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T. G. Steele

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

158 records · Page 9Linked to original sources
arXiv1998

Compatibility of $α_s(M_τ)$ with $α_s(M_Z)$

The current phenomenological determinations of $α_s(M_τ)$ and $α_s(M_Z)$ are shown to be only marginally consistent with the QCD evolution of the strong coupling constant between $M_Z$ and $M_τ$. This motivates a revised estimate of $α_s(M_τ)$ since the perturbative series used to extract $α_s(M_τ)$ from the $τ$ hadronic width exhibits slow convergence. Padé summation techniques provide an estimate of these unknown higher-order effects, leading to the revised determination $α_s(M_τ)=0.333\pm 0.030 $. This value is 10% smaller than current estimates, improving the compatibility of phenomenological estimates for $α_s(M_τ)$ and $α_s(M_Z)$ with the QCD evolution of the strong coupling constant.

hep-ph↗
arXiv1998

Pade-Improvement of QCD Running Coupling Constants, Running Masses, Higgs Decay Rates, and Scalar Channel Sum Rules

We discuss Padé-improvement of known four-loop order results based upon an asymptotic three-parameter error formula for Padé-approximants. We derive an explicit formula estimating the next-order coefficient $R_4$ from the previous coefficients in a series $1+R_1 x + R_2x^2 + R_3x^3$. We show that such an estimate is within 0.18% of the known five-loop order term in the O(1) $β$-function, and within 10% of the known five-loop term in the O(1) anomalous mass-dimension function $γ_m(g)$. We apply the same formula to generate a [2$|$2] Padé-summation of the QCD $β$-function and anomalous mass dimension in order to demonstrate both the relative insensitivity of the evolution of $α_s(μ)$ and the running quark masses to higher order corrections, as well as a somewhat increased compatibility of the present empirical range for $α_s(m_τ)$ with the range anticipated via evolution from the present empirical range for $α_s(M_z)$. For $3 \leq n_f \leq 6$ we demonstrate that positive zeros of any [2$|$2] Padé-summation estimate of the all-orders $β$-function which incorporates known two-, three-, and four-loop contributions necessarily correspond to ultraviolet fixed points, regardless of the unknown five-loop term. Padé-improvement of higher-order perturbative expressions is presented for the decay rates of the Higgs into two gluons and into a $b \bar{b}$ pair, and is used to show the relative insensitivity of these rates to higher order effects. However, Padé-improvement of the purely-perturbative component of scalar/pseudoscalar current correlation functions is indicative of large theoretical uncertainties in QCD sum rules for these channels, particularly if the continuum-threshold parameter $s_0$ is near 1 GeV$^2$.

hep-ph↗
arXiv1998

QCD Sum-Rule Consistency of Lowest-Lying Quark Scalar Resonances

We investigate lowest-lying scalar meson properties predicted from QCD Laplace sum rules based upon isovector and isoscalar non-strange $\bar{q}q$ currents. The hadronic content of these sum rules incorporates deviations from the narrow resonance approximation anticipated from physical resonance widths. The field theoretical content of these sum rules incorporates purely-perturbative QCD contributions to three-loop order, the direct single-instanton contribution in the instanton liquid model, and leading contributions from QCD-vacuum condensates. In the isovector channel, the results we obtain are compatible with a$_0$(1450) being the lowest-lying $q\bar{q}$ resonance, and are indicative of a non-$q\bar{q}$ interpretation for a$_0$(980). In the isoscalar channel, the results we obtain are compatible with the lowest lying $q\bar{q}$ resonance being f$_0$(980) or a state somewhat lighter than f$_0$(980) whose width is less than half of its mass. The dilaton scenario for such a narrower $σ$-resonance is discussed in detail, and is found compatible with sum rule predictions for the resonance coupling only if the anomalous gluon-field portion of $Θ_μ^μ$ dominates the matrix element $<σ|Θ_μ^μ|0>$. A linear sigma-model interpretation of the lowest-lying resonance's coupling, when compared to the coupling predicted by sum rules, is indicative of a renormalization-group invariant light-quark mass between 4 and 6 MeV.

hep-ph↗
arXiv1997

QCD Sum Rules and the Lowest-Lying I=0 Scalar Resonance

A QCD Laplace sum rule framework is employed to investigate the relationship between the mass and the decay width of the sigma, the lowest-lying isoscalar resonance in the spin-zero meson channel. Our analysis differs from prior analyses, not only by incorporating finite-width departures from the narrow resonance approximation, but also through the inclusion of direct-instanton contributions and three-loop-order perturbative effects. Assuming that the sigma is the dominant subcontinuum resonance in this channel, the least upper bound we obtain for the sigma-mass is shown to increase with the sigma-width, and suggests that a sigma lighter than 800 MeV should have a total width substantially smaller than its mass.

