The principle of maximal transcendentality and the four-loop collinear anomalous dimension

Dixon, Lance J.

doi:10.1007/jhep01(2018)075

Title: The principle of maximal transcendentality and the four-loop collinear anomalous dimension

Abstract

Here, we use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar N = 4 super-Yang-Mills theory from recent QCD results, obtaining $$\hat{g}$$$$(4)\atop{0}$$ =$$-$$300ζ₇$$-$$256ζ₂ζ₅$$-$$384ζ₃ζ₄. This value agrees with a previous numerical result to within 0.2%. It also provides the Regge trajectory, threshold soft anomalous dimension and rapidity anomalous dimension through four loops.

Authors:

^[1]

SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States)

Publication Date:: 2018-01-16

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE; Munich Institute for Astro-and Particle Physics (MIAPP)

OSTI Identifier:: 1419976

Grant/Contract Number:: AC02-76SF00515

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; Scattering Amplitudes; Supersymmetric Gauge Theory; 1/N Expansion; Theoretical Physics

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                    Dixon, Lance J. The principle of maximal transcendentality and the four-loop collinear anomalous dimension.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep01(2018)075.

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                    Dixon, Lance J. The principle of maximal transcendentality and the four-loop collinear anomalous dimension.  United States.  https://doi.org/10.1007/jhep01(2018)075

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                    Dixon, Lance J. Tue .  
"The principle of maximal transcendentality and the four-loop collinear anomalous dimension".  United States.  https://doi.org/10.1007/jhep01(2018)075.  https://www.osti.gov/servlets/purl/1419976.

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@article{osti_1419976,

  title        = {The principle of maximal transcendentality and the four-loop collinear anomalous dimension},

  author       = {Dixon, Lance J.},

  abstractNote = {Here, we use the principle of maximal transcendentality and the universal nature of subleading infrared poles to extract the analytic value of the four-loop collinear anomalous dimension in planar N = 4 super-Yang-Mills theory from recent QCD results, obtaining $\hat{g}$$(4)\atop{0}$ =$-$300ζ7$-$256ζ2ζ5$-$384ζ3ζ4. This value agrees with a previous numerical result to within 0.2%. It also provides the Regge trajectory, threshold soft anomalous dimension and rapidity anomalous dimension through four loops.},

  doi          = {10.1007/jhep01(2018)075},

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

  number       = 1,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {1}

}

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The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

Journal Article Bern, Zvi ; Czakon, Michael ; Dixon, Lance J ; ... - Physical Review D

We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allowsmore »« less
Full Text Available
Four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory

Journal Article Bern, Zvi ; Czakon, Michael ; Dixon, Lance J ; ... - Physical Review. D, Particles Fields

We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon}=0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/{epsilon}{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test amore »« less
https://doi.org/10.1103/PHYSREVD.75.085010
Hexagon functions and the three-loop remainder function

Journal Article Dixon, Lance J. ; Drummond, James M. ; von Hippel, Matt ; ... - Journal of High Energy Physics (Online)

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function ismore »« less
https://doi.org/10.1007/JHEP12(2013)049

Full Text Available
The property of maximal transcendentality: Calculation of anomalous dimensions in the N = 4 SYM and master integrals

Journal Article Kotikov, A. V. - Physics of Particles and Nuclei

We review results for the universal anomalous dimension γ{sub uni}(j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory having the property of maximal transcendentality. It is shown that the similar property is ibserved in the results for master integrals.
https://doi.org/10.1134/S1063779613020196

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Title: The principle of maximal transcendentality and the four-loop collinear anomalous dimension

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Citation Formats

Four-loop non-singlet splitting functions in the planar limit and beyond text, January 2017

Supersymmetry, supergravity theories and the dual spinor model journal, April 1977

Conformal properties of four-gluon planar amplitudes and Wilson loops journal, May 2008

Hexagon functions and the three-loop remainder function journal, December 2013

Two-loop corrections to Higgs boson production journal, January 2005

On planar gluon amplitudes/Wilson loops duality journal, May 2008

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations journal, December 2016

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

Dynamical threshold enhancement and resummation in Drell-Yan production journal, July 2008

Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang–Mills model journal, August 2004

MHV amplitudes in super-Yang–Mills and Wilson Loops journal, May 2008

Anomalous dimensions of Wilson operators in N=4 SYM theory journal, March 2003

Correspondence between Soft and Rapidity Anomalous Dimensions journal, February 2017

