On the double counting subtraction at NLO${}^{\star }$ of the high-energy factorization approach

We suggest improvements for double counting subtraction scheme, which is needed for the consistent treatment of real corrections in the high-energy limit, and apply it to the single photon production at the NLO${}^{\star }$ approximation of the high-energy factorization approach. The presented improvements allow us to avoid the oversubtraction problem.