arXiv subjects

Robin G. Stuart

Publications and source records attributed to Robin G. Stuart.

At least 19 recordsLinked to original sources

arXiv1999

An Improved Determination of the Fermi Coupling Constant, G_F

Over 40 years after the calculation of the 1-loop QED corrections to the muon lifetime, new theoretical developments have made it possible to obtain an analytic expression for the complete 2-loop QED contributions in the Fermi theory. The exact result for the effects of virtual and real photons, virtual electrons, muons and hadrons as well as e+e- pair creation is Delta Gamma^(2)=Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2) -(895/36)zeta(3)+(67/8)zeta(4) +53zeta(2)ln(2)-(0.042+/-0.002)] where Gamma_0 is the tree-level width. This eliminates the theoretical error in the extracted value of the Fermi coupling constant, G_F, which was previously the source of the dominant uncertainty. The new value is G_F=(1.16637 +/- 0.00001) x 10^-5 GeV^-2 The overall error has been roughly halved and is now entirely experimental. Several experiments are planned for the next generation of muon lifetime measurements and these can proceed unhindered by theoretical uncertainties.

hep-ph↗

arXiv1999

On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime

The determination of the Fermi coupling constant, G_F, is examined in the light of recently calculated 2-loop QED corrections and planned experiments to measure the muon lifetime to a level below 1ppm. The methods used in the calculation of the QED corrections are described in detail. Sources of the dominant theoretical and experimental uncertainties are identified. Finally the incorporation of G_F into analyses using the full electroweak Standard Model is discussed.

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arXiv1999

Complete O(N_f alpha^2) Weak Contributions to the Muon Lifetime

The complete O(N_f alpha^2) weak contributions to the muon lifetime, denoted as Delta r^(2), are calculated in the MS-bar renormalization scheme. These come from 2-loop Feynman diagrams containing a loop formed by complete generations of massless fermions. They form an independent, gauge-invariant set of corrections that, because of the large number of light fermions in the Standard Model, is expected to make a significant contribution. In the MS-bar renormalization scheme with mu'= (pi e^gamma)^(1/2) mu = M_Z and for a Higgs mass, M_H, in the range 100-1000 GeV the contribution varies from -0.55x10^-4 to -1.54x10^-4 for each massless generation of fermions.

hep-ph↗

arXiv1998

Complete 2-loop quantum electrodynamic contributions to the muon lifetime in the Fermi model

The complete 2-loop QED contributions to the muon lifetime have been calculated analytically in the Fermi theory. The exact result for the effects of virtual and real photons, virtual electrons, muons and hadrons as well as e+e- pair creation is Delta Gamma^(2)=Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2) -(895/36)zeta(3)+(67/8)zeta(4) +53zeta(2)ln(2)-(0.042+/-0.002)] where Gamma_0 is the tree-level width. This eliminates the theoretical error in the extracted value of the Fermi coupling constant, G_F, which was previously the source of the dominant uncertainty. The new value is G_F=(1.16637 +/- 0.00001) x 10^-5 GeV^-2 with the error being entirely experimental. Several experiments are planned for the next generation of muon lifetime measurements and these can proceed unhindered by theoretical uncertainties.

hep-ph↗

arXiv1998

Complete 2-loop Quantum Electrodynamic Contributions to the Muon Lifetime in the Fermi Model

The complete 2-loop quantum electrodynamic corrections to the muon lifetime are calculated in the Fermi theory. The exact result for the effects of virtual and real photons, virtual electrons, muons as well as e+e- pair creation is Delta Gamma_QED = Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2)-(895/36)zeta(3) +(67/8)zeta(4)+53zeta(2)ln(2)] = Gamma_0(alpha/pi)^2(6.743) where Gamma_0 is the tree-level width. The theoretical error in the value of the Fermi coupling constant, G_F, is now rendered negligible compared to the experimental uncertainty coming from the measurement of the muon lifetime. The overall error in G_F is then roughly halved giving G_F = (1.16637 +/- 0.00001) x 10^(-5) GeV^(-2).

