Low-energy effective field theory below the electroweak scale: anomalous dimensions

Jenkins, Elizabeth E.; Manohar, Aneesh V.; Stoffer, Peter

doi:10.1007/jhep01(2018)084

Title: Low-energy effective field theory below the electroweak scale: anomalous dimensions

Abstract

We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. As a result, the use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.

Authors:

Jenkins, Elizabeth E. ^[1]; Manohar, Aneesh V. ^[1]; Stoffer, Peter ^[1]

Univ. of California at San Diego, La Jolla, CA (United States). Dept. of Physics

Publication Date:: Thu Jan 18 00:00:00 EST 2018

Research Org.:: Univ. of California, San Diego, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1503683

Grant/Contract Number:: SC0009919

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Renormalization Group

Citation Formats


                    Jenkins, Elizabeth E., Manohar, Aneesh V., and Stoffer, Peter. Low-energy effective field theory below the electroweak scale: anomalous dimensions.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep01(2018)084.

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                    Jenkins, Elizabeth E., Manohar, Aneesh V., & Stoffer, Peter. Low-energy effective field theory below the electroweak scale: anomalous dimensions.  United States.  https://doi.org/10.1007/jhep01(2018)084

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                    Jenkins, Elizabeth E., Manohar, Aneesh V., and Stoffer, Peter. Thu .  
"Low-energy effective field theory below the electroweak scale: anomalous dimensions".  United States.  https://doi.org/10.1007/jhep01(2018)084.  https://www.osti.gov/servlets/purl/1503683.

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@article{osti_1503683,

  title        = {Low-energy effective field theory below the electroweak scale: anomalous dimensions},

  author       = {Jenkins, Elizabeth E. and Manohar, Aneesh V. and Stoffer, Peter},

  abstractNote = {We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. As a result, the use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.},

  doi          = {10.1007/jhep01(2018)084},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 1,

  volume       = 2018,

  place        = {United States},

  year         = {Thu Jan 18 00:00:00 EST 2018},

  month        = {Thu Jan 18 00:00:00 EST 2018}

}

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Cited by: 101 works

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Figures / Tables:

Table 1: LEFT operators of dimension three and five, as well as LEFT operators of dimension six that conserve baryon and lepton number, reproduced from ref. [20].

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Standard Model Neutrino Effective Field Theory (SMNEFT) is an effective theory with Standard Model (SM) gauge-invariant operators constructed only from SM and right-handed neutrino fields. For the full set of dimension-six SMNEFT operators, we present the gauge coupling terms of the one-loop anomalous dimension matrix for renormalization group evolution (RGE) of the Wilson coefficients between a new physics scale and the electroweak scale. We find that the SMNEFT operators can be divided into five subsets which are closed under RGE. Our results apply for both Dirac and Majorana neutrinos. We also discuss the operator mixing pattern numerically and comment onmore »« less
https://doi.org/10.1007/jhep02(2021)015

Full Text Available
Renormalization of the Standard Model Effective Field Theory from geometry

Journal Article Helset, Andreas ; Jenkins, Elizabeth E. ; Manohar, Aneesh V. - Journal of High Energy Physics (Online)

S-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature Rijkl of this combined space, with indices i, j, k, l chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariantsmore »« less
https://doi.org/10.1007/jhep02(2023)063

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Title: Low-energy effective field theory below the electroweak scale: anomalous dimensions

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Weak decays beyond leading logarithms journal, October 1996

Neutrinoless quadruple beta decay journal, August 2013

Reduced effective lagrangians journal, January 1995

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

Spin-dependent μ→e conversion journal, August 2017

The universal one-loop effective action journal, March 2016

The complete HEFT Lagrangian after the LHC Run I journal, July 2016

Naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions journal, November 2013

DsixTools: the standard model effective field theory toolkit journal, June 2017

The Chiral Approach to the Electroweak Interactions journal, November 1993

On the renormalization of the electroweak chiral Lagrangian with a Higgs journal, March 2015

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

Complete electroweak chiral Lagrangian with a light Higgs at NLO journal, March 2014

Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays journal, September 2017

Power corrections at short distances journal, January 1980

Non-standard charged current interactions: beta decays versus the LHC journal, February 2013

Semileptonic B -physics anomalies: A general EFT analysis within U ( 2 ) n flavor symmetry journal, July 2017

Nonrenormalization Theorems without Supersymmetry journal, August 2015

B physics beyond the Standard Model at one loop: complete renormalization group evolution below the electroweak scale journal, September 2017

The SMEFTsim package, theory and tools journal, December 2017

On-shell effective field theory journal, September 1991

The effective chiral Lagrangian for a light dynamical “Higgs particle” journal, May 2013

