A new method for estimating unknown one-order higher QCD corrections to the perturbative series using the linear regression through the origin

[2505.05131] A new method for estimating unknown one-order higher QCD corrections to the perturbative series using the linear regression through the origin Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Phenomenology arXiv:2505.05131 (hep-ph) [Submitted on 8 May 2025 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: A new method for estimating unknown one-order higher QCD corrections to the perturbative series using the linear regression through the origin Authors: Zhi-Fei Wu , Xing-Gang Wu , Jiang Yan , Xu-Dong Huang , Jian-Ming Shen View a PDF of the paper titled A new method for estimating unknown one-order higher QCD corrections to the perturbative series using the linear regression through the origin, by Zhi-Fei Wu and 4 other authors View PDF HTML (experimental) Abstract: It is generally believed that the QCD theory is the fundamental theory for strong interactions. Due to the asymptotic freedom at the short distances, after proper factorization, one can predict the value of high-energy physical observable by using the perturbative QCD (pQCD). It has been demonstrated that by recursively using of renormalization group equation with the help of Principle of Maximum Conformality (PMC), one can eliminate conventional renormalization scheme-and-scale ambiguities existed in the initial fixed-order pQCD series. To extend the predictive power of pQCD, we are still facing the problem of how to reliably estimate the contributions from the unknown higher-order (UHO) terms. In this paper, using the PMC scheme-and-scale invariant series as the starting point, we suggest a novel method of using linear regression through the origin (LRTO) to fix the asymptotic form of the pQCD series, which subsequently predicts the reasonable magnitude of the one-order higher UHO-terms. As an explicit example, we apply the method to deal with the ratio $R_\tau$, which has been calculated up to four-loop QCD corrections. Our results show that the LRTO method works well, demonstrating its reliability and significant predictive power for estimating the UHO-terms. Especially, we show that the scale-invariant and more convergent PMC series exhibits a much better predictive power with stability and reliability than the initial scale-dependent pQCD series. Comments: 22 pages, 8 figures Subjects: High Energy Physics - Phenomenology (hep-ph) Cite as: arXiv:2505.05131 [hep-ph] (or arXiv:2505.05131v2 [hep-ph] for this version) https://doi.org/10.48550/arXiv.2505.05131 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1140/epjc/s10052-026-15506-5 Focus to learn more DOI(s) linking to related resources Submission history From: Zhifei Wu [ view email ] [v1] Thu, 8 May 2025 11:09:40 UTC (300 KB) [v2] Fri, 10 Apr 2026 06:26:42 UTC (297 KB) Full-text links: Access Paper: View a PDF of the paper titled A new method for estimating unknown one-order higher QCD corrections to the perturbative series using the linear regression through the origin, by Zhi-Fei Wu and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: hep-ph < prev | next > new | recent | 2025-05 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Order jumps in Spectral Deferred Corrections#1131499
• Revisiting light-flavor diquarks in the inverse matrix method of QCD sum rules#401620
• Dynamics of gravitational clustering V. Subleading corrections in the quasi-linear regime#1053328
• Stable initial conditions and analytical investigations of cosmological perturbations in a modified loop quantum cosmology#147091
• Hyperon non-leptonic decays in relativistic Chiral Perturbation Theory with resonances#1129213