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

## TL;DR

This paper explores the connection between collinear and $k_t$-factorization, showing that the latter provides a fundamental basis for the hard scale choice and clarifies the associated uncertainties.

## Contribution

It demonstrates that $k_t$-factorization justifies the hard scale choice in collinear factorization and clarifies the inherent uncertainties.

## Key findings

- $k_t$-factorization justifies the hard scale $Q^2$ choice.
- Uncertainty in scale choice persists in collinear factorization.
- $k_t$-factorization removes the scale uncertainty.

## 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.