Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Kälin, Gregor; Mogull, Gustav; Ochirov, Alexander; Verbeek, Bram

doi:10.1007/jhep01(2020)068

Title: Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Abstract

Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon N = 2 supersymmetric QCD amplitude, with Nf massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where N_f = 2N_c for gauge group SU(N_c). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 - D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.

Authors:

Kälin, Gregor ^[1];

^[2]; Ochirov, Alexander ^[3]; Verbeek, Bram ^[2]

Uppsala Univ. (Sweden); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Uppsala Univ. (Sweden)
ETH Zurich (Switzerland)

Publication Date:: 2020-01-13

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

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

OSTI Identifier:: 1605201

Report Number(s):: SLAC-PUB-17488
Journal ID: ISSN 1029-8479; TRN: US2104393

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: 2020; 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

Citation Formats


                    Kälin, Gregor, Mogull, Gustav, Ochirov, Alexander, and Verbeek, Bram. Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes.  United States: N. p., 2020. 
Web.  doi:10.1007/jhep01(2020)068.

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                    Kälin, Gregor, Mogull, Gustav, Ochirov, Alexander, & Verbeek, Bram. Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes.  United States.  https://doi.org/10.1007/jhep01(2020)068

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                    Kälin, Gregor, Mogull, Gustav, Ochirov, Alexander, and Verbeek, Bram. Mon .  
"Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes".  United States.  https://doi.org/10.1007/jhep01(2020)068.  https://www.osti.gov/servlets/purl/1605201.

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@article{osti_1605201,

  title        = {Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes},

  author       = {Kälin, Gregor and Mogull, Gustav and Ochirov, Alexander and Verbeek, Bram},

  abstractNote = {Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon N = 2 supersymmetric QCD amplitude, with Nf massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where Nf = 2Nc for gauge group SU(Nc). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 - D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.},

  doi          = {10.1007/jhep01(2020)068},

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

  number       = 1,

  volume       = 2020,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

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Works referenced in this record:

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Title: Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Abstract

Citation Formats

Nielsen’s Generalized Polylogarithms journal, September 1986

Non-planar integrands for two-loop QCD amplitudes conference, October 2016

Breakdown of unitarity in the dimensional reduction scheme journal, January 1985

Multi-loop amplitudes and resummation journal, January 2003

Gluon scattering in N=4 Super-Yang-Mills theory: from weak to strong coupling conference, April 2008

Two-Loop Six Gluon All-Plus Helicity Amplitude journal, August 2016

4D Conformal Field Theories and Strings on Orbifolds journal, June 1998

Supersymmetry and non-perturbative beta functions journal, May 1988

Long-distance singularities in multi-leg scattering amplitudes conference, October 2016

Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD conference, October 2018

Recent progress on infrared singularities conference, July 2018

Supersymmetric dimensional regularization via dimensional reduction journal, June 1979

Multiple polylogarithms, cyclotomy and modular complexes journal, January 1998

A theorem on analytical calculability of 4-loop renormalization group functions journal, March 1981

Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD text, January 2018

Gluon scattering in N=4 super-Yang-Mills theory from weak to strong coupling text, January 2008

Long-distance singularities in multi-leg scattering amplitudes preprint, January 2016

4d Conformal Field Theories and Strings on Orbifolds text, January 1998

Nielsen’s Generalized Polylogarithms
journal, September 1986

Non-planar integrands for two-loop QCD amplitudes
conference, October 2016

Breakdown of unitarity in the dimensional reduction scheme
journal, January 1985

Multi-loop amplitudes and resummation
journal, January 2003

Gluon scattering in N=4 Super-Yang-Mills theory: from weak to strong coupling
conference, April 2008

Two-Loop Six Gluon All-Plus Helicity Amplitude
journal, August 2016

4D Conformal Field Theories and Strings on Orbifolds
journal, June 1998

Supersymmetry and non-perturbative beta functions
journal, May 1988

Long-distance singularities in multi-leg scattering amplitudes
conference, October 2016

Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD
conference, October 2018

Recent progress on infrared singularities
conference, July 2018

Supersymmetric dimensional regularization via dimensional reduction
journal, June 1979

Multiple polylogarithms, cyclotomy and modular complexes
journal, January 1998

A theorem on analytical calculability of 4-loop renormalization group functions
journal, March 1981

Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD
text, January 2018

Gluon scattering in N=4 super-Yang-Mills theory from weak to strong coupling
text, January 2008

Long-distance singularities in multi-leg scattering amplitudes
preprint, January 2016

4d Conformal Field Theories and Strings on Orbifolds
text, January 1998