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

Threshold resummation for dijet cross sections journal, August 1998

The Bethe-ansatz for Script N = 4 super Yang-Mills journal, March 2003

Review of AdS/CFT Integrability: An Overview journal, October 2011

Two-loop SL(2) form factors and maximal transcendentality journal, December 2016

Evolution of color exchange in QCD hard scattering journal, October 1998

Gluon scattering amplitudes at strong coupling journal, June 2007

Regge behavior of gluon scattering amplitudes in SYM theory journal, May 2008

Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD journal, March 2017

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, March 2010

Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy journal, May 2008

Simple loop integrals and amplitudes in $ \mathcal{N} = 4 $ SYM journal, May 2011

Bootstrapping the three-loop hexagon journal, November 2011

Spacetime and Flux Tube S -Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory journal, August 2013

The five-loop beta function of Yang-Mills theory with fermions journal, February 2017

Exponentiation of eikonal cross sections in nonabelian gauge theories journal, December 1983

Infrared factorization, Wilson lines and the heavy quark limit journal, April 1992

Scattering into the fifth dimension of $$ \mathcal{N} $$ = 4 super Yang-Mills journal, January 2010

Form factors and scattering amplitudes in $ \mathcal{N} = 4 $ SYM in dimensional and massive regularizations journal, December 2011

Higgs-regularized three-loop four-gluon amplitude in $ \mathcal{N} = 4 $ SYM: exponentiation and Regge limits journal, April 2010

More loops and legs in Higgs-regulated $$ \mathcal{N} = 4 $$ SYM amplitudes journal, August 2010

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM journal, May 2010

Supersymmetric Yang-Mills theories journal, March 1977

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes journal, February 2010

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

Harmonic Polylogarithms journal, February 2000

Three-loop results for quark and gluon form factors journal, October 2005

DGLAP and BFKL equations in the N=4 supersymmetric gauge theory journal, June 2003

Dual-conformal regularization of infrared loop divergences and the chiral box expansion journal, January 2015

Beyond cusp anomalous dimension from integrability journal, May 2009

Multi-loop amplitudes and resummation journal, January 2003

Analytic two-loop form factors in $ \mathcal{N} = 4 $ SYM journal, May 2012

Classical Polylogarithms for Amplitudes and Wilson Loops journal, October 2010

A planar four-loop form factor and cusp anomalous dimension in QCD journal, May 2016

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory journal, May 2012

Quantum Spectral Curve for Planar N = 4 Super-Yang-Mills Theory journal, January 2014

The quark form factor at higher orders journal, August 2005

Non-abelian eikonal exponentiation journal, November 1984

Four-loop non-singlet splitting functions in the planar limit and beyond journal, October 2017

Double logarithmic asymptotics in QCD journal, January 1989

Hexagon Wilson loop = six-gluon MHV amplitude journal, July 2009

Calculation of the quark and gluon form factors to three loops in QCD journal, June 2010

One-loop corrections to five-gluon amplitudes journal, May 1993

The three-loop splitting functions in QCD: the non-singlet case journal, June 2004

Universal structure of subleading infrared poles in gauge theory amplitudes journal, August 2008

On-shell methods for the two-loop dilatation operator and finite remainders journal, October 2015

Renormalization of the Wilson loops beyond the leading order journal, January 1987

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory journal, June 2014

The dilatation operator of conformal super-Yang–Mills theory journal, August 2003

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation journal, January 2017

Dressing and wrapping journal, October 2007

Calculation of the quark and gluon form factors to three loops in QCD text, January 2010

A planar four-loop form factor and cusp anomalous dimension in QCD text, January 2016

Correspondence between Soft and Rapidity Anomalous Dimensions text, January 2017

Dynamical Threshold Enhancement and Resummation in Drell-Yan Production text, January 2007

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes text, January 2007

Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy text, January 2008

Hexagon Wilson loop = six-gluon MHV amplitude text, January 2008

Universal structure of subleading infrared poles in gauge theory amplitudes text, January 2008

Beyond cusp anomalous dimension from integrability text, January 2009

Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits text, January 2010

Classical Polylogarithms for Amplitudes and Wilson Loops text, January 2010

Review of AdS/CFT Integrability: An Overview text, January 2010

Bootstrapping the three-loop hexagon text, January 2011

Four-loop non-singlet splitting functions in the planar limit and beyond
text, January 2017

Supersymmetry, supergravity theories and the dual spinor model
journal, April 1977

Conformal properties of four-gluon planar amplitudes and Wilson loops
journal, May 2008

Hexagon functions and the three-loop remainder function
journal, December 2013

Two-loop corrections to Higgs boson production
journal, January 2005

On planar gluon amplitudes/Wilson loops duality
journal, May 2008

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
journal, December 2016

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

Dynamical threshold enhancement and resummation in Drell-Yan production
journal, July 2008

Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang–Mills model
journal, August 2004

