Calculation of theO(? s 2 ) parity-violating structure functions in $$e^ + e^ - \to q\bar qg$$

We calculate the two nonvanishingO(αs2) parity-violating structure functions that contribute to\(e^ + e^ - \xrightarrow{{\gamma ,Z}}q\bar qg\). We discuss how these can be measured. We work with massless quarks and gluons and use dimensional regularization to regularize ultra-violet and infrared singularities. We carefully discuss how to deal withγ5 in the dimensional regularization scheme when infrared singularities are present.