Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ )
Abstract We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order 1/N f , we construct the full 2-parameter transseries and perform the s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2023)103 |
| _version_ | 1797371238354518016 |
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| author | Eric Laenen Coenraad Marinissen Marcel Vonk |
| author_facet | Eric Laenen Coenraad Marinissen Marcel Vonk |
| author_sort | Eric Laenen |
| collection | DOAJ |
| description | Abstract We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order 1/N f , we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in 1/N f . We compute 3-loop planar diagrams, at order 1/ N f 2 $$ {N}_f^2 $$ , and for each diagram study the asymptotic behavior and resulting non-perturbative information in the transseries. A structure emerges that, from a resurgence point of view, is quite different from toy models hitherto studied. We study in particular the first and second non-perturbative sectors, their relation to UV and IR renormalons, and how their presence influences the perturbative expansions in neighbouring sectors. Finally, finding that many non-perturbative sectors have asymptotic series, we derive relations among all of them, thus providing an interesting new perspective on the alien lattice for the Adler function. |
| first_indexed | 2024-03-08T18:17:02Z |
| format | Article |
| id | doaj.art-cf3fd4e76c2e44b99724b08789edf693 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:17:02Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-cf3fd4e76c2e44b99724b08789edf6932023-12-31T12:07:10ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023918610.1007/JHEP09(2023)103Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ )Eric Laenen0Coenraad Marinissen1Marcel Vonk2Institute of Physics, University of AmsterdamInstitute of Physics, University of AmsterdamInstitute of Physics, University of AmsterdamAbstract We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order 1/N f , we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in 1/N f . We compute 3-loop planar diagrams, at order 1/ N f 2 $$ {N}_f^2 $$ , and for each diagram study the asymptotic behavior and resulting non-perturbative information in the transseries. A structure emerges that, from a resurgence point of view, is quite different from toy models hitherto studied. We study in particular the first and second non-perturbative sectors, their relation to UV and IR renormalons, and how their presence influences the perturbative expansions in neighbouring sectors. Finally, finding that many non-perturbative sectors have asymptotic series, we derive relations among all of them, thus providing an interesting new perspective on the alien lattice for the Adler function.https://doi.org/10.1007/JHEP09(2023)103Large-Order Behaviour of Perturbation TheoryRenormalonsNonperturbative Effects |
| spellingShingle | Eric Laenen Coenraad Marinissen Marcel Vonk Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ ) Journal of High Energy Physics Large-Order Behaviour of Perturbation Theory Renormalons Nonperturbative Effects |
| title | Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ ) |
| title_full | Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ ) |
| title_fullStr | Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ ) |
| title_full_unstemmed | Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ ) |
| title_short | Resurgence analysis of the Adler function at O $$ \mathcal{O} $$ (1/ N f 2 $$ {N}_f^2 $$ ) |
| title_sort | resurgence analysis of the adler function at o mathcal o 1 n f 2 n f 2 |
| topic | Large-Order Behaviour of Perturbation Theory Renormalons Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP09(2023)103 |
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