Geometry of the scalar sector

Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.

doi:10.1007/JHEP08(2016)101

Title: Geometry of the scalar sector

Abstract

The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold M is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved M, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only ifMhas a SU(2)_L U(1)_Y invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of M such as sectional curvatures, which are of order 1/Λ² , where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general G → H symmetry breaking pattern. The one-loopmore »« less

Authors:

Alonso, Rodrigo ^[1]; Jenkins, Elizabeth E. ^[2]; Manohar, Aneesh V. ^[2]

University of California, San Diego, La Jolla, CA (United States). Department of Physics
University of California, San Diego, La Jolla, CA (United States). Department of Physics; CERN TH Division, Geneva (Switzerland)

Publication Date:: Wed Aug 17 00:00:00 EDT 2016

Research Org.:: University of California, San Diego, La Jolla, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1434582

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: 2016; Journal Issue: 8; 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; Gauge Symmetry; Sigma Models

Citation Formats


                    Alonso, Rodrigo, Jenkins, Elizabeth E., and Manohar, Aneesh V. Geometry of the scalar sector.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP08(2016)101.

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                    Alonso, Rodrigo, Jenkins, Elizabeth E., & Manohar, Aneesh V. Geometry of the scalar sector.  United States.  https://doi.org/10.1007/JHEP08(2016)101

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                    Alonso, Rodrigo, Jenkins, Elizabeth E., and Manohar, Aneesh V. Wed .  
"Geometry of the scalar sector".  United States.  https://doi.org/10.1007/JHEP08(2016)101.  https://www.osti.gov/servlets/purl/1434582.

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@article{osti_1434582,

  title        = {Geometry of the scalar sector},

  author       = {Alonso, Rodrigo and Jenkins, Elizabeth E. and Manohar, Aneesh V.},

  abstractNote = {The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold M is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved M, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only ifMhas a SU(2)L U(1)Y invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of M such as sectional curvatures, which are of order 1/Λ2 , where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general G → H symmetry breaking pattern. The one-loop radiative correction in HEFT is determined using a covariant expansion which preserves manifest invariance of M under coordinate redefinitions. The formula for the radiative correction is simple when written in terms of the curvature of M and the gauge curvature field strengths. We also extend the CCWZ formalism to non-compact groups, and generalize the HEFT curvature computation to the case of multiple singlet scalar fields.},

  doi          = {10.1007/JHEP08(2016)101},

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

  number       = 8,

  volume       = 2016,

  place        = {United States},

  year         = {Wed Aug 17 00:00:00 EDT 2016},

  month        = {Wed Aug 17 00:00:00 EDT 2016}

}

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Works referencing / citing this record:

Field redefinitions in effective theories at higher orders
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Criado, J. C.; Pérez-Victoria, M.
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Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity
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Title: Geometry of the scalar sector

Abstract

Citation Formats

Structure of Phenomenological Lagrangians. II journal, January 1969

The universal one-loop effective action journal, March 2016

The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model journal, June 1981

An algorithm for the poles at dimension four in the dimensional regularization procedure journal, October 1973

The Chiral Approach to the Electroweak Interactions journal, November 1993

Symmetric space scalar field theory journal, February 1982

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

Born helicity amplitudes and cross-sections in non-Abelian gauge theories journal, November 1976

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

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Higgs ultraviolet softening journal, December 2014

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The minimal composite Higgs model journal, July 2005

Geometrical structure and ultraviolet finiteness in the supersymmetric ?-model journal, September 1981

Chiral multi-loops journal, January 1972

SU(2) × U(1) breaking by vacuum misalignment journal, March 1984

Heat kernel expansion: user's manual journal, December 2003

Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs journal, June 2014

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

Derivation of gauge invariance from high-energy unitarity bounds on the S matrix journal, August 1974

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

Structure of Phenomenological Lagrangians. I journal, January 1969

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Sigma decomposition: the CP-odd Lagrangian journal, April 2016