Three-loop matching of the dipole operators for b→sγ and b→sg journal, April 2004

Compilation of low-energy constraints on 4-fermion operators in the SMEFT journal, August 2017

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

How to use the Standard Model effective field theory journal, January 2016

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

Dimension-5 C P -odd operators: QCD mixing and renormalization journal, December 2015

$$\mu \rightarrow e \gamma $$ μ → e γ and matching at $$\varvec{m_W}$$ m W journal, July 2016

Integrating out heavy particles with functional methods: a simplified framework journal, September 2016

Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence journal, January 2014

Analysis of general power counting rules in effective field theory journal, September 2016

Chiral quarks and the non-relativistic quark model journal, March 1984

Derivative Expansion of the Effective Action journal, November 1985

One loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson journal, October 2015

The effective one-loop scalar lagrangian with derivative couplings journal, May 1986

Higgs-Higgs bound state due to new physics at a TeV journal, October 2007

Renormalization group evolution of dimension-six baryon number violating operators journal, June 2014

A geometric formulation of Higgs Effective Field Theory: Measuring the curvature of scalar field space journal, March 2016

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

Renormalisation-group improved analysis of μ → e processes in a systematic effective-field-theory approach journal, May 2017

QCD heavy-quark potential to order v 2 : One loop matching conditions journal, September 2000

NNLO QCD counterterm contributions to B ¯ → X s γ for the physical value of m c journal, July 2017

The background field method beyond one loop journal, July 1981

Semileptonic B-physics anomalies: A general EFT analysis within U(2)n flavor symmetry text, January 2017

DsixTools: the standard model effective field theory toolkit text, January 2017

B physics beyond the Standard Model at one loop: complete renormalization group evolution below the electroweak scale text, January 2017

Semileptonic B -physics anomalies: A general EFT analysis within U(2)n flavor symmetry text, January 2017

A Higgs-Higgs bound state due to New Physics at a TeV text, January 2007

The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle" text, January 2012

Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions text, January 2013

Renormalization group evolution of dimension-six baryon number violating operators text, January 2014

On the renormalization of the electroweak chiral Lagrangian with a Higgs text, January 2014

How to use the Standard Model effective field theory preprint, January 2014

Non-renormalization Theorems without Supersymmetry text, January 2015

One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs text, January 2015

A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space text, January 2015

The Universal One-Loop Effective Action text, January 2015

Analysis of General Power Counting Rules in Effective Field Theory text, January 2016

The complete HEFT Lagrangian after the LHC Run I text, January 2016

Integrating out heavy particles with functional methods: a simplified framework text, January 2016

Compilation of low-energy constraints on 4-fermion operators in the SMEFT text, January 2017

The SMEFTsim package, theory and tools text, January 2017

The Chiral Approach to the Electroweak Interactions text, January 1993

Weak Decays Beyond Leading Logarithms text, January 1995

Dimension-Six Terms in the Standard Model Lagrangian text, January 2010

CP violation in η muonic decays journal, January 2019

The phenomenology of electric dipole moments in models of scalar leptoquarks journal, January 2019

Field redefinitions in effective theories at higher orders journal, March 2019

The CKM parameters in the SMEFT journal, May 2019

Updated global SMEFT fit to Higgs, diboson and electroweak data journal, June 2018

Global fit to b → cτν transitions journal, September 2019

Consistency of the standard model effective field theory journal, December 2019

Revisiting the new-physics interpretation of the b → cτν data journal, December 2019

Higgs phenomenology as a probe of sterile neutrinos journal, December 2019

Low- and high-energy phenomenology of a doubly charged scalar journal, February 2019

Weak decays beyond leading logarithms
journal, October 1996

Neutrinoless quadruple beta decay
journal, August 2013

Reduced effective lagrangians
journal, January 1995

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

Spin-dependent μ→e conversion
journal, August 2017

The universal one-loop effective action
journal, March 2016

The complete HEFT Lagrangian after the LHC Run I
journal, July 2016

Naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions
journal, November 2013

DsixTools: the standard model effective field theory toolkit
journal, June 2017

The Chiral Approach to the Electroweak Interactions
journal, November 1993

On the renormalization of the electroweak chiral Lagrangian with a Higgs
journal, March 2015

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

Complete electroweak chiral Lagrangian with a light Higgs at NLO
journal, March 2014

Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays
journal, September 2017

Power corrections at short distances
journal, January 1980

Non-standard charged current interactions: beta decays versus the LHC
journal, February 2013

