Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion
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| Format: | Preprint |
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2026
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| _version_ | 1866918528670498816 |
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| author | Huang, Rijun Jin, Qingjun Li, Yi |
| author_facet | Huang, Rijun Jin, Qingjun Li, Yi |
| contents | We apply the Operator Product Expansion (OPE) algorithm to the renormalization of scalar-QED theory, with a specific focus on the fixed-charge operator $ϕ^Q$. Within the OPE framework, the anomalous dimension of the $ϕ^Q$ operator is perturbatively computed to four-loop order in the modified minimal subtraction scheme, extending beyond the previously available three-loop result. The beta functions, as well as the mass and field anomalous dimensions, are also computed at this order. An alternative loop-integrand construction method is proposed, based on graph decomposition and skeleton expansion techniques, for deriving the integrands of one-Particle-Irreducible correlation functions. This work represents the first non-trivial validation of the OPE algorithm for higher-loop renormalization beyond pure scalar theories. The present successful computations further confirm the efficiency and versatility of the OPE algorithm in renormalization analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion Huang, Rijun Jin, Qingjun Li, Yi High Energy Physics - Theory High Energy Physics - Phenomenology We apply the Operator Product Expansion (OPE) algorithm to the renormalization of scalar-QED theory, with a specific focus on the fixed-charge operator $ϕ^Q$. Within the OPE framework, the anomalous dimension of the $ϕ^Q$ operator is perturbatively computed to four-loop order in the modified minimal subtraction scheme, extending beyond the previously available three-loop result. The beta functions, as well as the mass and field anomalous dimensions, are also computed at this order. An alternative loop-integrand construction method is proposed, based on graph decomposition and skeleton expansion techniques, for deriving the integrands of one-Particle-Irreducible correlation functions. This work represents the first non-trivial validation of the OPE algorithm for higher-loop renormalization beyond pure scalar theories. The present successful computations further confirm the efficiency and versatility of the OPE algorithm in renormalization analysis. |
| title | Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2604.13464 |