Realization of Chiral Symmetry in a Curved Isospin Space journal, April 1969

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

Low-energy impact of a heavy Higgs boson sector journal, September 1981

CP violation with a dynamical Higgs journal, October 2014

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

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Anatomy of a composite Higgs model journal, January 1985

Application of invariant renormalization to the non-linear chiral invariant pion Lagrangian in the one-loop approximation journal, December 1971

Left-handed neutrino mass scale and spontaneously broken lepton number journal, March 1981

Nonlinear models in 2 + ε dimensions journal, September 1985

On Kaluza-Klein theory journal, July 1982

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

Invariant Affine Connections on Homogeneous Spaces journal, January 1954

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

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

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

Phenomenological Lagrangians journal, April 1979

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

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

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Gravitation, gauge theories and differential geometry journal, December 1980

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

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Structure of Phenomenological Lagrangians. II
journal, January 1969

The universal one-loop effective action
journal, March 2016

The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model
journal, June 1981

An algorithm for the poles at dimension four in the dimensional regularization procedure
journal, October 1973

The Chiral Approach to the Electroweak Interactions
journal, November 1993

Symmetric space scalar field theory
journal, February 1982

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

Born helicity amplitudes and cross-sections in non-Abelian gauge theories
journal, November 1976

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

Disentangling a dynamical Higgs
journal, March 2014

Higgs ultraviolet softening
journal, December 2014

Sigma models with negative curvature
journal, May 2016

The minimal composite Higgs model
journal, July 2005

Geometrical structure and ultraviolet finiteness in the supersymmetric ?-model
journal, September 1981

Chiral multi-loops
journal, January 1972

SU(2) × U(1) breaking by vacuum misalignment
journal, March 1984

Heat kernel expansion: user's manual
journal, December 2003

Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs
journal, June 2014

Chiral perturbation theory to one loop
journal, November 1984

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

Derivation of gauge invariance from high-energy unitarity bounds on the $S$ matrix
journal, August 1974

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

Structure of Phenomenological Lagrangians. I
journal, January 1969

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

Sigma decomposition: the CP-odd Lagrangian
journal, April 2016

Realization of Chiral Symmetry in a Curved Isospin Space
journal, April 1969

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

Low-energy impact of a heavy Higgs boson sector
journal, September 1981

CP violation with a dynamical Higgs
journal, October 2014

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

Anatomy of a composite Higgs model
journal, January 1985

Application of invariant renormalization to the non-linear chiral invariant pion Lagrangian in the one-loop approximation
journal, December 1971

Left-handed neutrino mass scale and spontaneously broken lepton number
journal, March 1981

Nonlinear models in 2 + ε dimensions
journal, September 1985

On Kaluza-Klein theory
journal, July 1982

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

Invariant Affine Connections on Homogeneous Spaces
journal, January 1954

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

Derivative Expansion for the One-Loop Effective Actions with Internal Symmetry
journal, September 1986

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

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

Phenomenological Lagrangians
journal, April 1979

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

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

Effective-Action Expansion in Perturbation Theory
journal, March 1985

Sigma decomposition
journal, December 2014

Gravitation, gauge theories and differential geometry
journal, December 1980

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

Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity
journal, October 2019

Ward identities for the standard model effective field theory
journal, January 2020

Distinguishing a Higgs-like dilaton scenario with a complete bosonic effective field theory basis
journal, October 2017

Renormalization group evolution of Higgs effective field theory
journal, February 2018

Baryon non-invariant couplings in Higgs effective field theory
journal, March 2017

ALPs effective field theory and collider signatures
journal, August 2017

The minimal axion minimal linear $$\sigma $$σ model
journal, May 2018

Baryon Non-Invariant Couplings in Higgs Effective Field Theory
text, January 2016

Distinguishing A Higgs-Like Dilaton Scenario With A Complete Bosonic Effective Field Theory Basis
text, January 2017

Renormalization group evolution of Higgs effective field theory
text, January 2017

Field redefinitions in effective theories at higher orders
text, January 2018

Ward Identities for the Standard Model Effective Field Theory
text, January 2019