Implicit Regularization and Renormalization of QCD

Sampaio, Marcos; Scarpelli, A. P. Baêta; Ottoni, José Eloy; Nemes, M. C.

doi:10.1007/s10773-006-9045-z

Cited by 30 publications

(30 citation statements)

References 20 publications

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“…For theories with poor symmetry content, MRI manisfests itself as an important ingredient in the calculation of the universal coefficients of the β-function. In recent works we have verified that MRI is also important to preserve the Slavnov Taylor identities for non-abelian gauge theories and supersymmetric gauge theories [13], [16], [17], [27]. A formal proof for these cases is an ongoing work based on diagrammatics and the quantum action principle [28].…”

Section: Examples a Momentum Routing Invariance And Supersymmetrymentioning

confidence: 90%

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

et al. 2012

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We illustrate with examples that quantum symmetry breakings in perturbation theory are connected to breakdown of momentum routing invariance (MRI) in the loops of a Feynman diagram.We show that MRI is a necessary and sufficient condition to preserve abelian gauge symmetry at arbitrary loop order. We adopt the implicit regularization framework in which surface terms that are directly connected to momentum routing can be constructed to arbitrary loop order. The interplay between momentum routing invariance, surface terms and anomalies is discussed. We also illustrate that MRI is important to preserve supersymmetry. For theories with poor symmetry content, such as scalar field theories, MRI is shown to be important in the calculation of renormalization group functions.

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Section: Examples a Momentum Routing Invariance And Supersymmetrymentioning

confidence: 90%

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

et al. 2012

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“…Similar analyses, in many different theories and contexts, have been carried out in Refs. [78][79][80][81][82][83][84][85][86][87][88][89][90][91].…”

Section: Ireg: Implicit Regularizationmentioning

confidence: 99%

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

et al. 2017

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“…(18) In the case of gauge symmetry, both abelian and nonabelian, a constrained version of IR in which such surface terms are set to vanish delivers gauge invariant amplitudes automatically [15], which is illustrated in the simple example above . The cancellation of these surface terms is also a requirement to preserve Supersymmetry [17].…”

Section: The Basic Divergent Integrals Which Encodementioning

confidence: 99%

Implicit regularization beyond one-loop order: scalar field theories

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Sampaio

et al. 2007

J. Phys. G: Nucl. Part. Phys.

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Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop level. In this paper, we aim at generalizing systematically IR to be applicable beyond one loop order. We use a scalar field theory as an example and pave the way for the extension to quantum field theories which are richer from the symmetry content viewpoint. Particularly, we show that a natural (minimal) renormalization scheme emerges, in which the infinities displayed in terms of integrals in one internal momentum are subtracted, whereas infrared and ultraviolet modes do not mix and therefore leave no room for ambiguities. A systematic cancelation of the infrared divergences at any loop order takes place between the ultraviolet finite and divergent parts of the amplitude for non-exceptional momenta leaving, as a byproduct, a renormalization group scale.

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Implicit Regularization and Renormalization of QCD

Cited by 30 publications

References 20 publications

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

Implicit regularization beyond one-loop order: scalar field theories

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