Four loop renormalization of QCD in the Curci-Ferrari gauge
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913724245213184 |
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| author | Gracey, J. A. |
| author_facet | Gracey, J. A. |
| contents | We renormalize Quantum Chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MSbar) scheme. We reproduce the four loop QCD MSbar beta-function from the Slavnov-Taylor identity for this gauge which relates the coupling constant renormalization to the gluon, Faddeev-Popov ghost and gauge parameter anomalous dimensions. This is carried out for a nonzero gauge parameter, without having to evaluate a vertex function. The anomalous dimension of the BRST invariant dimension two gluon and ghost mass term is deduced from a similar Slavnov-Taylor identity for this gauge. Consequently we construct the renormalization group functions in the minimal momentum subtraction scheme to four loops. As a corollary we deduce the five loop beta-function and quark mass anomalous dimensions in the same scheme. We also outline the pros and cons of employing the Curci-Ferrari gauge to access the six loop QCD beta-function in the MSbar scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Four loop renormalization of QCD in the Curci-Ferrari gauge Gracey, J. A. High Energy Physics - Theory We renormalize Quantum Chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MSbar) scheme. We reproduce the four loop QCD MSbar beta-function from the Slavnov-Taylor identity for this gauge which relates the coupling constant renormalization to the gluon, Faddeev-Popov ghost and gauge parameter anomalous dimensions. This is carried out for a nonzero gauge parameter, without having to evaluate a vertex function. The anomalous dimension of the BRST invariant dimension two gluon and ghost mass term is deduced from a similar Slavnov-Taylor identity for this gauge. Consequently we construct the renormalization group functions in the minimal momentum subtraction scheme to four loops. As a corollary we deduce the five loop beta-function and quark mass anomalous dimensions in the same scheme. We also outline the pros and cons of employing the Curci-Ferrari gauge to access the six loop QCD beta-function in the MSbar scheme. |
| title | Four loop renormalization of QCD in the Curci-Ferrari gauge |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.20950 |