A Practical Approach for Exponentiation of QED Corrections in Arbitrary Processes

It is a well-known fact that, among the electroweak corrections, QED radiation gives the largest contribution and the needed precision requires a re-summation of the large logarithms which show up in perturbation theory. For two fermion annihilation processes initial state radiation is a definable, gauge-invariant, concept and one has general tools to deal with it; the structure function approach and also the parton-shower method. However, when one tries to apply the algorithm to four-fermion processes that include non-annihilation channels a problem is faced: is it still possible to include QED corrections by making use of the standard tools? A systematization is attempted of several, recently proposed, algorithms. In particular, it is shown that starting from the exponentiation of soft photons one can still derive a description of QED radiation in terms of structure functions, i.e. the kernel for the hard scattering is convoluted with generalized structure functions where each of them is no longer function of one scale.