Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

Henn, Johannes M.; Melnikov, Kirill; Smirnov, Vladimir A.

doi:10.1007/JHEP05(2014)090

Title: Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

Abstract

We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals in this class are the two-loop four-point functions where two external lines are on the light-cone and two other external lines have different invariant masses. We compute these and other relevant integrals analytically using differential equations in external kinematic variables and express our results in terms of Goncharov polylogarithms. The case of two equal off-shellnesses, recently considered in Ref. [1], appears as a particular case of our general solution.

Authors:

Henn, Johannes M. ^[1]; Melnikov, Kirill ^[2]; Smirnov, Vladimir A. ^[3]

Inst. for Advanced Study, Princeton, NJ (United States)
Johns Hopkins Univ., Baltimore, MD (United States)
Moscow State Univ. (Russia). Skobeltsyn Inst. of Nuclear Physics

Publication Date:: Wed May 21 00:00:00 EDT 2014

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Science Foundation (NSF)

OSTI Identifier:: 1598517

Grant/Contract Number:: SC0009988; PHY-1214000

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: 2014; Journal Issue: 5; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; master integral; n-point function: 4; n-point function: analytic properties; hadron hadron: scattering; vector boson: pair production; off-shell; light cone; quantum chromodynamics: correction; correction: higher-order; higher-order: 2; NLO computations; QCD phenomenology

Citation Formats


                    Henn, Johannes M., Melnikov, Kirill, and Smirnov, Vladimir A. Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions.  United States: N. p., 2014. 
Web.  doi:10.1007/JHEP05(2014)090.

Copy to clipboard


                    Henn, Johannes M., Melnikov, Kirill, & Smirnov, Vladimir A. Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions.  United States.  https://doi.org/10.1007/JHEP05(2014)090

Copy to clipboard


                    Henn, Johannes M., Melnikov, Kirill, and Smirnov, Vladimir A. Wed .  
"Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions".  United States.  https://doi.org/10.1007/JHEP05(2014)090.  https://www.osti.gov/servlets/purl/1598517.

Copy to clipboard


                    
@article{osti_1598517,

  title        = {Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions},

  author       = {Henn, Johannes M. and Melnikov, Kirill and Smirnov, Vladimir A.},

  abstractNote = {We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals in this class are the two-loop four-point functions where two external lines are on the light-cone and two other external lines have different invariant masses. We compute these and other relevant integrals analytically using differential equations in external kinematic variables and express our results in terms of Goncharov polylogarithms. The case of two equal off-shellnesses, recently considered in Ref. [1], appears as a particular case of our general solution.},

  doi          = {10.1007/JHEP05(2014)090},

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

  number       = 5,

  volume       = 2014,

  place        = {United States},

  year         = {Wed May 21 00:00:00 EDT 2014},

  month        = {Wed May 21 00:00:00 EDT 2014}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP05(2014)090

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 55 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Magnus and Dyson Series for Master Integrals
conference, August 2014

Mastrolia, Pierpaolo; Argeri, Mario; Di Vita, Stefano
Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014)
DOI: 10.22323/1.211.0007

Multiloop integrals in dimensional regularization made simple
text, January 2013

Henn, Johannes M.
arXiv
DOI: 10.48550/arxiv.1304.1806

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

Chetyrkin, K. G.; Tkachov, F. V.
Nuclear Physics B, Vol. 192, Issue 1
DOI: 10.1016/0550-3213(81)90199-1

$$W^+W^-$$ W + W - , $$WZ$$ W Z and $$ZZ$$ Z Z production in the POWHEG-BOX-V2
journal, January 2014

Nason, Paolo; Zanderighi, Giulia
The European Physical Journal C, Vol. 74, Issue 1
DOI: 10.1140/epjc/s10052-013-2702-5

NNLO QCD corrections to jet production at hadron colliders from gluon scattering
journal, January 2014

Currie, James; Ridder, Aude Gehrmann-De; Glover, E. W. N.
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)110

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
journal, July 2000

Anastasiou, C.; Gehrmann, T.; Oleari, C.
Nuclear Physics B, Vol. 580, Issue 1-2
DOI: 10.1016/S0550-3213(00)00251-0

Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
text, January 2013

Henn, Johannes M.; Smirnov, Alexander V.; Smirnov, Vladimir A.
arXiv
DOI: 10.48550/arxiv.1306.2799

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

Henn, Johannes M.
Physical Review Letters, Vol. 110, Issue 25
DOI: 10.1103/PhysRevLett.110.251601

Geometric approach to asymptotic expansion of Feynman integrals
journal, April 2011

Pak, A.; Smirnov, A.
The European Physical Journal C, Vol. 71, Issue 4
DOI: 10.1140/epjc/s10052-011-1626-1

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

Smirnov, V. A.
Physics Letters B, Vol. 460, Issue 3-4
DOI: 10.1016/S0370-2693(99)00777-7

Non-planar massless two-loop Feynman diagrams with four on-shell legs
text, January 1999

Tausk, J. B.
arXiv
DOI: 10.48550/arxiv.hep-ph/9909506

Analytic results for two-loop master integrals for Bhabha scattering I
journal, November 2013

Henn, Johannes M.; Smirnov, Vladimir A.
Journal of High Energy Physics, Vol. 2013, Issue 11
DOI: 10.1007/JHEP11(2013)041

Double Parton Scattering Singularity in One-Loop Integrals
text, January 2011

Gaunt, Jonathan R.; Stirling, W. James
arXiv
DOI: 10.48550/arxiv.1103.1888

FIRE4, LiteRed and accompanying tools to solve integration by parts relations
journal, December 2013

Smirnov, A. V.; Smirnov, V. A.
Computer Physics Communications, Vol. 184, Issue 12
DOI: 10.1016/j.cpc.2013.06.016

Analytic continuation of massless two-loop four-point functions
journal, September 2002

Gehrmann, T.; Remiddi, E.
Nuclear Physics B, Vol. 640, Issue 1-2
DOI: 10.1016/S0550-3213(02)00569-2

Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution
text, January 2013

Ridder, Aude Gehrmann-De; Gehrmann, Thomas; Glover, E. W. N.
arXiv
DOI: 10.48550/arxiv.1301.7310

Two-loop master integrals for $ q\overline{q}\to VV $ : the planar topologies
journal, August 2013

Gehrmann, Thomas; Tancredi, Lorenzo; Weihs, Erich
Journal of High Energy Physics, Vol. 2013, Issue 8
DOI: 10.1007/JHEP08(2013)070

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

Bärnreuther, Peter; Czakon, Michał; Mitov, Alexander
Physical Review Letters, Vol. 109, Issue 13
DOI: 10.1103/PhysRevLett.109.132001

Two-loop master integrals for $ q\overline{q}\to VV $ : the planar topologies
text, January 2013

Gehrmann, Thomas; Tancredi, Lorenzo; Weihs, Erich
Springer
DOI: 10.5167/uzh-80702

Analytic results for two-loop master integrals for Bhabha scattering I
text, January 2013

Henn, Johannes M.; Smirnov, Vladimir A.
arXiv
DOI: 10.48550/arxiv.1307.4083

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

Czakon, Michał; Fiedler, Paul; Mitov, Alexander
Physical Review Letters, Vol. 110, Issue 25
DOI: 10.1103/PhysRevLett.110.252004

NNLO QCD corrections to jet production at hadron colliders from gluon scattering
text, January 2014

Currie, James; Gehrmann-De Ridder, Aude; Glover, E. W. N.
ETH Zurich
DOI: 10.3929/ethz-b-000096077

Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators
journal, January 2000

Smirnov, V. A.; Veretin, O. L.
Nuclear Physics B, Vol. 566, Issue 1-2
DOI: 10.1016/S0550-3213(99)00686-0

Magnus and Dyson Series for Master Integrals
text, January 2014

Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo
arXiv
DOI: 10.48550/arxiv.1401.2979

Expansion by regions: revealing potential and Glauber regions automatically
journal, September 2012

