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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.14741 |
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| _version_ | 1866913038117896192 |
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| author | Zhang, Jinpeng Jin, Qingjun |
| author_facet | Zhang, Jinpeng Jin, Qingjun |
| contents | We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $ϕ^4$ and $ϕ^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors of these composite operators are determined by OPE coefficients of lower-dimensional traceless symmetric tensor operators, and establish a recursive renormalization framework. We report the five-loop anomalous dimensions for operators with $Δ\le5$ in the $ϕ^4$ model and the two-loop anomalous dimensions for operators with $Δ\le10$ in the $ϕ^3$ model. These results further demonstrate the versatility and efficiency of the OPE-based algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14741 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The OPE Approach to Renormalization: Operator Mixing Zhang, Jinpeng Jin, Qingjun High Energy Physics - Theory We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $ϕ^4$ and $ϕ^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors of these composite operators are determined by OPE coefficients of lower-dimensional traceless symmetric tensor operators, and establish a recursive renormalization framework. We report the five-loop anomalous dimensions for operators with $Δ\le5$ in the $ϕ^4$ model and the two-loop anomalous dimensions for operators with $Δ\le10$ in the $ϕ^3$ model. These results further demonstrate the versatility and efficiency of the OPE-based algorithm. |
| title | The OPE Approach to Renormalization: Operator Mixing |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.14741 |