Hard scale uncertainty in collinear factorization: Perspective from $k_t$-factorization

Abstract

We analyze two consequences of the relationship between collinear factorization and $k_t$-factorization. First, we show that the $k_t$-factorization gives a fundamental justification for the choice of the hard scale $Q^2$ done in the collinear factorization. Second, we show that in the collinear factorization there is an uncertainty on this choice which will not be reduced by higher orders. This uncertainty is absent within the $k_t$-factorization formalism.