Jantzen, Bernd; Smirnov, Alexander V.; Smirnov, Vladimir A.
The European Physical Journal C, Vol. 72, Issue 9
DOI: 10.1140/epjc/s10052-012-2139-2

Second-order QCD corrections to jet production at hadron colliders: the all-gluon contribution
text, January 2013

Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W. N.
American Physical Society
DOI: 10.5167/uzh-80480

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

Kotikov, A. V.
Physics Letters B, Vol. 254, Issue 1-2
DOI: 10.1016/0370-2693(91)90413-K

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

Gehrmann, T.; Remiddi, E.
Nuclear Physics B, Vol. 601, Issue 1-2
DOI: 10.1016/S0550-3213(01)00074-8

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

Tkachov, F. V.
Physics Letters B, Vol. 100, Issue 1
DOI: 10.1016/0370-2693(81)90288-4

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

Tausk, J. B.
Physics Letters B, Vol. 469, Issue 1-4
DOI: 10.1016/S0370-2693(99)01277-0

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

Gehrmann, T.; Remiddi, E.
Nuclear Physics B, Vol. 601, Issue 1-2
DOI: 10.1016/S0550-3213(01)00057-8

Algorithm FIRE—Feynman Integral REduction
journal, October 2008

Smirnov, A. V.
Journal of High Energy Physics, Vol. 2008, Issue 10
DOI: 10.1088/1126-6708/2008/10/107

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

Gehrmann, T.; Remiddi, E.
Nuclear Physics B, Vol. 580, Issue 1-2
DOI: 10.1016/S0550-3213(00)00223-6

Three-mass triangle integrals and single-valued polylogarithms
text, January 2012

Chavez, Federico; Duhr, Claude
arXiv
DOI: 10.48550/arxiv.1209.2722

Asymptotic expansion of Feynman integrals near threshold
journal, June 1998

Beneke, M.; Smirnov, V. A.
Nuclear Physics B, Vol. 522, Issue 1-2
DOI: 10.1016/S0550-3213(98)00138-2

Three-mass triangle integrals and single-valued polylogarithms
journal, November 2012

Chavez, Federico; Duhr, Claude
Journal of High Energy Physics, Vol. 2012, Issue 11
DOI: 10.1007/JHEP11(2012)114

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
text, January 2000

Anastasiou, C.; Gehrmann, T.; Oleari, C.
arXiv
DOI: 10.48550/arxiv.hep-ph/0003261

Second-Order QCD Corrections to Jet Production at Hadron Colliders: The All-Gluon Contribution
journal, April 2013

Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W. N.
Physical Review Letters, Vol. 110, Issue 16
DOI: 10.1103/PhysRevLett.110.162003

Magnus and Dyson series for Master Integrals
text, January 2014

Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo
Springer
DOI: 10.5167/uzh-107578

Helicity amplitudes for O(αs) production of W+W−, W±Z, ZZ, W±γ, or Zγ pairs at hadron colliders
journal, October 1998

Dixon, L.; Kunszt, Z.; Signer, A.
Nuclear Physics B, Vol. 531, Issue 1-3
DOI: 10.1016/S0550-3213(98)00421-0

Differential equations for Feynman graph amplitudes
journal, December 1997

Remiddi, E.
Il Nuovo Cimento A, Vol. 110, Issue 12
DOI: 10.1007/BF03185566

Works referencing / citing this record:

Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion
text, January 2015

Caola, F.; Henn, J. M.; Melnikov, K.
Karlsruhe
DOI: 10.5445/ir/1000049599

Next-to-leading order QCD corrections to the decay width H → Zγ
text, January 2015

Bonciani, Roberto; Del Duca, Vittorio; Frellesvig, Hjalte
ETH Zurich
DOI: 10.3929/ethz-b-000104207

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
text, January 2019

Hartanto, Heribertus Bayu; Badger, Simon; Brønnum-Hansen, Christian
Springer
DOI: 10.5167/uzh-175225

$W^{+} W^{-}$ Production at Hadron Colliders in Next to Next to Leading Order QCD
journal, November 2014

Gehrmann, T.; Grazzini, M.; Kallweit, S.
Physical Review Letters, Vol. 113, Issue 21
DOI: 10.1103/physrevlett.113.212001