MHV amplitudes in super-Yang–Mills and Wilson Loops
journal, May 2008

Anomalous dimensions of Wilson operators in N=4 SYM theory
journal, March 2003

Correspondence between Soft and Rapidity Anomalous Dimensions
journal, February 2017

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

Threshold resummation for dijet cross sections
journal, August 1998

The Bethe-ansatz for Script N = 4 super Yang-Mills
journal, March 2003

Review of AdS/CFT Integrability: An Overview
journal, October 2011

Two-loop SL(2) form factors and maximal transcendentality
journal, December 2016

Evolution of color exchange in QCD hard scattering
journal, October 1998

Gluon scattering amplitudes at strong coupling
journal, June 2007

Regge behavior of gluon scattering amplitudes in SYM theory
journal, May 2008

Four-loop photon quark form factor and cusp anomalous dimension in the large-N c limit of QCD
journal, March 2017

An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, March 2010

Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
journal, May 2008

Simple loop integrals and amplitudes in $ \mathcal{N} = 4 $ SYM
journal, May 2011

Bootstrapping the three-loop hexagon
journal, November 2011

Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory
journal, August 2013

The five-loop beta function of Yang-Mills theory with fermions
journal, February 2017

Exponentiation of eikonal cross sections in nonabelian gauge theories
journal, December 1983

Infrared factorization, Wilson lines and the heavy quark limit
journal, April 1992

Scattering into the fifth dimension of $$ \mathcal{N} $$ = 4 super Yang-Mills
journal, January 2010

Form factors and scattering amplitudes in $ \mathcal{N} = 4 $ SYM in dimensional and massive regularizations
journal, December 2011

Higgs-regularized three-loop four-gluon amplitude in $ \mathcal{N} = 4 $ SYM: exponentiation and Regge limits
journal, April 2010

More loops and legs in Higgs-regulated $$ \mathcal{N} = 4 $$ SYM amplitudes
journal, August 2010

The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM
journal, May 2010

Supersymmetric Yang-Mills theories
journal, March 1977

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
journal, February 2010

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

Harmonic Polylogarithms
journal, February 2000

Three-loop results for quark and gluon form factors
journal, October 2005

DGLAP and BFKL equations in the N=4 supersymmetric gauge theory
journal, June 2003

Dual-conformal regularization of infrared loop divergences and the chiral box expansion
journal, January 2015

Beyond cusp anomalous dimension from integrability
journal, May 2009

Multi-loop amplitudes and resummation
journal, January 2003

Analytic two-loop form factors in $ \mathcal{N} = 4 $ SYM
journal, May 2012

Classical Polylogarithms for Amplitudes and Wilson Loops
journal, October 2010

A planar four-loop form factor and cusp anomalous dimension in QCD
journal, May 2016

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory
journal, May 2012

Quantum Spectral Curve for Planar $N = 4$ Super-Yang-Mills Theory
journal, January 2014

The quark form factor at higher orders
journal, August 2005

Non-abelian eikonal exponentiation
journal, November 1984

Four-loop non-singlet splitting functions in the planar limit and beyond
journal, October 2017

Double logarithmic asymptotics in QCD
journal, January 1989

Hexagon Wilson loop = six-gluon MHV amplitude
journal, July 2009

Calculation of the quark and gluon form factors to three loops in QCD
journal, June 2010

One-loop corrections to five-gluon amplitudes
journal, May 1993

The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004

Universal structure of subleading infrared poles in gauge theory amplitudes
journal, August 2008

On-shell methods for the two-loop dilatation operator and finite remainders
journal, October 2015

Renormalization of the Wilson loops beyond the leading order
journal, January 1987

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory
journal, June 2014

The dilatation operator of conformal super-Yang–Mills theory
journal, August 2003

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation
journal, January 2017

Dressing and wrapping
journal, October 2007

Calculation of the quark and gluon form factors to three loops in QCD
text, January 2010

A planar four-loop form factor and cusp anomalous dimension in QCD
text, January 2016

Correspondence between Soft and Rapidity Anomalous Dimensions
text, January 2017

Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
text, January 2007

Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
text, January 2007

Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
text, January 2008

Hexagon Wilson loop = six-gluon MHV amplitude
text, January 2008

Universal structure of subleading infrared poles in gauge theory amplitudes
text, January 2008

Beyond cusp anomalous dimension from integrability
text, January 2009

Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
text, January 2010

Classical Polylogarithms for Amplitudes and Wilson Loops
text, January 2010

Review of AdS/CFT Integrability: An Overview
text, January 2010

Bootstrapping the three-loop hexagon
text, January 2011

Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
text, January 2011

A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
text, January 2012

The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
text, January 2014