely-perturbative contribution to the decay rate is minimally sensitive to renormalization scale at $μ= 1.775 GeV$, at which scale the three-loop contribution is estimated to be only 1.4% of the leading tree-order contribution. We estimate the full perturbative decay rate to be $192π^3Γ(b\to u\barν_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2070 {\rm GeV^5} \pm 16%$, inclusive of theoretical uncertainties from series truncation, the input parameters, and the estimation procedure.

hep-ph↗
arXiv2000

Hoelder Inequalities and Isospin Splitting of the Quark Scalar Mesons

A Hoelder inequality analysis of the QCD Laplace sum-rule which probes the non-strange (n\bar n) components of the I={0,1} (light-quark) scalar mesons supports the methodological consistency of an effective continuum contribution from instanton effects. This revised formulation enhances the magnitude of the instanton contributions which split the degeneracy between the I=0 and I=1 channels. Despite this enhanced isospin splitting effect, analysis of the Laplace and finite-energy sum-rules seems to preclude identification of a_0(980) and a light broad sigma-resonance state as the lightest isovector and isoscalar spin-zero $n\bar n$ mesons. This apparent decoupling of sigma [\equiv f_0(400-1200)] and a_0(980) from the quark n\bar n scalar currents suggests either a non-q \bar q or a dominantly s\bar s interpretation of these resonances, and further suggests the possible identification of the f_0(980) and a_0(1450) as the lightest I={0,1} scalar mesons containing a substantial n\bar n component.

hep-ph↗
arXiv1999

Pade-Improvement of CP-odd Higgs Decay Rate into Two Gluons

We present an asymptotic Pade-approximant estimate for the four-loop coefficients within the linear combination of correlators entering the recently calculated decay rate of a CP-odd Higgs boson, with an assumed mass $m_A = 100 GeV$, into two gluons. All but one of these coefficients are shown to be determined for arbitrary $m_A$ from the known 3-loop-order rate by renormalization group methods. Asymptotic Pade-approximant estimates for these coefficients are all seen to be within 12% of their correct values. The four-loop term in the decay rate for $m_A = 100 GeV$ is estimated to be only 4.3% of its leading one-loop contribution.

hep-ph↗
arXiv1999

QCD Sum-Rule Invisibility of the sigma Meson

QCD Laplace sum-rules for light-quark I=0,1 scalar currents are used to investigate candidates for the lightest $q\bar q$ scalar mesons. The theoretical predictions for the sum-rules include instanton contributions which split the degeneracy between the I=0 and I=1 channels. The self-consistency of the theoretical predictions is verified through a Hölder inequality analysis, confirming the existence of an effective instanton contribution to the continuum. The sum-rule analysis indicates that the f_0(980) and a_0(1450) should be interpreted as the lightest $q\bar q$ scalar mesons. This apparent decoupling of the f_0(400-1200) (or $σ$) and a_0(980) from the quark scalar currents suggests a non-$q\bar q$ interpretation of these resonances.

hep-ph↗
arXiv1999

Pade-Improved Extraction of $α_s(M_τ)$ from $R_τ$

The perturbative series used to extract $α_s(M_τ)$ from the $τ$ hadronic width exhibits slow convergence. Asymptotic Pade-approximant and Pade summation techniques provide an estimate of these unknown higher-order effects, leading to values for $α_s(M_τ)$ that are about 10% smaller than current estimates. Such a reduction improves the agreement of $α_s(M_τ)$ with the QCD evolution of the strong coupling constant from $α_s(M_z)$.

hep-ph↗
arXiv1998

Asymptotic Pade-Approximant Methods and QCD Current Correlation Functions

Asymptotic Pade-approximant methods are utilized to estimate the leading-order unknown (i.e., not-yet-calculated) contributions to the perturbative expansions of two-current QCD correlation functions obtained from scalar-channel fermion and gluon currents, as well as from vector-channel fermion currents. Such contributions to the imaginary part of each correlator are polynomials of logarithms whose coefficients (other than the constant term within the polynomial) may be extracted from prior-order contributions by use of the renormalization-group (RG) equation appropriate for each correlator. We find surprisingly good agreement between asymptotic Pade-approximant predictions and RG-determinations of such coefficients for each correlation function considered, although such agreement is seen to diminish with increasing numbers of quark flavours. The RG-determined coefficients we obtain are then utilized in conjunction with asymptotic Pade-approximant methods to predict the RG-inaccessible constant terms of the leading-order unknown contributions for all three correlators. The vector channel predictions lead to estimates for the order $(α_s^4)$ contribution to $R(s) \equiv[σ(e^+ e^- \to hadrons) / σ(e^+ e^- \to μ^+ μ^-)]$ for three, four, and five flavours.

hep-ph↗
arXiv1998

Asymptotic Pade-Approximant Predictions for Renormalization-Group Functions of Massive $ϕ^4$ Scalar Field Theory

Within the context of massive N-component $ϕ^4$ scalar field theory, we use asymptotic Pade-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant beta-function $β_g$, the anomalous mass dimension $γ_m$, the vacuum-energy beta-function $β_v$, and the anomalous dimension $γ_2$ of the scalar field propagator. These estimates are then compared with explicit calculations of the five-loop contributions to $β_g$, $γ_m$, $β_v$, and are seen to be respectively within 5%, 18%, and 27% of their true values for $N$ between 1 and 5. We then extend asymptotic Pade-approximant methods to predict the presently unknown six-loop contributions to $β_g$, $γ_m$, and $β_v$. These predictions, as well as the six-loop prediction for $γ_2$, provide a test of asymptotic Pade-approximant methods against future calculations.

hep-ph↗
arXiv1998

Fixed point structure of Pade-summation approximations to the QCD beta-function

Padé-improvement of four-loop beta-functions in massive phi^4 scalar field theory is shown to predict the known five-loop contribution with astonishing (0.2%) accuracy, supporting the applicability of Pade-summations for approximating all-orders MS-bar QCD beta-functions, as suggested by Ellis, Karliner, and Samuel. Surprisingly, the most general set of [2|2] approximants consistent with known two-, three-, and four-loop contributions to the QCD beta-function with up to six flavours fail to exhibit any zeros that could be interpreted as positive infrared fixed points, regardless of the unknown five-loop term. When they occur, positive zeros of such [2|2] approximants are preceded by singularities, leading to a double-valued beta-function that is decoupled entirely from the infrared region, similar to the beta-function of SUSY gluodynamics.

hep-ph↗