Trace-anomaly-subtracted $σ$-mass for Heavy Quarks and Matching from Lattice QCD

[2509.10786] Trace-anomaly-subtracted $σ$-mass for Heavy Quarks and Matching from Lattice QCD Skip to main content Search Submit Donate Log in High Energy Physics - Phenomenology arXiv:2509.10786 (hep-ph) [Submitted on 13 Sep 2025 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Trace-anomaly-subtracted $σ$-mass for Heavy Quarks and Matching from Lattice QCD Authors: Long Chen , Cong Zhao View PDF HTML (experimental) Abstract: We demonstrate that the leading IR-renormalon divergence in the perturbative pole mass of a massive quark resides entirely in the contribution from the trace anomaly of the energy-momentum tensor in QCD. Consequently, the recently proposed trace-anomaly-subtracted $\sigma$-mass definition for heavy quarks is not only scheme- and scale-invariant, hence unique for each flavor, but also free from the leading IR-renormalon ambiguity. We further derive a formula connecting this $\sigma$-mass to the perturbative pole mass, solely in terms of the QCD $\beta$-function, quark-mass anomalous dimension $\gamma_m$ and a proper rewritten form of the pole-to-$\overline{\mathrm{MS}}$ mass conversion factor. Utilizing this formula together with the ingredients available in the literature, we present the explicit five-loop result for the perturbative relationship between the $\sigma$-mass and the perturbative pole mass in QCD under the approximation of keeping only a single quark massive. Furthermore, we outline how $\sigma$-mass for a heavy quark can in principle be determined from lattice QCD through an intermediate regularization-independent renormalization and continuum perturbative matching, for which we analyze the matching factor through four loops with appealing features revealed. Given the aforementioned theoretical merits of this mass definition and the availability of high-precision conversion relations as well as the feasibility of direct extraction from lattice QCD, it is well suited for acting as a promising candidate reference scheme for comparing or combining quark masses of the same flavor obtained in different schemes. Comments: a lattice-QCD matching strategy for determining $σ$-mass added; typos fixed; references added Subjects: High Energy Physics - Phenomenology (hep-ph) ; High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th) Cite as: arXiv:2509.10786 [hep-ph] (or arXiv:2509.10786v2 [hep-ph] for this version) https://doi.org/10.48550/arXiv.2509.10786 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Long Chen [ view email ] [v1] Sat, 13 Sep 2025 02:07:23 UTC (27 KB) [v2] Tue, 25 Aug 2026 02:50:25 UTC (37 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Ancillary-file links: Ancillary files ( details ) : TASmassRelations_4and5Loop.m Current browse context: hep-ph < prev | next > new | recent | 2025-09 Change to browse by: hep-lat hep-th References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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