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
journal, September 2014

Caola, Fabrizio; Henn, Johannes M.; Melnikov, Kirill
Journal of High Energy Physics, Vol. 2014, Issue 9
DOI: 10.1007/jhep09(2014)043

Analytic result for the nonplanar hexa-box integrals
text, January 2019

Chicherin, D.; Gehrmann, T.; Henn, J. M.
Springer
DOI: 10.5167/uzh-171678

W+W- production at Hadron Colliders in next to next to leading order QCD
text, January 2014

Gehrmann, T.; Grazzini, M.; Kallweit, S.
American Physical Society
DOI: 10.5167/uzh-107409

Analytic result for the nonplanar hexa-box integrals
text, January 2018

Chicherin, D.; Gehrmann, Thomas; Henn, J. M.
University of Zurich
DOI: 10.5167/uzh-161924

Analytic result for the nonplanar hexa-box integrals
journal, March 2019

Chicherin, D.; Gehrmann, T.; Henn, J. M.
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)042

Two-loop doubly massive four-point amplitude involving a half-BPS and Konishi operator
journal, May 2019

Ahmed, Taushif; Dhani, Prasanna K.
Journal of High Energy Physics, Vol. 2019, Issue 5
DOI: 10.1007/jhep05(2019)066

On the status of expansion by regions
journal, February 2019

Semenova, Tatiana Yu.; Smirnov, Alexander V.; Smirnov, Vladimir A.
The European Physical Journal C, Vol. 79, Issue 2
DOI: 10.1140/epjc/s10052-019-6653-3

Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
text, January 2015

Bourjaily, Jacob L.; Trnka, Jaroslav
arXiv
DOI: 10.48550/arxiv.1505.05886

Systematic approximation of multi-scale Feynman integrals
text, January 2018

Borowka, Sophia; Gehrmann, Thomas; Hulme, Daniel
arXiv
DOI: 10.48550/arxiv.1804.06824

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
journal, September 2019

Hartanto, Heribertus Bayu; Badger, Simon; Brønnum-Hansen, Christian
Journal of High Energy Physics, Vol. 2019, Issue 9
DOI: 10.1007/jhep09(2019)119

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron
text, January 2016

Czakon, Michal Wiktor; Fiedler, Paul; Heymes, David
RWTH Aachen University
DOI: 10.18154/rwth-2016-10937

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
text, January 2014

Caola, Fabrizio; Henn, Johannes M.; Melnikov, Kirill
arXiv
DOI: 10.48550/arxiv.1404.5590

Systematic approximation of multi-scale Feynman integrals
text, January 2018

Borowka, Sophia; Gehrmann, Thomas; Hulme, Daniel
Springer
DOI: 10.5167/uzh-157573

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron
text, January 2016

Czakon, Michal; Fiedler, Paul; Heymes, David
arXiv
DOI: 10.48550/arxiv.1601.05375

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence
journal, December 2016

Bonciani, Roberto; Del Duca, Vittorio; Frellesvig, Hjalte
Journal of High Energy Physics, Vol. 2016, Issue 12
DOI: 10.1007/jhep12(2016)096

The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons
text, January 2015

Von Manteuffel, A.; Tancredi, L.
Karlsruhe
DOI: 10.5445/ir/1000050896

Pentagon functions for massless planar scattering amplitudes
text, January 2018

Gehrmann, T.; Henn, J. M.; Lo Presti, N. A.
Springer
DOI: 10.5167/uzh-157572

Systematic approximation of multi-scale Feynman integrals
journal, August 2018

Borowka, Sophia; Gehrmann, Thomas; Hulme, Daniel
Journal of High Energy Physics, Vol. 2018, Issue 8
DOI: 10.1007/jhep08(2018)111

The two-loop helicity amplitudes for q q ¯ ′ → V 1 V 2 → 4 $$ q\overline{q}^{\prime}\to {V}_1{V}_2\to 4 $$ leptons
journal, September 2015

