Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?
Abstract The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU(N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigate...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2018)161 |
| _version_ | 1819018962882527232 |
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| author | A. V. Garkusha A. L. Kataev V. S. Molokoedov |
| author_facet | A. V. Garkusha A. L. Kataev V. S. Molokoedov |
| author_sort | A. V. Garkusha |
| collection | DOAJ |
| description | Abstract The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU(N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the Oas4 $$ \mathcal{O}\left({a}_s^4\right) $$ level of perturbation theory. It is known that in the gauge-invariant renormalization MS¯ $$ \overline{\mathrm{MS}} $$-scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the MS¯ $$ \overline{\mathrm{MS}} $$-scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the Oas3 $$ \mathcal{O}\left({a}_s^3\right) $$ level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = −3, −1 and ξ = 0. In the Oas4 $$ \mathcal{O}\left({a}_s^4\right) $$ order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = −3 at the Oas3 $$ \mathcal{O}\left({a}_s^3\right) $$ approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well. |
| first_indexed | 2024-12-21T03:27:45Z |
| format | Article |
| id | doaj.art-f1009a3be8e046c09e8367dc1d37cfc4 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T03:27:45Z |
| publishDate | 2018-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f1009a3be8e046c09e8367dc1d37cfc42022-12-21T19:17:33ZengSpringerOpenJournal of High Energy Physics1029-84792018-02-012018214610.1007/JHEP02(2018)161Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?A. V. Garkusha0A. L. Kataev1V. S. Molokoedov2Higher School of Economics, Math DepartmentInstitute for Nuclear Research of the Russian Academy of SciencesInstitute for Nuclear Research of the Russian Academy of SciencesAbstract The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU(N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the Oas4 $$ \mathcal{O}\left({a}_s^4\right) $$ level of perturbation theory. It is known that in the gauge-invariant renormalization MS¯ $$ \overline{\mathrm{MS}} $$-scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the MS¯ $$ \overline{\mathrm{MS}} $$-scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the Oas3 $$ \mathcal{O}\left({a}_s^3\right) $$ level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = −3, −1 and ξ = 0. In the Oas4 $$ \mathcal{O}\left({a}_s^4\right) $$ order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = −3 at the Oas3 $$ \mathcal{O}\left({a}_s^3\right) $$ approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.http://link.springer.com/article/10.1007/JHEP02(2018)161Perturbative QCDRenormalization Group |
| spellingShingle | A. V. Garkusha A. L. Kataev V. S. Molokoedov Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property? Journal of High Energy Physics Perturbative QCD Renormalization Group |
| title | Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property? |
| title_full | Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property? |
| title_fullStr | Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property? |
| title_full_unstemmed | Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property? |
| title_short | Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property? |
| title_sort | renormalization scheme and gauge in dependence of the generalized crewther relation what are the real grounds of the β factorization property |
| topic | Perturbative QCD Renormalization Group |
| url | http://link.springer.com/article/10.1007/JHEP02(2018)161 |
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