Low-energy photons in elementary particle collisions

Abstract

General equations of local field theory (including quantum electrodynamics in all orders in e) have been used to obtain the first two terms in the series expansion of the bremsstrahlung matrix element in the momenta of the soft photons. For bremsstrahlung of one photon with momentum k the first term of this expansion is of order k−1, the second one is of order e 2lnk, and the third term is independent of k. The coefficients of the first and second terms are proportional to the matrix element for the corresponding process without emission of the soft photons. With the aid of this expansion the first two terms in the series expansion of the bremsstrahlung cross section in the radiated energy are obtained; a term of order k 2lnk in the series expansion of the total cross section for scattering of a photon with momentum k by a charged particle is found. It is shown that the imaginary part of the elastic Compton scattering amplitude at fixed momentum transfer is a generalized power function of the energy s near the threshold s = m 2; the first term in the expansion of the amplitude in powers of s − m 2 is found and the next term is estimated. It is shown that the factorization of infrared divergences of any scattering amplitude follows from simple physical considerations and the spectral condition.