hep-ph↗

arXiv1998

Hadronic Contributions to the Muon Lifetime

Hadronic corrections to the muon lifetime are calculated in the Fermi theory in the presence of QED using dispersion relations. The result, after convolution of hadron data with the calculated perturbative kernel is Delta Gamma_had = -Gamma_0(alpha/pi)^2(0.042) where Gamma_0 is the tree-level width. The results are also used to obtain the corrections to the muon lifetime coming from virtual muon and tau loops Delta Gamma_muon = Gamma_0(alpha/pi)^2[(16987/576)-(85/36)zeta(2)-(64/3)zeta(3)] = -Gamma_0(alpha/pi)^2(0.0364333) Delta Gamma_tau = -Gamma_0(alpha/pi)^2)(0.00058)

hep-ph↗

arXiv1998

O(N_f alpha^2) Electromagnetic Charge Renormalization in the Standard Model

The O(N_f alpha^2) electroweak radiative corrections to the Thomson scattering matrix element are calculated for a general renormalization scheme with massless fermions. All integrals can be evaluated exactly in dimensional regularization which in several cases yields new results that are remarkably simple in form. A number of stringent internal consistency checks are performed. The Z-gamma mixing complicates the calculation of 1-particle reducible diagrams considerably at this order and a general treatment of this problem is given. Conditions satisfied by O(N_f alpha^2) counterterms are derived and may be applied to other calculations at this order.

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arXiv1998

Reduction of One-loop Tensor Form-Factors to Scalar Integrals: A General Scheme

A general method for reducing tensor form factors, that appear in one-loop calculations in dimensional regularization, to scalar integrals is presented. The method is an extension of the reduction scheme introduced by Passarino and Veltman and is applicable in all regions of parameter space including those where kinematic Gram determinant vanishes. New relations between the the form factors that valid for vanishing Gram determinant play a key role in the extended scheme.

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arXiv1997

$O(N_fα^2)$ Radiative Corrections in Low-Energy Electroweak Processes

Of the the three best-measured electroweak observables, $α$, $G_μ$ and $M_Z$, the first two are extracted from low-energy processes. Both $G_μ$ and $M_Z$ are now known to an accuracy of about 2 parts in $10^5$ and there is a proposal to improve the measurement of the muon lifetime by a factor of 10 in an experiment at Brookhaven. Yet calculations of electroweak radiative corrections currently do no better than a few parts in $10^3$--$10^4$ and therefore cannot exploit to available experimental precision. We report on the calculation of the ${\cal O}(N_fα^2)$ corrections to Thomson scattering and the muon lifetime from which $α$ and $G_μ$, respectively, are obtained. The ${\cal O}(N_fα^2)$ corrections are expected to be a dominant gauge-invariant subset of 2-loop corrections.

hep-ph↗

arXiv1997

Production Cross-sections for Unstable Particles

The top-quark, $W$ and $Z^0$ bosons have widths that are a sizable fraction of their masses and will be produced copiously at upcoming accelerators. Yet S-matrix theory cannot treat unstable particles as external states. Dealing with complete matrix elements involving their decay products complicates calculations considerably and is unnecessary in many practical situations. It is shown how to construct physically meaningful production cross-sections for unstable particles by extracting that part of the matrix element that corresponds to finite-range space-time propagation. This procedure avoids the need to define unstable particles in external states and we argue its favour as providing a solution to a long-standing problem in physics. As an example the results are applied to the calculation of the cross-section $σ(e^+e^-\to Z^0Z^0)$.

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arXiv1997

Order $N_fα^2$ Corrections in Low-Energy Electroweak Processes

We provide a compendium of techniques that can be used to compute $O(N_fα^2)$ corrections to low-energy electroweak processes. Specifically, these are the 2-loop electroweak corrections containing a light fermion loop. It is shown that the vast majority of such corrections can be reduced to expressions involving a universal master integral for which an exact analytic form in dimensional regularization is given. The only exceptions are certain photon vacuum polarization diagrams. Examples are presented for diagrams that occur in a variety of processes of practical interest.

