Nonrenormalization and Operator Mixing via On-Shell Methods

Bern, Zvi; Parra-Martinez, Julio; Sawyer, Eric

doi:10.1103/PhysRevLett.124.051601

Title: Nonrenormalization and Operator Mixing via On-Shell Methods

Abstract

Using on-shell methods, we present a new perturbative non-renormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions we show that longer operators are often restricted from renormalizing shorter operators at the first order where there exist Feynman diagrams. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the Standard Model Effective Field Theory, including examples of nontrivial zeros in the anomalous-dimension matrix at one through four loops. The zeros at two and higher loops go beyond those previously explained using helicity selection rules. We also include explicit sample calculations at two loops.

Authors:

Bern, Zvi; Parra-Martinez, Julio;

Publication Date:: Tue Feb 04 00:00:00 EST 2020

Research Org.:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1599492

Alternate Identifier(s):: OSTI ID: 1608824; OSTI ID: 1735474

Grant/Contract Number:: SC0009937

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 5; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective field theory; Form factors; Renormalization

Citation Formats


                    Bern, Zvi, Parra-Martinez, Julio, and Sawyer, Eric. Nonrenormalization and Operator Mixing via On-Shell Methods.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevLett.124.051601.

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                    Bern, Zvi, Parra-Martinez, Julio, & Sawyer, Eric. Nonrenormalization and Operator Mixing via On-Shell Methods.  United States.  https://doi.org/10.1103/PhysRevLett.124.051601

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                    Bern, Zvi, Parra-Martinez, Julio, and Sawyer, Eric. Tue .  
"Nonrenormalization and Operator Mixing via On-Shell Methods".  United States.  https://doi.org/10.1103/PhysRevLett.124.051601.

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@article{osti_1599492,

  title        = {Nonrenormalization and Operator Mixing via On-Shell Methods},

  author       = {Bern, Zvi and Parra-Martinez, Julio and Sawyer, Eric},

  abstractNote = {Using on-shell methods, we present a new perturbative non-renormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions we show that longer operators are often restricted from renormalizing shorter operators at the first order where there exist Feynman diagrams. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the Standard Model Effective Field Theory, including examples of nontrivial zeros in the anomalous-dimension matrix at one through four loops. The zeros at two and higher loops go beyond those previously explained using helicity selection rules. We also include explicit sample calculations at two loops.},

  doi          = {10.1103/PhysRevLett.124.051601},

  journal      = {Physical Review Letters},

  number       = 5,

  volume       = 124,

  place        = {United States},

  year         = {Tue Feb 04 00:00:00 EST 2020},

  month        = {Tue Feb 04 00:00:00 EST 2020}

}

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Similar Records

Title: Nonrenormalization and Operator Mixing via On-Shell Methods

Abstract

Citation Formats

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Factorization structure of gauge theory amplitudes and application to hard scattering processes at the LHC journal, November 2009

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One-loop amplitudes for e+e− to four partons journal, March 1998

An Introduction to Quantum Field Theory book, January 1993

Effective lagrangian analysis of new interactions and flavour conservation journal, May 1986

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The singular behaviour of QCD amplitudes at two-loop order journal, May 1998

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Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences journal, November 2015

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes journal, June 1994

Higgs Amplitudes from N = 4 Supersymmetric Yang-Mills Theory journal, October 2017

Renormalization group coefficients and the S-matrix journal, December 2016

Higgs windows to new physics through d = 6 operators: constraints and one-loop anomalous dimensions journal, November 2013

One-loop n-point gauge theory amplitudes, unitarity and collinear limits journal, August 1994

Two-loop renormalization of quantum gravity simplified journal, February 2017

Renormalization group scaling of Higgs operators and h → γγ decay journal, April 2013

Multi-parton amplitudes in gauge theories journal, February 1991

Higher-order corrections to jet cross sections in e + e − annihilation journal, September 1992

Dimension-six terms in the Standard Model Lagrangian journal, October 2010

Renormalization group evolution of the Standard Model dimension six operators III: gauge coupling dependence and phenomenology journal, April 2014

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Massive loop amplitudes from unitarity journal, May 1996

The standard model as an effective field theory journal, February 2019

Analytic continuation of the Sudakov form factor in QCD journal, December 1990

Renormalization of dimension-six operators relevant for the Higgs decays h → γγ, γZ journal, August 2013

Tr(F3) supersymmetric form factors and maximal transcendentality. Part II. 0 journal, December 2018

Holomorphy without supersymmetry in the Standard Model Effective Field Theory journal, December 2014

Generalized unitarity and one-loop amplitudes in super-Yang–Mills journal, October 2005

Renormalization group evolution of the standard model dimension six operators. I: formalism and λ dependence
journal, October 2013

Factorization structure of gauge theory amplitudes and application to hard scattering processes at the LHC
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Fusing gauge theory tree amplitudes into loop amplitudes
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Naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions
journal, November 2013

One-loop amplitudes for e+e− to four partons
journal, March 1998

An Introduction to Quantum Field Theory
book, January 1993

Effective lagrangian analysis of new interactions and flavour conservation
journal, May 1986

The SU(2|3) dynamic two-loop form factors
journal, August 2016

The singular behaviour of QCD amplitudes at two-loop order
journal, May 1998

One-loop non-renormalization results in EFTs
journal, July 2015

Nonrenormalization Theorems without Supersymmetry
journal, August 2015

Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
journal, November 2015

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes
journal, June 1994

Higgs Amplitudes from $N = 4$ Supersymmetric Yang-Mills Theory
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Renormalization group coefficients and the S-matrix
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Higgs windows to new physics through d = 6 operators: constraints and one-loop anomalous dimensions
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One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994

Two-loop renormalization of quantum gravity simplified
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Renormalization group scaling of Higgs operators and h → γγ decay
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Multi-parton amplitudes in gauge theories
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Higher-order corrections to jet cross sections in $e^{+} e^{-}$ annihilation
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Dimension-six terms in the Standard Model Lagrangian
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Renormalization group evolution of the Standard Model dimension six operators III: gauge coupling dependence and phenomenology
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Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence
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