Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs

doi:10.1007/JHEP11(2017)198

Title: Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs

Abstract

Here, we evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus exponential series to determine a canonical set of integrals, finally expressed as a Taylor series around four space-time dimensions, with coefficients written as combination of generalized poly-logarithms. The electron is treated as massless, while we retain full dependence on the muon mass. The considered integrals are also relevant for crossing-related processes, such as di-muon production at e⁺e^–-colliders, as well as for the QCD corrections to top-pair production at hadron colliders.

Authors:

Mastrolia, Pierpaolo ^[1]; Passera, Massimo ^[2]; Primo, Amedeo ^[1]; Schubert, Ulrich ^[3]

Univ. di Padova, Padova (Italy); INFN - Sezione di Padova, Padova (Italy)
INFN - Sezione di Padova, Padova (Italy)
Argonne National Lab. (ANL), Argonne, IL (United States)

Publication Date:: 2017-11-29

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: National Science Foundation (NSF); Perimeter Institute for Theoretical Physics; USDOE

OSTI Identifier:: 1494708

Grant/Contract Number:: AC02-06CH11357

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: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; NLO Computations

Citation Formats


                    Mastrolia, Pierpaolo, Passera, Massimo, Primo, Amedeo, and Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs.  United States: N. p., 2017. 
        Web.  doi:10.1007/JHEP11(2017)198.

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                    Mastrolia, Pierpaolo, Passera, Massimo, Primo, Amedeo, & Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs.  United States.  doi:10.1007/JHEP11(2017)198.

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                    Mastrolia, Pierpaolo, Passera, Massimo, Primo, Amedeo, and Schubert, Ulrich. Wed .  
        "Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs".  United States.  doi:10.1007/JHEP11(2017)198.  https://www.osti.gov/servlets/purl/1494708.

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@article{osti_1494708,

  title        = {Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs},

  author       = {Mastrolia, Pierpaolo and Passera, Massimo and Primo, Amedeo and Schubert, Ulrich},

  abstractNote = {Here, we evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus exponential series to determine a canonical set of integrals, finally expressed as a Taylor series around four space-time dimensions, with coefficients written as combination of generalized poly-logarithms. The electron is treated as massless, while we retain full dependence on the muon mass. The considered integrals are also relevant for crossing-related processes, such as di-muon production at e+e–-colliders, as well as for the QCD corrections to top-pair production at hadron colliders.},

  doi          = {10.1007/JHEP11(2017)198},

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

  number       = 11,

  volume       = 2017,

  place        = {United States},

  year         = {2017},

  month        = {11}

}

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DOI: 10.1007/JHEP11(2017)198

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Cited by: 18 works

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Figure 1: Two-loop four-point topologies for μe scattering.

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Works referenced in this record:

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Title: Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs

Abstract

Citation Formats

Figures / Tables:

Magnus and Dyson Series for Master Integrals conference, August 2014

Measuring the leading hadronic contribution to the muon g-2 via $$\mu e$$ μ e scattering journal, March 2017

Integration by parts: The algorithm to calculate β-functions in 4 loops journal, November 1981

The Production of High-Energy Knock-On Electrons and Bremsstrahlung by μ-Mesons journal, June 1962

On the maximal cut of Feynman integrals and the solution of their differential equations journal, March 2017

Evaluating multiple polylogarithm values at sixth roots of unity up to weight six journal, June 2017

Production of knock-on electrons by cosmic-ray muons underground (148 m w.e.) journal, January 1965

Two-loop QCD corrections to the heavy-to-light quark decay journal, November 2008

Muon-electron scattering cross section to order α3 journal, May 1971

Multiloop Integrals in Dimensional Regularization Made Simple journal, June 2013

Left-right asymmetries in polarized e − μ scattering journal, October 1998

Analytical result for dimensionally regularized massless on-shell double box journal, August 1999

Scattering of 8-GeV μ Mesons on Electrons journal, March 1963

Radiative corrections in polarised electron-muon elastic scattering journal, June 1987

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel journal, January 2011

NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels journal, December 2012

Electromagnetic Interactions of High-Energy Muons journal, April 1965

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes journal, August 2012

Helicity of μ − Mesons from π -Meson Decay journal, April 1961

Scattering of High-Energy Positive and Negative Muons on Electrons journal, September 1969

Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry journal, July 2004

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations journal, December 2000

Percent-Level-Precision Physics at the Tevatron: Next-to-Next-to-Leading Order QCD Corrections to q q ¯ → t t ¯ + X journal, September 2012

Parity violating asymmetries in polarized electron scattering journal, September 1979

Two-loop planar corrections to heavy-quark pair production in the quark-antiquark channel journal, August 2009

Cloud-Chamber Study of Hard Collisions of Cosmic-Ray Muons with Electrons journal, March 1961

Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O ( α S 4 ) journal, June 2013

Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel journal, July 2008

Radiative corrections to muon-electron scattering journal, December 1963

Differential equations method. New technique for massive Feynman diagram calculation journal, January 1991

Two-loop master integrals for jets: the non-planar topologies journal, May 2001

SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop journal, November 2015

Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph journal, August 2017

Magnus and Dyson series for Master Integrals journal, March 2014

Harmonic Polylogarithms journal, February 2000

Numerical evaluation of multiple polylogarithms journal, May 2005

Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral journal, June 2016

Scattering of High-Energy Positive and Negative Muons on Electrons journal, July 1968

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

Non-planar massless two-loop Feynman diagrams with four on-shell legs journal, December 1999

NNLO corrections to inclusive semileptonic B decays in the shape-function region journal, May 2009

Three-loop master integrals for ladder-box diagrams with one massive leg journal, September 2014

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering journal, September 2016

A new approach to evaluate the leading hadronic corrections to the muon g -2 journal, June 2015

A muon polarimeter based on elastic muon-electron scattering conference, January 1989

Radiative corrections to muon-electron scattering journal, March 1961

Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel journal, December 2013

Differential equations for two-loop four-point functions journal, July 2000

Radiative corrections to lepton–lepton scattering revisited journal, October 2010

Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a W pair and to the triple gauge couplings ZW W and γ∗ W W journal, April 2017

Tops from light quarks: Full mass dependence at two-loops in QCD journal, June 2008

NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction journal, January 2013

Numerical evaluation of harmonic polylogarithms journal, November 2001

On a two-loop crossed six-line master integral with two massive lines journal, March 2009

Electron-muon scattering in the electroweak unified theory journal, December 1983

Two-loop QCD correction to differential semi-leptonic decays in the shape-function region journal, April 2009

Massive 3-loop Feynman diagrams reducible to SC $^*$ primitives of algebras of the sixth root of unity journal, April 1999

Evaluating multi-loop Feynman integrals numerically through differential equations journal, March 2019

Elliptic Feynman integrals and pure functions journal, January 2019

Muon-electron scattering at NLO journal, February 2019

Double-Higgs boson production in the high-energy limit: planar master integrals journal, March 2018

Master integrals for the NNLO virtual corrections to μe scattering in QED: the non-planar graphs journal, September 2018

Master integrals for the NNLO virtual corrections to $$ q\overline{q}\to t\overline{t} $$ scattering in QCD: the non-planar graphs journal, June 2019

Hadronic corrections to μ-e scattering at NNLO with space-like data journal, February 2019

Evaluating multi-loop Feynman integrals numerically through differential equations journal, March 2019

Explicit form of the R- ratio of electron–positron annihilation into hadrons journal, October 2019

Muon-Electron Scattering at Next-To-Next-To-Leading Order: The Hadronic Corrections journal, May 2019

Two-loop master integrals for heavy-to-light form factors of two different massive fermions journal, February 2018

Magnus and Dyson Series for Master Integrals
conference, August 2014

Measuring the leading hadronic contribution to the muon g-2 via $$\mu e$$ μ e scattering
journal, March 2017

Integration by parts: The algorithm to calculate β-functions in 4 loops
journal, November 1981

The Production of High-Energy Knock-On Electrons and Bremsstrahlung by μ-Mesons
journal, June 1962

On the maximal cut of Feynman integrals and the solution of their differential equations
journal, March 2017

Evaluating multiple polylogarithm values at sixth roots of unity up to weight six
journal, June 2017

Production of knock-on electrons by cosmic-ray muons underground (148 m w.e.)
journal, January 1965

Two-loop QCD corrections to the heavy-to-light quark decay
journal, November 2008

