Low-energy theorem revisited and OPE in massless QCD
Abstract We revisit a low-energy theorem (LET) of NSVZ type in SU(N) QCD with N f massless quarks derived in [1] by implementing it in dimensional regularization. The LET relates n-point correlators in the l.h.s. to n + 1-point correlators with the extra insertion of TrF 2 at zero momentum in the r....
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2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)145 |
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| author | Marco Bochicchio Elisabetta Pallante |
| author_facet | Marco Bochicchio Elisabetta Pallante |
| author_sort | Marco Bochicchio |
| collection | DOAJ |
| description | Abstract We revisit a low-energy theorem (LET) of NSVZ type in SU(N) QCD with N f massless quarks derived in [1] by implementing it in dimensional regularization. The LET relates n-point correlators in the l.h.s. to n + 1-point correlators with the extra insertion of TrF 2 at zero momentum in the r.h.s. We demonstrate that, for 2-point correlators of an operator O in the l.h.s., the LET implies that, in general, the integrated 3-point correlator in the r.h.s. needs in perturbation theory an infinite additive renormalization in addition to the multiplicative one. We relate the above counterterm to a corresponding divergent contact term in a certain coefficient of the OPE of TrF 2 with O in the momentum representation, thus extending to any operator O an independent argument that first appeared for O = TrF 2 in [2]. Finally, we demonstrate that in the asymptotically free phase of QCD the aforementioned counterterm in the LET is actually finite nonperturbatively after resummation to all perturbative orders. We also briefly recall the implications of the LET in the gauge-invariant framework of dimensional regularization for the perturbative and nonperturbative renormalization in large-N QCD. The implications of the LET inside and above the conformal window of SU(N) QCD with N f massless quarks will appear in a forthcoming paper. |
| format | Article |
| id | doaj-art-e2735822055f43f5b448cfa2892aac7f |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e2735822055f43f5b448cfa2892aac7f2024-11-24T12:04:55ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024816510.1007/JHEP08(2024)145Low-energy theorem revisited and OPE in massless QCDMarco Bochicchio0Elisabetta Pallante1Physics Department, INFN Roma1Van Swinderen Institute for Particle Physics and Gravity, University of GroningenAbstract We revisit a low-energy theorem (LET) of NSVZ type in SU(N) QCD with N f massless quarks derived in [1] by implementing it in dimensional regularization. The LET relates n-point correlators in the l.h.s. to n + 1-point correlators with the extra insertion of TrF 2 at zero momentum in the r.h.s. We demonstrate that, for 2-point correlators of an operator O in the l.h.s., the LET implies that, in general, the integrated 3-point correlator in the r.h.s. needs in perturbation theory an infinite additive renormalization in addition to the multiplicative one. We relate the above counterterm to a corresponding divergent contact term in a certain coefficient of the OPE of TrF 2 with O in the momentum representation, thus extending to any operator O an independent argument that first appeared for O = TrF 2 in [2]. Finally, we demonstrate that in the asymptotically free phase of QCD the aforementioned counterterm in the LET is actually finite nonperturbatively after resummation to all perturbative orders. We also briefly recall the implications of the LET in the gauge-invariant framework of dimensional regularization for the perturbative and nonperturbative renormalization in large-N QCD. The implications of the LET inside and above the conformal window of SU(N) QCD with N f massless quarks will appear in a forthcoming paper.https://doi.org/10.1007/JHEP08(2024)145Renormalization and RegularizationRenormalization Group |
| spellingShingle | Marco Bochicchio Elisabetta Pallante Low-energy theorem revisited and OPE in massless QCD Journal of High Energy Physics Renormalization and Regularization Renormalization Group |
| title | Low-energy theorem revisited and OPE in massless QCD |
| title_full | Low-energy theorem revisited and OPE in massless QCD |
| title_fullStr | Low-energy theorem revisited and OPE in massless QCD |
| title_full_unstemmed | Low-energy theorem revisited and OPE in massless QCD |
| title_short | Low-energy theorem revisited and OPE in massless QCD |
| title_sort | low energy theorem revisited and ope in massless qcd |
| topic | Renormalization and Regularization Renormalization Group |
| url | https://doi.org/10.1007/JHEP08(2024)145 |
| work_keys_str_mv | AT marcobochicchio lowenergytheoremrevisitedandopeinmasslessqcd AT elisabettapallante lowenergytheoremrevisitedandopeinmasslessqcd |