Gehrmann, Thomas; von Manteuffel, Andreas; Tancredi, Lorenzo
Journal of High Energy Physics, Vol. 2015, Issue 9
DOI: 10.1007/jhep09(2015)128

Transforming differential equations of multi-loop Feynman integrals into canonical form
text, January 2016

Meyer, Christoph
arXiv
DOI: 10.48550/arxiv.1611.01087

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence
text, January 2016

Bonciani, Roberto; Del Duca, Vittorio; Frellesvig, Hjalte
ETH Zurich
DOI: 10.3929/ethz-b-000124893

Similar Records in DOE PAGES and OSTI.GOV collections:

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons

Journal Article Caola, Fabrizio ; Henn, Johannes M. ; Melnikov, Kirill ; ... - Journal of High Energy Physics (Online)

We present the calculation of all non-planar master integrals that are needed to describe production of two off-shell vector bosons in collisions of two massless partons through NNLO in perturbative QCD. The integrals are computed analytically using differential equations in external kinematic variables and expressed in terms of Goncharov polylogarithms. These results provide the last missing ingredient needed for the computation of two-loop amplitudes that describe the production of two gauge bosons with different invariant masses in hadron collisions.
Cited by 52
https://doi.org/10.1007/JHEP09(2014)043

Full Text Available
Evaluating single-scale and/or non-planar diagrams by differential equations

Journal Article Henn, Johannes M. ; Smirnov, Alexander V. ; Smirnov, Vladimir A. - Journal of High Energy Physics (Online)

We apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of the differential equations to single-scale Feynman integrals. Moreover, the information about singular limits significantly simplifies finding boundary constants for the differential equations. To illustrate these points we consider two families of three-loop integrals. The first are form-factor integrals with two external legs on the light cone. We introduce one more scale by taking one more leg off-shell,more »« less
Cited by 67
https://doi.org/10.1007/JHEP03(2014)088

Full Text Available
Master integrals for two-loop QCD corrections to quark quasi PDFs

Journal Article Chen, Long-Bin ; Wang, Wei ; Zhu, Ruilin - Journal of High Energy Physics (Online)

We compute the master integrals for the two-loop QCD corrections to quark quasi parton distribution functions (PDFs) in the large momentum effective theory (LaMET). With a proper canonical basis, we derive the analytical results for the three families of master integrals using the method of differential equations. The final expressions for the master integrals are given in terms of Goncharov polylogarithms. These results allow us to extract the two-loop short-distant matching coefficients between quark quasi and lightcone PDFs in LaMET, and are valuable to improve the determination of the nucleon PDFs from first principles in future.
https://doi.org/10.1007/jhep10(2020)079

Full Text Available
Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in quark-antiquark collisions

Journal Article Caola, Fabrizio ; Henn, Johannes M. ; Melnikov, Kirill ; ... - Journal of High Energy Physics (Online)

Knowledge of two-loop QCD amplitudes for processes qq'→V₁V₂→(l₁more »« less
Cited by 25
https://doi.org/10.1007/JHEP11(2014)041

Full Text Available
Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs

Journal Article Di Vita, Stefano ; Laporta, Stefano ; Mastrolia, Pierpaolo ; ... - Journal of High Energy Physics (Online)

In this study, we evaluate the master integrals for the two-loop non-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 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 polylogarithms. 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 QCDmore »« less
Cited by 42
https://doi.org/10.1007/JHEP09(2018)016

Full Text Available

Similar Records

Title: Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

Abstract

Citation Formats

Magnus and Dyson Series for Master Integrals conference, August 2014

Multiloop integrals in dimensional regularization made simple text, January 2013

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

$$W^+W^-$$ W + W - , $$WZ$$ W Z and $$ZZ$$ Z Z production in the POWHEG-BOX-V2 journal, January 2014

NNLO QCD corrections to jet production at hadron colliders from gluon scattering journal, January 2014

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs journal, July 2000

Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation text, January 2013

Multiloop Integrals in Dimensional Regularization Made Simple journal, June 2013

Geometric approach to asymptotic expansion of Feynman integrals journal, April 2011

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

Non-planar massless two-loop Feynman diagrams with four on-shell legs text, January 1999

