Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions

We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula...

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Autores principales: Jenkins, Elizabeth E., Manohar, Aneesh V., Trott, Michael
Lenguaje:eng
Publicado: 2013
Materias:
Particle Physics - Phenomenology
Acceso en línea:https://dx.doi.org/10.1016/j.physletb.2013.09.020
http://cds.cern.ch/record/1597342
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author Jenkins, Elizabeth E.
Manohar, Aneesh V.
Trott, Michael
author_facet Jenkins, Elizabeth E.
Manohar, Aneesh V.
Trott, Michael
author_sort Jenkins, Elizabeth E.
collection CERN
description We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this paper are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2013
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spelling cern-15973422019-09-30T06:29:59Zdoi:10.1016/j.physletb.2013.09.020http://cds.cern.ch/record/1597342engJenkins, Elizabeth E.Manohar, Aneesh V.Trott, MichaelNaive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous DimensionsParticle Physics - PhenomenologyWe show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this paper are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory.We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this paper are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory.We show that naive dimensional analysis (NDA) is equivalent to the result that L -loop scattering amplitudes have perturbative order N=L+Δ , with a shift Δ that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this Letter, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this Letter are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory.CERN-PH-TH-2013-213arXiv:1309.0819CERN-PH-TH-2013-213oai:cds.cern.ch:15973422013-09-03
spellingShingle Particle Physics - Phenomenology
Jenkins, Elizabeth E.
Manohar, Aneesh V.
Trott, Michael
Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
title Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
title_full Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
title_fullStr Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
title_full_unstemmed Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
title_short Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
title_sort naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1016/j.physletb.2013.09.020
http://cds.cern.ch/record/1597342
work_keys_str_mv AT jenkinselizabethe naivedimensionalanalysiscountingofgaugetheoryamplitudesandanomalousdimensions
AT manoharaneeshv naivedimensionalanalysiscountingofgaugetheoryamplitudesandanomalousdimensions
AT trottmichael naivedimensionalanalysiscountingofgaugetheoryamplitudesandanomalousdimensions

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