Exponentiation of soft photons in a process involving hard photons.

We present a simple method of removing the singularities associated with soft photon emission to all orders in perturbation theory through exponentiation, while keeping a consistent description of hard photon emission. We apply this method to the process e + e ? ! + ? + n where we include both Z 0 and exchange and retain the muon mass dependence. The photonic radiation is allowed to be radiated oo any charged leg, and so we include all initial and nal state radiation, as well as all interference eeects. The eeect of exponentiation is to suppress soft photon emission over the cross-section you would obtain from working at strictly leading order. We also show how one would extend the method to treat the collinear singularity; and remove the associated leading mass logarithms.