# Radiative Correction

## radiative correction

[′rād·ē‚ād·iv kə′rek·shən]*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Radiative Correction

in quantum electrodynamics, a correction due to the interaction of a charged particle with its electromagnetic field to the value of some physical quantity or to the cross section of some process as calculated by the formulas of relativistic quantum mechanics. Radiative corrections may be considered a result of the emission and absorption of virtual photons and electron-position pairs by particles.

A radiative correction is calculated through the use of perturbation theory. The correction is represented as a power series in the fine structure constant *α* = *e*^{2}/*ℏc* ≈ 1/137, where *e* is the elementary electric charge, ℏ is Planck’s constant, and *c* is the speed of light in a vacuum. First-order corrections are proportional to a, second-order corrections are proportional to *α*^{2}, and so forth. In calculating the radiative corrections it is assumed that the radiative corrections to the mass and charge of a particle taken separately have no physical meaning. Physical meaning is attributed to the total magnitude of the mass or charge after the radiative corrections are incorporated and the experimental values are used for these quantities in calculations—a procedure called renormalization of mass and charge.

The most important radiative corrections include the anomalous magnetic moment of the electron and muon, the radiative shift of atomic energy levels (level shift), and radiative corrections to the cross sections for the scattering of an electron by an electron or atomic nucleus. The results of calculations of radiative corrections up to third-order quantities are in remarkable agreement with experimental data and attest to the validity of quantum electrodynamics at least at distances greater than 10^{–15} cm. Radiative corrections increase with increasing energy. At high energies, the effective parameter of expansion is α In (*E/m*) or, in some cases, α In (*E/m*) In (*E/ΔE*), where *E* is the energy of the particle in a center-of-mass system, *m* is the particle’s mass, and ΔE is the experimental resolution of the instrument.

In some cases, radiative corrections can be calculated not only for electrodynamic processes but also for processes caused by other interactions. For processes due to the strong interaction, however, radiative corrections usually cannot be rigorously calculated because of the lack of a complete theory of strong interactions.

When radiative corrections for electrodynamic quantities are calculated with an accuracy above the third order, an important contribution is made by the virtual production of hadrons, or strongly interacting particles, and by the effects of the weak interaction. The calculation of these effects is hindered by the lack of a consistent theory of the weak interaction and by the insufficiency of experimental data on the processes of hadron production through the electromagnetic interaction.

### REFERENCE

Akhiezer, A. I., and V. B. Berestetskii.*Kvantovaia elektrodinamika*, 3rd ed. Moscow, 1969. Chapter 5.

B. L. IOFFE