hep-ph↗
arXiv1997

Broad Sub-Continuum Resonances and the Case for Finite-Energy Sum-Rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We first discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We then show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension > 6 condensates containing at least one q-bar q pair. We extract the direct single-instanton contribution to the F_1 sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass resonance contributions within the pseudoscalar channel.

hep-ph↗
arXiv1997

QCD Sum Rules and the Pi(1300) Resonance

Global fits to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters are performed, leading to predictions for the pion-resonance mass and decay constant. Two scenarios are considered which differ only in their treatment of the dimension-six quark condensate $< O_6>$. The first scenario assumes an effective scale for $< O_6>$ from other sum-rule applications which is assumed to be independent of the physical value of the quark mass, while the second scenario requires self-consistency between the value of $< O_6>$ and the current algebra constraint $2m< \bar q q>=-f_π^2m_π^2$. Predictions of the pion-resonance mass $M_π$ and decay constant $F_π$ are obtained in these two scenarios. A byproduct of this analysis is a prediction of the renormalization-group invariant quark mass $(\hat m_u+\hat m_d)/2$.

hep-ph↗
arXiv1997

QCD Laplace Sum Rules and the $Π(1300)$ Resonance

A global fit to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters is performed, leading to predictions for the pion-resonance mass and decay constant. This fit leads to predictions of $M_π = 1.15 \pm 0.15 GeV$ for the pion-resonance mass, and $F_π^2=(4.5\pm 2.1).(f_π^2m_π^4/M_π^4)$ for the pion-resonance decay constant.

hep-ph↗
arXiv1997

Beyond the Narrow Resonance Approximation: Decay Constant and Width of the First Pion-Excitation State

We consider the first pion excitation as a sub-continuum resonance in the pseudoscalar channel, and we obtain parameters characterizing this resonance through a global fit of the Borel-parameter dependence of the field-theoretical pseudoscalar Laplace sum rule to its hadronic (pion + pion-excitation + QCD-continuum) content. Our analysis incorporates finite-width deviations from the narrow resonance approximation, instanton effects, and higher-loop perturbative contributions to the pseudoscalar correlator. We obtain the following values (uncertainties reflect 90% confidence levels): mass $M_Π= 1.15 \pm 0.28 GeV$, width $Γ_Π= < 0.48 GeV$, decay constant $r \equiv [F_ΠM_Π^2 / f_πm_π^2]^2 = 4.7 \pm 2.8$.

hep-ph↗
arXiv1997

Sum-Rule Inequalities and a Toy Model Paradox

Fundamental inequalities for QCD sum-rules are applied to resolve a paradox recently encountered in a sum-rule calculation. This paradox was encountered in a toy model known to be free of resonances that yields an apparent resonance using a standard sum-rule stability analysis. Application of the inequalities does not support the existence of a well defined sum-rule calculation, and shows a strong distinction from typical behaviour in QCD.

hep-ph↗
arXiv1995

Lower Bound on the Pion Polarizability from QCD Sum Rules

Making use of QCD sum rules a lower bound is found which relates the electromagnetic polarizability $α_{_E}$ and mean-square radius $\langle r_π^2\rangle$ of charged pions through the intrinsic polarizability $\tildeα_{_E}= α_{_E}-α\langle r_π^2\rangle/(3M_π)$. We find that if present constraints on the QCD continuum (duality) threshold are accepted, this lower bound on the intrinsic polarizability $\tildeα_{_E}$ is incompatible with some previous determinations of $α_{_E}$ and $\langle r_π^2\rangle$.

hep-ph↗
arXiv1995

Constraints on QCD Sum-rules from the Hölder Inequalities

A new technique based on Hölder's integral inequality is applied to QCD sum-rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum-rules are to consistently describe integrated physical cross-sections, but these constraints do not require any experimental data and therefore can be applied to any hadronic spectral function. As an illustration of this technique the Laplace sum-rules of the light-quark correlation function for the vector and the axial-vector currents are examined in detail. We find examples of inconsistency between the inequalities and sum-rule parameters used in some previous analyses of the vector and axial-vector channels.

hep-ph↗
arXiv1994

The Nielsen Identities for the Two-Point Functions of QED and QCD

We consider the Nielsen identities for the two-point functions of full QCD and QED in the class of Lorentz gauges. For pedagogical reasons the identities are first derived in QED to demonstrate the gauge independence of the photon self-energy, and of the electron mass shell. In QCD we derive the general identity and hence the identities for the quark, gluon and ghost propagators. The explicit contributions to the gluon and ghost identities are calculated to one-loop order, and then we show that the quark identity requires that in on-shell schemes the quark mass renormalisation must be gauge independent. Furthermore, we obtain formal solutions for the gluon self-energy and ghost propagator in terms of the gauge dependence of other, independent Green functions.

hep-th↗