Fried-Yennie Gauge Research Articles

Fried-Yennie Gauge in Pseudo-QED.

The Fried-Yennie gauge is a covariant gauge for which the mass-shell renormalization procedure can be performed without introducing spurious infrared divergences to the theory. It is usually applied in calculations in regular Quantum Electrodynamics (QED), but it is particularly interesting when employed in the framework of pseudo-QED (PQED), where fermions are constrained to 2 + 1 dimensions while the dynamical fields interacting with these fermions live in the bulk of a 3 + 1 space. In this context, the gauge parameter can be adjusted to match the power of the external momentum in the denominator of the photon propagator, simplifying the infrared region without the need for a photon mass. In this work, we apply this machinery, for the first time, to PQED, generalizing the procedure to calculate the self energy in arbitrary dimensions, allowing, of course, for different dimensionalities of fermions and gauge fields.

Nuclear radiative recoil corrections to the hyperfine structure of S-states in muonic hydrogen

Nuclear radiative recoil corrections of order α(Zα)5 to the hyperfine splitting of S-states in muonic hydrogen are calculated on the basis of quasipotential method in quantum electrodynamics. The calculation is performed in the infrared safe Fried-Yennie gauge. Modern experimental data on the proton form factors are used.

Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy

We apply the principle of maximum conformality (PMC) to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron intercept at the next-to-leading logarithmic (NLL) accuracy. The PMC eliminates the conventional renormalization scale ambiguity by absorbing the non-conformal $\{\beta_i\}$-terms into the running coupling, and a more accurate pQCD estimation can be obtained. After PMC scale setting, the QCD perturbative convergence can be greatly improved due to the elimination of renormalon terms in pQCD series, and the BFKL Pomeron intercept has a weak dependence on the virtuality of the reggeized gluon. For example, by taking the Fried-Yennie gauge, we obtain $\omega_{\rm MOM}^{\rm PMC}(Q^{2},0)\in [0.149,0.176]$ for $Q^2\in[1,100]\;{\rm GeV}^2$. This is a good property to apply to the high-energy phenomenology. Further more, to compare with the data, it is found that the physical ${\rm MOM}$-scheme is more reliable than the $\overline{\rm MS}$-scheme. The ${\rm MOM}$-scheme is gauge dependent, which can also be greatly suppressed after PMC scale setting. We discuss the MOM-scheme gauge dependence for the Pomeron intercept by adopting three gauges, i.e. the Landau gauge, the Feynman gauge and the Fried-Yennie gauge, and we obtain $\omega_{\rm MOM}^{\rm PMC}(Q^{2}=15\;{\rm GeV}^2,0) = 0.166^{+0.010}_{-0.017}$; i.e. about $10\%$ gauge dependence is observed. We apply the BFKL Pomeron intercept to the photon-photon collision process, and compare the theoretical predictions with the data from the OPAL and L3 experiments.

Second-order electron self-energy loop-after-loop correction for low-Z hydrogen-like ions

The second-order electron self-energy loop-after-loop correction is investigated for hydrogen-like ions in the region of low nuclear charge numbers Z. Both irreducible and reducible parts of this correction are evaluated for the 1s1/2-state within the Fried–Yennie gauge. We confirm the result obtained first by Mallampalli and Sapirstein. The reducible part of this correction is evaluated numerically for the first time and it is consistent with the corresponding analytical αZ-expansion.

Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Zatoms

We present a numerical evaluation of the loop-after-loop contribution to the second-order self-energy for the ground state of hydrogenlike atoms with low nuclear charge numbers Z. The calculation is carried out in the Fried-Yennie gauge and without an expansion in $Z\ensuremath{\alpha}.$ Our calculation confirms the results of Mallampalli and Sapirstein and disagrees with the calculation by Goidenko and co-workers. A discrepancy between different calculations is investigated. An accurate fitting of the numerical results provides a detailed comparison with analytic calculations based on an expansion in the parameter $Z\ensuremath{\alpha}.$ We confirm the analytic results of order ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha}{)}^{5}$ but disagree with Karshenboim's calculation of the ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha}{)}^{6}{\mathrm{ln}}^{3}(Z\ensuremath{\alpha}{)}^{\ensuremath{-}2}$ contribution.

Radiative corrections toWand quark propagators in the resonance region

We discuss radiative corrections to $W$ and quark propagators in the resonance region $|s\ensuremath{-}{M}^{2}|\ensuremath{\lesssim}M\ensuremath{\Gamma}.$ We show that conventional mass renormalization, when applied to photonic or gluonic corrections, leads in next to leading order (NLO) to contributions proportional to $[M\ensuremath{\Gamma}/(s\ensuremath{-}{M}^{2}){]}^{n},$ $(n=1,2,\dots{}),$ i.e., to a non-convergent series in the resonance region, a difficulty that affects all unstable particles coupled to massless quanta. A solution of this problem, based on the concepts of pole mass and width, is presented. It elucidates the issue of renormalization of amplitudes involving unstable particles, and automatically circumvents the problem of apparent on-shell singularities. The roles of the Fried-Yennie gauge and the pinch technique prescription are discussed. Because of special properties of the photonic and gluonic contributions, and in contrast with the $Z$ case, the gauge dependence of the conventional on-shell definition of mass is unbounded in NLO. The evaluations of the width in the conventional and pole formulations are compared and shown to agree in NLO but not beyond.

Corrections of order alpha 2(Z alpha )5 to the hyperfine splitting and the Lamb shift.

