Locally finite gauge theory amplitudes: a case example

We study the singularity structure of QED amplitudes for multi photon production in massless electron-positron annihilation and develop counterterms which remove their infrared and ultraviolet divergences point by point in the loop in te-grand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the one-loop amplitude. They consist of simple one- and two loop integrals with at most three external momenta and can be integrated analytically in a simple manner with established methods. We uncover novel aspects of fully local IR factorization, where vertex and self-energy sub-diagrams must be modified by sophisticated symmetrizations over loop momenta in order to expose their tree-like tensor structures and hence factorization of IR singularities prior to loop integration. This work is a first step towards isolating locally the hard contributions of generic gauge theory amplitudes and rendering them integrable in exactly four dimensions with numerical methods.


Moderator: Dionysios Triantafyllopoulos



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