Non-local Lagrangians from renormalons and analyzable functions

Maiezza, Alessio; Vásquez, Juan C.

doi:10.1016/j.aop.2019.04.015

Cited by 27 publications

(55 citation statements)

References 53 publications

(122 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is what has been recently resummed in a generalized sense in Ref. [2], leaving only a single undetermined parameter. In the framework of analyzable functions, the operation of resummation along a Stokes line must be in a one-to-one correspondence with an ODE, which in Ref.…”

Section: Remarksmentioning

confidence: 62%

“…While a consistent solution has been recently proposed in Ref. [2], in this article we have analyzed the formal emergence of renormalons from the renormalization group equation. Specifically, we have proved that the Borel transform of a given Green function satisfying the renormalization group equation has a Stokes line with poles spaced by 1/|β 1 |.…”

Section: Discussionmentioning

confidence: 98%

“…Amusingly, a non-local operator also emerges from the synthesis of the renormalons, i.e. resumming them in the generalized sense (at least in the φ 4 model) [2]. After this resummation is performed there is no need of adding the higher-dimensional operators of Ref.…”

Section: Ir Renormalonsmentioning

confidence: 99%

“…Using the synthesis of the renormalons as in Ref [2], it is straightforward to show that only the first disconnected sector G 1 (z) is non-null whenever the Borel transform for G 0 (z) is of the form G 0 (z) = 1/(z 0 − z) n , with n an integer number (see Sec. 3 of Ref.…”

Section: Higher Order Corrections and The Resurgence Formalismmentioning

confidence: 99%

“…Bottom line: all the corrections to the result of Ref. [2] due to higher non-perturbative sectors must be proportional to β 2 (or higher terms of the beta function).…”

Section: Higher Order Corrections and The Resurgence Formalismmentioning

confidence: 99%

See 4 more Smart Citations

Resurgence of the renormalization group equation

2020

Self Cite

View full text Add to dashboard Cite

We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.

show abstract

Section: Remarksmentioning

confidence: 62%

Section: Discussionmentioning

confidence: 98%

Section: Ir Renormalonsmentioning

confidence: 99%

Section: Higher Order Corrections and The Resurgence Formalismmentioning

confidence: 99%

“…Bottom line: all the corrections to the result of Ref. [2] due to higher non-perturbative sectors must be proportional to β 2 (or higher terms of the beta function).…”

Section: Higher Order Corrections and The Resurgence Formalismmentioning

confidence: 99%

See 3 more Smart Citations

Resurgence of the renormalization group equation

2020

Self Cite

View full text Add to dashboard Cite

show abstract

Renormalons in quantum mechanics

Cihan

Bleeken

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac δ-potential-known to require renormalizationand a 1d Dirac δ-potential tilted at an angle. We argue that renormalons are not specific to this example and exist for a much wider class of potentials. The ambiguity in the Borel summation of the perturbative series due to the renormalon pole is resolved by the physical condition of causality through careful consideration of the i prescription. The suitably summed perturbative result coincides with the exact answer obtained through the operator formalism for scattering.

show abstract

Resurgence analysis of the Adler function at $$ \mathcal{O} $$(1/$$ {N}_f^2 $$)

Laenen,

Marinissen,

Vonk

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

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/$$ {N}_f^2 $$ 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.

show abstract

Non-local Lagrangians from renormalons and analyzable functions

Cited by 27 publications

References 53 publications

Resurgence of the renormalization group equation

Resurgence of the renormalization group equation

Renormalons in quantum mechanics

Resurgence analysis of the Adler function at $$ \mathcal{O} $$(1/$$ {N}_f^2 $$)

Contact Info

Product

Resources

About