Muon-electron scattering cross section to order α3
journal, May 1971

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

Left-right asymmetries in polarized $e - μ$ scattering
journal, October 1998

Analytical result for dimensionally regularized massless on-shell double box
journal, August 1999

Scattering of 8-GeV $μ$ Mesons on Electrons
journal, March 1963

Radiative corrections in polarised electron-muon elastic scattering
journal, June 1987

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel
journal, January 2011

NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels
journal, December 2012

Electromagnetic Interactions of High-Energy Muons
journal, April 1965

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
journal, August 2012

Helicity of $μ^{-}$ Mesons from $π$ -Meson Decay
journal, April 1961

Scattering of High-Energy Positive and Negative Muons on Electrons
journal, September 1969

Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry
journal, July 2004

High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations
journal, December 2000

Percent-Level-Precision Physics at the Tevatron: Next-to-Next-to-Leading Order QCD Corrections to $q \bar{q} \to t \bar{t} + X$
journal, September 2012

Parity violating asymmetries in polarized electron scattering
journal, September 1979

Two-loop planar corrections to heavy-quark pair production in the quark-antiquark channel
journal, August 2009

Cloud-Chamber Study of Hard Collisions of Cosmic-Ray Muons with Electrons
journal, March 1961

Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through $O (α_{S}^{4})$
journal, June 2013

Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel
journal, July 2008

Radiative corrections to muon-electron scattering
journal, December 1963

Differential equations method. New technique for massive Feynman diagram calculation
journal, January 1991

Two-loop master integrals for jets: the non-planar topologies
journal, May 2001

SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop
journal, November 2015

Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
journal, August 2017

Magnus and Dyson series for Master Integrals
journal, March 2014

Harmonic Polylogarithms
journal, February 2000

Numerical evaluation of multiple polylogarithms
journal, May 2005

Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
journal, June 2016

Scattering of High-Energy Positive and Negative Muons on Electrons
journal, July 1968

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

Non-planar massless two-loop Feynman diagrams with four on-shell legs
journal, December 1999

NNLO corrections to inclusive semileptonic B decays in the shape-function region
journal, May 2009

Three-loop master integrals for ladder-box diagrams with one massive leg
journal, September 2014

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
journal, September 2016

A new approach to evaluate the leading hadronic corrections to the muon g -2
journal, June 2015

A muon polarimeter based on elastic muon-electron scattering
conference, January 1989

Radiative corrections to muon-electron scattering
journal, March 1961

Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel
journal, December 2013

Differential equations for two-loop four-point functions
journal, July 2000

Radiative corrections to lepton–lepton scattering revisited
journal, October 2010

Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a W pair and to the triple gauge couplings ZW W and γ∗ W W
journal, April 2017

Tops from light quarks: Full mass dependence at two-loops in QCD
journal, June 2008

NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction
journal, January 2013

Numerical evaluation of harmonic polylogarithms
journal, November 2001

On a two-loop crossed six-line master integral with two massive lines
journal, March 2009

Electron-muon scattering in the electroweak unified theory
journal, December 1983

Two-loop QCD correction to differential semi-leptonic decays in the shape-function region
journal, April 2009

Massive 3-loop Feynman diagrams reducible to SC $^*$ primitives of algebras of the sixth root of unity
journal, April 1999

Evaluating multi-loop Feynman integrals numerically through differential equations
journal, March 2019

Elliptic Feynman integrals and pure functions
journal, January 2019

Muon-electron scattering at NLO
journal, February 2019

Double-Higgs boson production in the high-energy limit: planar master integrals
journal, March 2018

Master integrals for the NNLO virtual corrections to μe scattering in QED: the non-planar graphs
journal, September 2018

Master integrals for the NNLO virtual corrections to $$ q\overline{q}\to t\overline{t} $$ scattering in QCD: the non-planar graphs
journal, June 2019

Hadronic corrections to μ-e scattering at NNLO with space-like data
journal, February 2019

Evaluating multi-loop Feynman integrals numerically through differential equations
journal, March 2019

Explicit form of the R- ratio of electron–positron annihilation into hadrons
journal, October 2019

Muon-Electron Scattering at Next-To-Next-To-Leading Order: The Hadronic Corrections
journal, May 2019

Two-loop master integrals for heavy-to-light form factors of two different massive fermions
journal, February 2018