Renormalizing the gauged Wess-Zumino-Witten Lagrangian to one loop in a one-family technicolor model

We examine the problems of calculating processes to one loop in a Wess-Zumino-Witten model, using one-family technicolor as an example and gauging the QCD subgroup of the chiral symmetry of technifermions. In particular, we examine decay processes of certain technipions, often denoted P0' and P80'. We find that almost all of the ultraviolet divergences cancel. The cancellation of infrared divergences between processes with degenerate final states provides us with a constraint on our renormalization scheme. We also study the effects of different d-dimensional prescriptions for εμναβ and γ5 in dimensional regularization. (The matrix γ5 appears when we include possible extended technicolor couplings between technipions and ordinary fermions.) In the end, we choose M bar S renormalization, and a noncovariant prescription for εμναβ and γ5. We also present one-loop corrections to the width of the P0'. These turn out to be sizable