arXiv subjects

T. G. Steele

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

At least 127 records · Page 7Linked to original sources

arXiv2003

Gaussian Sum-Rule Analysis of Scalar Gluonium and Quark Mesons

Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum-rules, including instanton effects, for scalar gluonic and non-strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum-rules are remarkably consistent in their prediction of masses of approximately 1.0 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons.

hep-ph↗

arXiv2003

Can the Mechanism for $π_1\to ηπ,η'π$ Hybrid Decays be Detected?

Two mechanisms for the $π_1$ ($J^{PC}=1^{-+}$) hybrid meson decay processes $π_1\toηπ,η'π$ are investigated. These mechanisms are applied to $ϕ\toηγ,η'γ$ and $J/ψ\toηγ,η'γ$ decays to illustrate the validity of the decay mechanisms and to obtain independent information on the coupling of $η,η'$ to quark and gluonic operators. From this information, we find that $Γ(π_1\toηπ)/Γ(π_1\toη'π)$ is substantially different in the two decay mechanisms, and hence future experimental measurements of this ratio will provide valuable information for substantiating the hybrid nature of these states and for determining the mechanism for these hybrid decays.

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.

hep-th↗

arXiv2003

Instanton Effects on the Role of the Low-Energy Theorem for the Scalar Gluonic Correlation Function

Instanton contributions to the Laplace sum-rules for correlation functions of scalar gluonic currents are calculated. The role of the constant low-energy theorem term, whose substantial contribution is unique to the leading Laplace sum-rule $L_{-1}$, is shown to be diminished by instanton contributions, significantly increasing the resulting mass bounds for the ground state of scalar gluonium and improving compatibility with results from higher-weight sum-rules.

hep-ph↗

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

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

Improved Determination of the Mass of the $1^{-+}$ Light Hybrid Meson From QCD Sum Rules

We calculate the next-to-leading order (NLO) $α_s$-corrections to the contributions of the condensates $<αG^2>$ and $<\bar qq>^2$ in the current-current correlator of the hybrid current $g\barq(x)γ_νiF_{μν}^aT^aq(x)$ using the external field method in Feynman gauge. After incorporating these NLO contributions into the Laplace sum-rules, the mass of the $J^{PC}$=$1^{-+}$ light hybrid meson is recalculated using the QCD sum rule approach. We find that the sum rules exhibit enhanced stability when the NLO $α_s$-corrections are included in the sum rule analysis, resulting in a $1^{-+}$ light hybrid meson mass of approximately 1.6 GeV.

hep-ph↗

arXiv2002

Gaussian Sum-Rules, Scalar Gluonium, and Instantons

Gaussian sum-rules relate a QCD prediction to a two-parameter Gaussian-weighted integral of a hadronic spectral function, providing a clear conceptual connection to quark-hadron duality. In contrast to Laplace sum-rules, the Gaussian sum-rules exhibit enhanced sensitivity to excited states of the hadronic spectral function. The formulation of Gaussian sum-rules and associated analysis techniques for extracting hadronic properties from the sum-rules are reviewed and applied to scalar gluonium. With the inclusion of instanton effects, the Gaussian sum-rule analysis results in a consistent scenario where the gluonic resonance strength is spread over a broad energy range below 1.6 GeV, and indicates the presence of gluonium content in more than one hadronic state.

hep-ph↗

arXiv2002

Pade/renormalization-group improvement of inclusive semileptonic B decay rates

Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS} scheme works favorably in the b \to u case whereas the pole mass scheme shows better convergence in the b \to c case. Upon the inclusion of the estimated three-loop contribution, we find the full perturbative decay rate to be 192π^3Γ(b\to u\barν_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm GeV^5} and 192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)= 992 \pm 198 {\rm GeV^5}, respectively. The errors are inclusive of theoretical uncertainties and non-perturbative effects. Ultimately, these perturbative contributions reduce the theoretical uncertainty in the extraction of the CKM matrix elements |V_{ub}| and |V_{cb}| from their respective measured inclusive semileptonic branching ratio(s).

hep-ph↗

arXiv2002

Renormalization-Mass Scale Dependence in QCD Contributions to Semileptonic $b \to u$ Decay

QCD contributions to the $b \to u \ell^- \barν_\ell$ decay rate, which are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient dependence on the renormalization mass $μ$ to compromise phenomenological predictions for inclusive semileptonic $B \to X_u$ processes. Such scale dependence is ameliorated by the renormalization-group (RG) extraction and summation of all leading and RG-accessible subleading logarithms occurring subsequent to two-loop order in the perturbative series. This optimal RG-improvement of the known portion of the perturbative series virtually eliminates $μ$-dependence as a source of theoretical uncertainty in the predicted semileptonic $B \to X_u$ inclusive rate.

hep-ph↗

arXiv2002

Three Loop Estimate of the Inclusive Semileptonic $b\to c$ Decay Rate

The renormalization-scale ($μ$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\barν_\ell$ decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MS-bar scheme. Three-loop contributions to the decay rate are estimated by developing Pade approximant techniques particularly suited to perturbative calculations in the pole mass scheme. An optimized Pade estimate of the three-loop contributions is obtained by comparison of the Pade estimates with the three-loop terms determined by renormalization-group invariance. The resulting three-loop estimate in the pole-mass scheme exhibits minimal sensitivity to the renormalization scale near $μ=1.0 GeV$, leading to an estimated decay rate of $192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)=992\pm 217 GeV^5$ inclusive of theoretical uncertainties and non-perturbative effects.

