TY - JOUR
T1 - Resurgence analysis of the Adler function at O (1/ Nf2)
AU - Laenen, Eric
AU - Marinissen, Coenraad
AU - Vonk, Marcel
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/9
Y1 - 2023/9
N2 - 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/Nf, 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/Nf. We compute 3-loop planar diagrams, at order 1/ Nf2 , 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.
AB - 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/Nf, 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/Nf. We compute 3-loop planar diagrams, at order 1/ Nf2 , 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.
KW - Large-Order Behaviour of Perturbation Theory
KW - Nonperturbative Effects
KW - Renormalons
UR - http://www.scopus.com/inward/record.url?scp=85171666354&partnerID=8YFLogxK
U2 - 10.1007/JHEP09(2023)103
DO - 10.1007/JHEP09(2023)103
M3 - Article
AN - SCOPUS:85171666354
SN - 1126-6708
VL - 2023
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 9
M1 - 103
ER -