Scheme-invariant stratified factorization algebras for inclusive deep inelastic scattering

TL;DR

This paper introduces a unified, scheme-invariant framework for factorization in inclusive deep inelastic scattering, integrating various aspects into a formal proof structure that enhances theoretical understanding and computational diagnostics.

Contribution

It formulates a comprehensive proof object that combines asymptotic reconstruction, scheme invariance, and factorization components into a unified, formal structure for DIS.

Findings

Formal proof object unifies scheme invariance and factorization in DIS.

Provides diagnostics for missing regions and nonbalanced measurements.

Separates formal implications from analytic QCD requirements.

Abstract

Inclusive deep inelastic scattering factorization combines two features that are often treated separately: an asymptotic reconstruction of the current-current matrix element from hard and long-distance data, and an invariance under finite changes of collinear scheme or operator basis. We formulate these two features as a single proof object. The construction packages the leading-region analysis, overlap subtraction, Wilson-line reduction, finite scheme kernels and physical measurement into a typed, filtered structure on a compactified space of asymptotic regimes. Its central carrier is the balanced hard-collinear core over the interface algebra of finite scheme transformations. The hard QCD input is the construction of a scheme-balanced comparison map from this core to the collinear collar of the regime algebra. Once this comparison is an equivalence through the chosen power accuracy and the measurement descends to convolution, the standard DIS convolution formula follows formally and independently of the chosen scheme presentation. We separate this formal implication from the analytic QCD obligations needed to construct the collar equivalence, describe Collins-style subtraction as descent and M\"obius inversion on the region poset, and give a finite check relating $\overline{\mathrm{MS}}$ and DIS presentations. The framework is intended as proof infrastructure rather than as a new calculation of DIS coefficient functions. It supplies diagnostics for missing regions, nonclosed operator sectors, nonbalanced measurements and failed collar equivalences, and it gives a typed interface for future proof-assistant and machine-learning implementations of factorization workflows.