Resummed Distribution Functions: Making Perturbation Theory Positive and Normalized
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| Format: | Preprint |
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2025
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| _version_ | 1866912772394057728 |
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| author | Gambhir, Rikab Mastandrea, Radha |
| author_facet | Gambhir, Rikab Mastandrea, Radha |
| contents | Fixed-order perturbative calculations for differential cross sections can suffer from non-physical artifacts: they can be non-positive, non-normalizable, and non-finite, none of which occur in experimental measurements. We propose a framework, the Resummed Distribution Function (RDF), that, given a perturbative calculation for an observable to some finite order in $α_s$, will ``resum'' the expression in a way that is guaranteed to match the original expression order-by-order and be positive, normalized, and finite. Moreover, our ansatz parameterizes all possible finite, positive, and normalized completions consistent with the original fixed-order expression, which can include N$^n$LL resummed expressions. The RDF also enables a more direct notion of perturbative uncertainties, as we can directly vary higher-order parameters and treat them as nuisance parameters. We demonstrate the power of the RDF ansatz by matching to thrust to $\mathcal{O}(α_s^3)$ and extracting $α_s$ with perturbative uncertainties by fitting the RDF to ALEPH data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resummed Distribution Functions: Making Perturbation Theory Positive and Normalized Gambhir, Rikab Mastandrea, Radha High Energy Physics - Phenomenology High Energy Physics - Experiment Data Analysis, Statistics and Probability Fixed-order perturbative calculations for differential cross sections can suffer from non-physical artifacts: they can be non-positive, non-normalizable, and non-finite, none of which occur in experimental measurements. We propose a framework, the Resummed Distribution Function (RDF), that, given a perturbative calculation for an observable to some finite order in $α_s$, will ``resum'' the expression in a way that is guaranteed to match the original expression order-by-order and be positive, normalized, and finite. Moreover, our ansatz parameterizes all possible finite, positive, and normalized completions consistent with the original fixed-order expression, which can include N$^n$LL resummed expressions. The RDF also enables a more direct notion of perturbative uncertainties, as we can directly vary higher-order parameters and treat them as nuisance parameters. We demonstrate the power of the RDF ansatz by matching to thrust to $\mathcal{O}(α_s^3)$ and extracting $α_s$ with perturbative uncertainties by fitting the RDF to ALEPH data. |
| title | Resummed Distribution Functions: Making Perturbation Theory Positive and Normalized |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2512.04160 |