Two-loop QED Research Articles

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 two-loop QED corrections and planned experiments to measure the muon lifetime to a level below 1 ppm. 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.

Second order QCD corrections toΓ(t→Wb)

Corrections of $O(\alpha_s^2)$ to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum, q, as compared to the top quark mass, M_t. The physical point q^2 = M_t^2 is reached through Pad\'e approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate $b \to u l \bar\nu$ and the two-loop QED corrections to $\mu$-decay are performed.

Second order corrections to the muon lifetime and the semileptonic B decay

In this article two-loop QED corrections to the muon decay and corrections of order α s 2 to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Padé approximation. Via this method we confirm the existing results by an independent calculation.

α2Corrections to Parapositronium Decay

Two-loop QED corrections to the decay rate of parapositronium $(p\ensuremath{-}\mathrm{P}\mathrm{s})$ into two photons are presented. We find $\ensuremath{\Gamma}(p\ensuremath{-}\mathrm{P}\mathrm{s}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7989.50(2)\phantom{\rule{0ex}{0ex}}\ensuremath{\mu}{\mathrm{s}}^{\ensuremath{-}1}$. The nonlogarithmic $O({\ensuremath{\alpha}}^{2})$ corrections turn out to be small, contrary to some earlier estimates. We speculate that the so-called ``orthopositronium lifetime puzzle'' will not likely be solved by large QED corrections.

Two-loop euler-heisenberg lagrangian in dimensional regularization

By calculating the two-loop QED Euler-Heisenberg Lagrangian in dimensional regularization, we clarify a discrepancy between two previous calculations of this quantity performed in proper-time regularization.

Computing techniques for two-loop corrections to anomalous magnetic moments of leptons

Two-loop electroweak corrections to the electron, muon, and tau lepton anomalous magnetic moments have been computed recently. Effects of hadronic contributions to the photon propagator in two-loop QED corrections have also been reanalysed. The common technique used in both calculations was asymptotic expansion of Feynman diagrams in the ratio of lepton mass to some heavy mass scale. In this talk we present some details of this method paying particular attention to the expansion of multi-scale diagrams.

Multiloop calculations in the string-inspired formalism: The single spinor loop in QED.

We use the worldline path-integral approach to the Bern-Kosower formalism for developing a new algorithm for calculation of the sum of all diagrams with one spinor loop and fixed numbers of external and internal photons. The method is based on worldline supersymmetry, and on the construction of generalized worldline Green functions. The two-loop QED $\beta$ -- function is calculated as an example.

Multiloop calculations in QED by superparticle path integrals

We use the worldline path integral approach to the Bern-Kosower formalism for extending this formalism to the calculation of higher order corrections to N - photon scattering. The case of the two-loop QED beta-function is considered in detail. (Talk given by C. S. at the Workshop QCD 94, Montpellier, France, 7 - 13 July, 1994)

Two-loop O( αs2) correction to the [formula omitted] decay rate induced by the top quark

We present the two-loop QED and QCD corrections to the f fH Yukawa coupling that are induced by the exchange of a virtual photon or gluon, respectively, with a heavy-fermion loop inserted. As an application, we study the corresponding O (α s 2M 2 H m t 2) correction to the H → b b decay rate.

Causality between conducting plates

A two-loop QED effect, uncovered by Scharnhorst, causes the phase and group velocities of an electromagnetic wave with ω⪡ m e to slightly exceed c, when the wave is travelling in vacuo between, and perpendicular to, two parallel conducting plates. Using causal rather than Feynman graphs, we show that the wavefront still travels at exactly c. The two-loop effect thus poses no threat to causality in QED.

Two-loop QED corrections to Bhabha scattering near the Z 0

Leading logarithmic o( α 2) corrections to Bhabha scattering near the Z 0 are presented. These results improve previous analytical formulae for back-to-back e +e − pair production to an accuracy of a few 0 00 and can be therefore used for precision tests at LEP experiments.

On the two-loop QED vertex correction in the high energy limit

A simple and accurate expression for the high energy limit of the two-loop QED vertex correction is presented. Also the two-loop QED contribution to the electron form factor due to the diagram where in the electron-photon vertex the vacuum polarization of another fermion species is inserted is calculated. These expressions are required for order α 2 corrections to electron-positron collisions.