Monte Carlo study of NLO correction to QCD evolution kernel induced by the change of the factorization scale

The aim of the present study is to show that: the redefinition of the factorization scale $Q_i\to z_i Q_i$ in the ladder can be traded exactly for the NLO correction to the LO evolution kernel, $P(z)\to P(z)+(2C_F \alpha_S/\pi)\Delta(z)$ The above observation was done/exploited in the literature, but the present study demonstrates how this phenomenon is realized within the Markovian Monte Carlo parton shower - hence it might be relevant in MC practice.