An Alternative Approach to Infrared Divergences in Yang-Mills Theories with Broken Symmetries

Infrared safety is obtained in modern quantum theories using dimensional regularization, superseding earlier approaches in which a photon or gluon mass was inserted ad hoc. In Yang-Mills theories that have spontaneously broken symmetries, it is shown that consistency implies that otherwise massless virtual bosons should have mass during energy-changing interactions. This follows from (a) the running of the coupling constants with interaction energy, (b) the rapid random changes in fermion energies as they interact via quantized fields, and (c) the positive semidefinite quadratic forms in the coupling constants that arise for the boson mass matrices in theories with broken symmetries. The implied mass of virtual photons is calculated as a function of t-channel interaction energy from electroweak theory. The virtual photon mass is found to be a small fraction of the RMS photon exchange energy. The virtual gluon mass is similarly calculated from a BSM Yang-Mills theory that has a broken SU(3) symmetry.