hep-ph↗

arXiv2002

Decays of the $\hatρ(1^{-+})$ Exotic Hybrid and $η$-$η'$ Mixing

QCD sum-rules are used to calculate the $\hatρ(1^{-+})\toπη, πη'$ decay widths of the exotic hybrid in two different $η-η'$ mixing schemes. In the conventional flavour octet-singlet mixing scheme, the decay widths are both found to be small, while in the recently-proposed quark mixing scheme, the decay width $Γ_{\hatρ\toηπ}\approx 250 MeV$ is large compared with the decay width $Γ_{\hatρ\toη^\primeπ}\approx 20 MeV$. These results provide some insight into $η$-$η'$ mixing and hybrid decay features.

hep-ph↗

arXiv2002

Closed-Form Summation of RG-Accessible Logarithmic Contributions to Semileptonic B-Decays and Other Perturbative Processes

For any perturbative series that is known to $k$-subleading orders of perturbation theory, we utilise the process-appropriate renormalization-group (RG) equation in order to obtain all-orders summation of series terms proportional to $α^n \log^{n-k}(μ^2)$ with $k = {0,1,2,3}$, corresponding to the summation to all orders of the leading and subsequent-three-subleading logarithmic contributions to the full perturbative series. These methods are applied to the perturbative series for semileptonic $b$-decays in both MS-bar and pole-mass schemes, and they result in RG-summed series for the decay rates which exhibit greatly reduced sensitivity to the renormalization scale $μ$. Such summation via RG-methods of all logarithms accessible from known series terms is also applied to perturbative QCD series for vector- and scalar-current correlation functions, the perturbative static potential function, the (single-doublet standard-model) Higgs decay amplitude into two gluons, as well as the Higgs-mediated high-energy cross-section for $W^+W^-\to ZZ$ scattering. The resulting RG-summed expressions are also found to be much less sensitive to the renormalization scale than the original series for these processes.

hep-ph↗

arXiv2002

Constraints on Higher-Order Perturbative Corrections in $b\to u$ Semileptonic Decays from Residual Renormalization-Scale Dependence

The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group invariant quantities. This technique is applied to the inclusive semileptonic process $b\to u \barν_\ell\ell^-$ (explicitly known to two-loop order) to obtain bounds on the three- and four-loop perturbative coefficients that are not accessible via the renormalization group. Using the principle of minimal sensitivity, an estimate is obtained for the perturbative contributions to $Γ(b\to u \barν_\ell\ell^-)$ that incorporates theoretical uncertainty from as-yet-undetermined higher order QCD corrections.

hep-ph↗

arXiv2001

Two Topics in QCD Sum-Rules: Bounds on Light Quark and Scalar Gluonium Masses

QCD Laplace sum-rules are briefly reviewed and two sum-rule applications are presented. For scalar gluonium, upper bounds on the lightest state are obtained from ratios of Laplace sum-rules, and the role of instantons and the low-energy theorem on these bounds is investigated. For the light-quark masses, fundamental inequalities for Laplace sum-rules are developed, which lead to a lower bound on the average of the up and down quark masses.

hep-ph↗

arXiv2001

QCD Sum-Rule Bounds on the Light Quark Masses

QCD sum-rules are related to an integral of a hadronic spectral function, and hence must satisfy integral inequalities which follow from positivity of the spectral function. Development of these Holder inequalities and their application to the Laplace sum-rule for pions lead to a lower bound on the average of the non-strange 2 GeV light-quark masses in the MS-bar scheme.

hep-ph↗

arXiv2001

Pade Estimate of QCD's Infrared Boundary

A mass scale $μ_c$ representing the boundary between effective theories of strong interactions and perturbative QCD (infrared and ultraviolet regimes) exists when the $β$-function is characterized by a simple pole. This behaviour, which is known to occur in N=1 supersymmetric Yang-Mills theories, leads to an infrared attractor in the evolution of the coupling constant, with the mass scale $μ_c$ of the attractor providing a natural boundary between the infrared and ultraviolet regimes. It is demonstrated that [2|2], [3|1] and [1|3] Pade-approximant versions of the three-flavour QCD $β$-function each contain a simple pole corresponding to such an infrared attractor. All three approximants, separately considered, are seen to lead to nearly equivalent estimates for the mass scale $μ_c$.

hep-ph↗

arXiv2001

A Gaussian Sum-Rules Analysis of Scalar Glueballs

Although marginally more complicated than the traditional Laplace sum-rules, Gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading Gaussian sum-rule, the analysis of the lowest-weighted sum-rule (which contains a large scale-independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. However, the presence of instanton effects leads to approximately consistent mass scales in the lowest weighted and next-lowest weighted sum-rules. The analysis of the next-to-leading sum-rule demonstrates that a single narrow resonance model does not provide an adequate description of the hadronic spectral function. Consequently, we consider a wide variety of phenomenological models which distribute resonance strength over a broad region---some of which lead to excellent agreement between the theoretical prediction and phenomenological models. Including QCD uncertainties, our results indicate that the hadronic contributions to the spectral function stem from a pair of resonances with masses in the range 0.8--1.6 GeV, with the lighter of the two potentially having a large width.

hep-ph↗