Corrections to the hyperfine splitting and the Lamb shift of order ${\mathrm{\ensuremath{\alpha}}}^{2}$(Z\ensuremath{\alpha}${)}^{5}$ induced by diagrams with radiative photon insertions in the electron line are calculated in the Fried-Yennie gauge. These contributions are as large as -7.724(1)${\mathrm{\ensuremath{\alpha}}}^{2}$(Z\ensuremath{\alpha}${)}^{5}$/(\ensuremath{\pi}${\mathit{n}}^{3}$)(${\mathit{m}}_{\mathit{r}}$/m${)}^{3}$m and -0.6726(4)${\mathrm{\ensuremath{\alpha}}}^{2}$(Z\ensuremath{\alpha})/(\ensuremath{\pi}${\mathit{n}}^{3}$)${\mathit{E}}_{\mathit{F}}$ for the Lamb shift and the hyperfine splitting, respectively. Phenomenological implications of these results are discussed with special emphasis on the accuracy of the theoretical predictions for the Lamb shift and the experimental determination of the Rydberg constant. A precise value of the Rydberg constant is obtained on the basis of the improved theory and experimental data.

Corrections to hyperfine splitting and Lamb shift induced by diagrams with second-order radiative insertions in the electron line

Contributions to HFS and to the Lamb shift intervals of order /spl alpha//sup 2/(Z/spl alpha/)/sup 5/ induced by a gauge invariant set of 19 topologically different graphs with two radiative photons inserted in the electron line are considered. Corrections both to HFS and Lamb shift induced by nine of these 19 diagrams have been calculated in the Fried-Yennie gauge. >

Fried-Yennie gauge in dimensionally regularized QED.

The Fried-Yennie gauge in QED is a covariant gauge with agreeable infrared properties. That is, the mass-shell renormalization scheme can be implemented without introducing artificial infrared divergences, and terms having spuriously low orders in [alpha] disappear in certain bound-state calculations. The photon propagator in the Fried-Yennie gauge has the form [ital D][sub [beta]][sup [mu][nu]]([ital k])=([minus]1/[ital k][sup 2])[[ital g][sup [mu][nu]]+[beta][ital k][sup [mu]][ital k[nu]]/[ital k][sup 2]], where [beta] is the gauge parameter. In this work, I show that the Fried-Yennie gauge parameter is [beta]=2/(1[minus]2[epsilon]) when dimensional regularization (with [ital n]=4[minus]2[epsilon] dimensions of spacetime) is used to regulate the theory.

Calculation of the two-photon-annihilation contribution to the positronium hyperfine interval at ordermα6

The two-photon-annihilation contribution to the positronium hyperfine interval is obtained in analytic form at order m${\mathrm{\ensuremath{\alpha}}}^{6}$ using the Fried-Yennie gauge. The contribution to the hyperfine interval is -0.0325m${\mathrm{\ensuremath{\alpha}}}^{6}$=-0.606 MHz. This differs from the result of an earlier Feynman gauge evaluation. The errors in the earlier calculation are identified. The corrected Feynman gauge result agrees with the Fried-Yennie gauge result.

Analytic evaluation of the inner-vertex correction to the decay rate of orthopositronium in the Fried-Yennie gauge.

In this paper the order-\ensuremath{\alpha} contribution of the inner-vertex graph to the decay rate of orthopositronium in the Fried-Yennie gauge is obtained in analytic form.

Order- alpha corrections to the decay rate of orthopositronium in the Fried-Yennie gauge.

The order-{alpha} correction to the decay rate of orthopositronium is obtained using the Fried-Yennie gauge. The result ({ital m}{alpha}{sup 7}/{pi}{sup 2}) ({minus}1.987 84(11)) is consistent with but more accurate than the results of previous evaluations.

Analytic evaluation of the self-energy and outer-vertex corrections to the decay rate of orthopositronium in the Fried-Yennie gauge.

In this paper, the order-\ensuremath{\alpha} contributions of the self-energy and outer-vertex graphs to the decay rate of orthopositronium in the Fried-Yennie gauge are obtained in analytic form.

Calculation of the electron magnetic moment in Fried-Yennie-gauge QED.

The two-loop contribution to the electron magnetic moment is calculated in the Fried-Yennie gauge. This is the first treatment of the magnetic moment beyond one-loop order in a gauge other than the Feynman gauge. The Fried-Yennie gauge is infrared safe, and the calculation is done without introducing an infrared cutoff or photon mass. The Fried-Yennie-gauge result agrees with the Feynman-gauge result, as expected.

Fried-Yennie gauge recalculation of the electron line induced radiative-recoil corrections to muonium hyperfine splitting

A new analytic calculation of radiative-recoil corrections to muonium ground-state hyperfine splitting induced by electron line insertions is performed. The starting point of this calculation is presented by the Fried-Yennie gauge expression for the electron line factor. The final result confirms the one obtained previously from the apparently different expression in the Feynman gauge and removes the slight discrepancy which existed in the literature between the calculations in different gauges.

Radiative corrections to parapositronium decay

Radiative corrections to the two-gamma decay of parapositronium are examined. Special care is taken in the handling of the so-called binding diagram; in particular, the limiting procedure related to the infrared divergence is considered carefully. The general covariant gauges and the Fried-Yennie gauge are used in the computation to see that gauge invariance is accounted for. The order α correction of Harris and Brown is confirmed. In addition, from a sharp peak of the matrix element at low momentum and the low-momentum correction to the wave function, an α 2 ln α −1 correction is derived.

Note on the Fried-Yennie gauge

It is pointed out that the renormalization constants and the finite parts of the self energy and the vertex corrections in the infrared-free Fried-Yennie gauge are different, by finite amounts, from those which are computed as the limit of the general covariant gauge. This discrepancy occurs because of the appearance of an infrared divergence in the onmass-shell renormalization. This note provides an example where extra caution is needed in handling the limiting procedure, where an infrared divergence is involved.