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arXiv1997

Model-independent Representation of Electroweak Data

General model-independent expressions are developed for the polarized and unpolarized cross-sections for $e^+e^-\to f\bar f$ near the $Z^0$ resonance. The expressions assume only the analyticity of S-matrix elements. Angular dependence is included by means of a partial wave expansion. The resulting simple forms are suitable for use in fitting data or in Monte Carlo event generators. A distinction is made between model-independent and model-dependent QED corrections and a simple closed expression is given for the effect of initial-final state bremsstrahlung and virtual QED corrections.

hep-ph↗

arXiv1997

Gauge Invariance and the Unstable Particle

It is shown how to construct exactly gauge-invariant S-matrix elements for processes involving unstable gauge particles such as the $Z^0$ boson. The results are applied to derive a physically meaningful expression for the cross-section $σ(e^+e^-\to Z^0Z^0)$ and thereby provide a solution to the long-standing problem of the unstable particle.

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arXiv1997

Gauge Invariance in Boson Production

It is shown how to construct exactly gauge-invariant S-matrix elements for processes involving unstable gauge particles such as the $W$ and $Z^0$ bosons. The results are applied to derive a physically meaningful expression for the cross-section $σ(e^+e^-\to Z^0Z^0)$ and thereby provide a solution to the long-standing problem of the unstable particle. The problem of maintaining QED gauge-invariance in the process $e^+e^-\to\barν_e e^-W^+\to\barν_e e^-u\bar d$ is examined.

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arXiv1997

O(N_fα^2) Corrections to Muon Decay

The calculation of the $O(N_fα^2)$ corrections to muon decay is described. These are the 2-loop diagrams containing a massless fermion loop and they form an important gauge-invariant subclass. It is shown that all such diagrams can be expressed in terms of a universal master integral. We focus on the calculation of box diagrams and in particular on the removal of their infrared divergences.

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arXiv1996

Gauge Invariance in the Process $e^+e^-\to \bar ν_e e^-W^+\to\barν_e e^-u\bar d$

The process $e^+e^-\rightarrow \bar ν_e e^-W^+ \rightarrow\barν_e e^-u\bar d$ is considered as an example of the problems associated with maintaining gauge invariance in matrix elements involving unstable particles. It is shown how to construct a matrix element that correctly treats width effects for the intermediate unstable $W$ boson and that is both $SU(2)_L$ and $U(1)_{\rm e.m.}$ gauge-invariant. $SU(2)_L$ gauge-invariance is maintained by Laurent expansion in kinematic invariants and $U(1)_{\rm e.m.}$ gauge-invariance is enforced by means of a projection operator under which the exact matrix element is invariant.

hep-ph↗

arXiv1995

A Global Fit of LEP/SLC Data with Light Superpartners

We find that re-analyzing the LEP/SLC data with light superpartners and low $α_s(\mz^2)\simeq 0.112$ yields a better fit to the data than the Standard Model, giving a satisfactory description of the $R_b$ measurement, and a better fit to $A_{LR}$. A large body of low energy ($q^2 \ll \mz^2$) data and analyses provide compelling evidence for $α_s(\mz^2)\simeq 0.112$. Global fits to LEP/SLC data in the Standard Model, however, converge on a value of $α_s(\mz^2)\simeq 0.126$. Recently it has become increasingly clear that these should be viewed as incompatible rather than values that can be averaged. We investigate the possibility that new physics is causing the LEP high value. To this end we have conducted a global analysis of LEP/SLC data in the Standard Model and also in the Minimal Supersymmetric Standard Model. Several predictions could confirm (or rule out) the results of this paper: light chargino and stop, top decays into stop and neutralino, large $R_b$, large $A_{LR}$, and a higher $M_W$. We briefly discuss the implications of low $α_s$ for more fundamental high-scale supersymmetric theories.

hep-ph↗

arXiv1995

Unstable Particles

Unstable particles cannot be treated as asymptotic external states in $S$-matrix theory and when they occur as resonant states cannot be described by finite-order perturbation theory. The known facts concerning unstable particles are reviewed and it is shown how to construct gauge-invariant expressions for matrix elements containing intermediate unstable particles and physically meaningful production cross-sections for unstable particles. The results and methodology presented are relevant for $Z^0$ resonance physics, $W^+W^-$ and $Z^0Z^0$ pair production and can be straightforwardly applied to other processes.

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