Reply to "Comment on 'QCD factorization with multihadron fragmentation functions'"

TL;DR

The paper defends the standard, universal fragmentation-function definition for multihadron final states against claims that external-state–dependent prefactors or sum rules are required. It argues that all nonperturbative external-state dependence must reside in the fragmentation function $d(z,\{p_h\})$, with a process-independent hard part, preserving factorization. By detailing the operator construction of fragmentation functions and generalizing to $n$-hadron states, the authors show that introducing external-state–dependent normalizations or $1/\xi^n$ factors spoils factorization and undermines universality and evolution. The work reinforces the robustness of collinear factorization with multihadron fragmentation functions and highlights the importance of avoiding external-state–dependent modifications to the hard part, while pointing toward future nonperturbative QCD studies for first-principles insight.

Abstract

We respond to comments in arXiv:2502.15817v2 about our article, arXiv:2412.12282. We stand by our conclusions and defend them against the criticisms.