Ultraviolet and Infrared Divergences in Implicit Regularization: A Consistent Approach

Fargnoli, H. G.; Scarpelli, A. P. Baêta; Brito, L. C. T.; Hiller, Brigitte; Sampaio, Marcos; Nemes, M. C.; Osipov, A. A.

doi:10.1142/s0217732311034773

Cited by 10 publications

(14 citation statements)

References 31 publications

(41 reference statements)

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“…The first restriction is justified because, as we show in Section IV, to implement a mass independent renormalization scheme in IReg we need only the massless basic divergent integrals that we present below. When infrared divergences do appear, a dual version of IReg operating in coordinate space displays infrared divergences as basic divergent integrals as well, in a way that infrared and ultraviolet degrees of freedom are clearly distinguished [32]- [35].…”

Section: The Rules Of Implicit Regularizationmentioning

confidence: 99%

Systematic Implementation of Implicit Regularization for Multiloop Feynman Diagrams

Cherchiglia

Sampaio

Nemes

2011

Int. J. Mod. Phys. A

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Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory.

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Section: The Rules Of Implicit Regularizationmentioning

confidence: 99%

Systematic Implementation of Implicit Regularization for Multiloop Feynman Diagrams

Cherchiglia

Sampaio

Nemes

2011

Int. J. Mod. Phys. A

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“…In fact, the fermionic contributions have been computed recently [24] using 'four-dimensional regularization' (fdr) [25,26]. Similar to 'implicit regularization' [27][28][29] and 'loop regularization' [30,31], fdr is a four-dimensional framework to compute higher-order corrections. Another approach that is being investigated is to use loop-tree duality to deal with IR singularities at the integrand level [32,33].…”

Section: Introductionmentioning

confidence: 99%

Dimensional schemes for cross sections at NNLO

Gnendiger

Signer

2020

Eur. Phys. J. C

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So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of physical cross sections at next-tonext-to-leading order. As a case study we consider two-jet production in electron-positron annihilation and describe how to compute the various parts separately in different schemes. In particular, we verify that using dimensional reduction the double-real corrections are obtained simply by integrating the four-dimensional matrix element over the phase space. In addition, we confirm that the cross section is regularization-scheme independent. 1

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“…As we can see, the infrared divergence is concentrated in the F integral. To proper treat the IR divergence, one could, for example, resort to the IReg generalization presented in [46]. However, in the present case the integral F will cancel out with other contributions, not requiring any further treatment.…”

Section: N = 1 Sqed In the Standard Background Field Methodsmentioning

confidence: 99%

Subtleties in the beta-function calculation of $$N=1$$ N = 1 supersymmetric gauge theories

et al. 2016

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We investigate some peculiarities in the calculation of the two-loop betafunction of N = 1 supersymmetric models which are intimately related to the socalled "Anomaly Puzzle". There is an apparent paradox when the computation is performed in the framework of the covariant derivative background field method. In this formalism, it is obtained a finite two-loop effective action, although a nonnull coefficient for the beta-function is achieved by means of the renormalized two-point function in the background field. We show that if the standard background field method is used, this two-point function has a divergent part which allows for the calculation of the beta-function via the renormalization constants, as usual. Therefore, we conjecture that this paradox has its origin in the covariant supergraph formalism itself, possibly being an artifact of the rescaling anomaly.

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Ultraviolet and Infrared Divergences in Implicit Regularization: A Consistent Approach

Cited by 10 publications

References 31 publications

Systematic Implementation of Implicit Regularization for Multiloop Feynman Diagrams

Systematic Implementation of Implicit Regularization for Multiloop Feynman Diagrams

Dimensional schemes for cross sections at NNLO

Subtleties in the beta-function calculation of $$N=1$$ N = 1 supersymmetric gauge theories

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