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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.13439 |
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| _version_ | 1866917412773822464 |
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| author | Keller, Dustin |
| author_facet | Keller, Dustin |
| contents | Collinear factorization and the leading-twist operator product expansion (OPE) in perturbative QCD express suitably inclusive observables in scale-separated kinematics as composites of perturbative short-distance coefficients with universal long-distance non-perturbative correlators such as parton distribution functions (PDFs), up to controlled power corrections. A persistent structural feature is \emph{presentation non-uniqueness}: coefficients and correlators are not individually physical, but are defined only up to finite factorization-scheme redefinitions induced by collinear subtractions and renormalized-operator mixing. We formalize this redundancy categorically by introducing an \emph{interface algebra object} encoding admissible finite collinear counterterms/mixing kernels and by organizing coefficient data and hadronic data as right/left modules over this algebra in a symmetric monoidal category encoding the chosen recomposition calculus. Our main result, the \emph{Core Representation Theorem}, identifies the universal scheme-invariant carrier: the functor of balanced (scheme-invariant) pairings is represented by the relative tensor product $C\otimes_A f$, which is terminal among all quotients of the naive composite $C\otimes f$ that preserve scheme-invariant semantics. Finally, we show how standard physics inputs (symmetry constraints, locality/OPE, and a stated accuracy truncation) canonically induce the interface algebra and module structures, and we prove a minimal closure principle for completing a generating set of long-distance operators/correlators to an $A$-stable sector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Core Representation Theorem for Scheme-Invariant Collinear Factorization in QCD Keller, Dustin High Energy Physics - Phenomenology High Energy Physics - Theory Collinear factorization and the leading-twist operator product expansion (OPE) in perturbative QCD express suitably inclusive observables in scale-separated kinematics as composites of perturbative short-distance coefficients with universal long-distance non-perturbative correlators such as parton distribution functions (PDFs), up to controlled power corrections. A persistent structural feature is \emph{presentation non-uniqueness}: coefficients and correlators are not individually physical, but are defined only up to finite factorization-scheme redefinitions induced by collinear subtractions and renormalized-operator mixing. We formalize this redundancy categorically by introducing an \emph{interface algebra object} encoding admissible finite collinear counterterms/mixing kernels and by organizing coefficient data and hadronic data as right/left modules over this algebra in a symmetric monoidal category encoding the chosen recomposition calculus. Our main result, the \emph{Core Representation Theorem}, identifies the universal scheme-invariant carrier: the functor of balanced (scheme-invariant) pairings is represented by the relative tensor product $C\otimes_A f$, which is terminal among all quotients of the naive composite $C\otimes f$ that preserve scheme-invariant semantics. Finally, we show how standard physics inputs (symmetry constraints, locality/OPE, and a stated accuracy truncation) canonically induce the interface algebra and module structures, and we prove a minimal closure principle for completing a generating set of long-distance operators/correlators to an $A$-stable sector. |
| title | A Core Representation Theorem for Scheme-Invariant Collinear Factorization in QCD |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.13439 |