Semileptonic $B$ -physics anomalies: A general EFT analysis within $U (2)^{n}$ flavor symmetry
journal, July 2017

Nonrenormalization Theorems without Supersymmetry
journal, August 2015

B physics beyond the Standard Model at one loop: complete renormalization group evolution below the electroweak scale
journal, September 2017

The SMEFTsim package, theory and tools
journal, December 2017

On-shell effective field theory
journal, September 1991

The effective chiral Lagrangian for a light dynamical “Higgs particle”
journal, May 2013

Three-loop matching of the dipole operators for b→sγ and b→sg
journal, April 2004

Compilation of low-energy constraints on 4-fermion operators in the SMEFT
journal, August 2017

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

How to use the Standard Model effective field theory
journal, January 2016

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

Dimension-5 $C P$ -odd operators: QCD mixing and renormalization
journal, December 2015

$$\mu \rightarrow e \gamma $$ μ → e γ and matching at $$\varvec{m_W}$$ m W
journal, July 2016

Integrating out heavy particles with functional methods: a simplified framework
journal, September 2016

Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence
journal, January 2014

Analysis of general power counting rules in effective field theory
journal, September 2016

Chiral quarks and the non-relativistic quark model
journal, March 1984

Derivative Expansion of the Effective Action
journal, November 1985

One loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson
journal, October 2015

The effective one-loop scalar lagrangian with derivative couplings
journal, May 1986

Higgs-Higgs bound state due to new physics at a TeV
journal, October 2007

Renormalization group evolution of dimension-six baryon number violating operators
journal, June 2014

A geometric formulation of Higgs Effective Field Theory: Measuring the curvature of scalar field space
journal, March 2016

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

Renormalisation-group improved analysis of μ → e processes in a systematic effective-field-theory approach
journal, May 2017

QCD heavy-quark potential to order $v^{2} :$ One loop matching conditions
journal, September 2000

NNLO QCD counterterm contributions to $\bar{B} \to X_{s} γ$ for the physical value of m c
journal, July 2017

The background field method beyond one loop
journal, July 1981

Semileptonic B-physics anomalies: A general EFT analysis within U(2)n flavor symmetry
text, January 2017

DsixTools: the standard model effective field theory toolkit
text, January 2017

B physics beyond the Standard Model at one loop: complete renormalization group evolution below the electroweak scale
text, January 2017

Semileptonic B -physics anomalies: A general EFT analysis within U(2)n flavor symmetry
text, January 2017

A Higgs-Higgs bound state due to New Physics at a TeV
text, January 2007

The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"
text, January 2012

Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
text, January 2013

Renormalization group evolution of dimension-six baryon number violating operators
text, January 2014

On the renormalization of the electroweak chiral Lagrangian with a Higgs
text, January 2014

How to use the Standard Model effective field theory
preprint, January 2014

Non-renormalization Theorems without Supersymmetry
text, January 2015

One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs
text, January 2015

A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space
text, January 2015

The Universal One-Loop Effective Action
text, January 2015

Analysis of General Power Counting Rules in Effective Field Theory
text, January 2016

The complete HEFT Lagrangian after the LHC Run I
text, January 2016

Integrating out heavy particles with functional methods: a simplified framework
text, January 2016

Compilation of low-energy constraints on 4-fermion operators in the SMEFT
text, January 2017

The SMEFTsim package, theory and tools
text, January 2017

The Chiral Approach to the Electroweak Interactions
text, January 1993

Weak Decays Beyond Leading Logarithms
text, January 1995

Dimension-Six Terms in the Standard Model Lagrangian
text, January 2010

CP violation in η muonic decays
journal, January 2019

The phenomenology of electric dipole moments in models of scalar leptoquarks
journal, January 2019

Field redefinitions in effective theories at higher orders
journal, March 2019

The CKM parameters in the SMEFT
journal, May 2019

Updated global SMEFT fit to Higgs, diboson and electroweak data
journal, June 2018

Global fit to b → cτν transitions
journal, September 2019

Consistency of the standard model effective field theory
journal, December 2019

Revisiting the new-physics interpretation of the b → cτν data
journal, December 2019

Higgs phenomenology as a probe of sterile neutrinos
journal, December 2019

Low- and high-energy phenomenology of a doubly charged scalar
journal, February 2019

: a Python package for the running and matching of Wilson coefficients above and below the electroweak scale
journal, December 2018

$${b\rightarrow c\tau \nu }$$ b → c τ ν transitions in the standard model effective field theory
journal, March 2019

A global likelihood for precision constraints and flavour anomalies
journal, June 2019

EFT approach to the electron electric dipole moment at the two-loop level
text, January 2019