Resurgence analysis of the Adler function at order $1/N_f^2$

Eric Laenen, Coenraad Marinissen, Marcel Vonk

Research output: Working paperPreprintAcademic

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 $1/N_f^2$, 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.
Original languageEnglish
PublisherarXiv
DOIs
Publication statusPublished - 27 Feb 2023

Bibliographical note

85 pages, including 4 appendices; typos corrected, references added

Keywords

  • hep-ph
  • hep-th
  • math-ph
  • math.MP

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