Analytic results for two-loop master integrals for Bhabha scattering I journal, November 2013

Double Parton Scattering Singularity in One-Loop Integrals text, January 2011

FIRE4, LiteRed and accompanying tools to solve integration by parts relations journal, December 2013

Analytic continuation of massless two-loop four-point functions journal, September 2002

Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution text, January 2013

Two-loop master integrals for $ q\overline{q}\to VV $ : the planar topologies journal, August 2013

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

Two-loop master integrals for $ q\overline{q}\to VV $ : the planar topologies text, January 2013

Analytic results for two-loop master integrals for Bhabha scattering I text, January 2013

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

NNLO QCD corrections to jet production at hadron colliders from gluon scattering text, January 2014

Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators journal, January 2000

Magnus and Dyson Series for Master Integrals text, January 2014

Expansion by regions: revealing potential and Glauber regions automatically journal, September 2012

Second-order QCD corrections to jet production at hadron colliders: the all-gluon contribution text, January 2013

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

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

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

Algorithm FIRE—Feynman Integral REduction journal, October 2008

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

Three-mass triangle integrals and single-valued polylogarithms text, January 2012

Asymptotic expansion of Feynman integrals near threshold journal, June 1998

Three-mass triangle integrals and single-valued polylogarithms journal, November 2012

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs text, January 2000

Second-Order QCD Corrections to Jet Production at Hadron Colliders: The All-Gluon Contribution journal, April 2013

Magnus and Dyson series for Master Integrals text, January 2014

Helicity amplitudes for O(αs) production of W+W−, W±Z, ZZ, W±γ, or Zγ pairs at hadron colliders journal, October 1998

Differential equations for Feynman graph amplitudes journal, December 1997

Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion text, January 2015

Next-to-leading order QCD corrections to the decay width H → Zγ text, January 2015

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons text, January 2019

W + W − Production at Hadron Colliders in Next to Next to Leading Order QCD journal, November 2014

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons journal, September 2014

Analytic result for the nonplanar hexa-box integrals text, January 2019

W+W- production at Hadron Colliders in next to next to leading order QCD text, January 2014

Analytic result for the nonplanar hexa-box integrals text, January 2018

Analytic result for the nonplanar hexa-box integrals journal, March 2019

Two-loop doubly massive four-point amplitude involving a half-BPS and Konishi operator journal, May 2019

On the status of expansion by regions journal, February 2019

Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM text, January 2015

Systematic approximation of multi-scale Feynman integrals text, January 2018

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons journal, September 2019

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron text, January 2016

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons text, January 2014

Systematic approximation of multi-scale Feynman integrals text, January 2018

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron text, January 2016

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence journal, December 2016

The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons text, January 2015

Pentagon functions for massless planar scattering amplitudes text, January 2018

Systematic approximation of multi-scale Feynman integrals journal, August 2018

The two-loop helicity amplitudes for q q ¯ ′ → V 1 V 2 → 4 $$ q\overline{q}^{\prime}\to {V}_1{V}_2\to 4 $$ leptons journal, September 2015

Transforming differential equations of multi-loop Feynman integrals into canonical form text, January 2016

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence text, January 2016

Magnus and Dyson Series for Master Integrals
conference, August 2014

Multiloop integrals in dimensional regularization made simple
text, January 2013

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

$$W^+W^-$$ W + W - , $$WZ$$ W Z and $$ZZ$$ Z Z production in the POWHEG-BOX-V2
journal, January 2014

NNLO QCD corrections to jet production at hadron colliders from gluon scattering
journal, January 2014

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
journal, July 2000

Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
text, January 2013

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

Geometric approach to asymptotic expansion of Feynman integrals
journal, April 2011

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

Non-planar massless two-loop Feynman diagrams with four on-shell legs
text, January 1999

Analytic results for two-loop master integrals for Bhabha scattering I
journal, November 2013

Double Parton Scattering Singularity in One-Loop Integrals
text, January 2011

FIRE4, LiteRed and accompanying tools to solve integration by parts relations
journal, December 2013

Analytic continuation of massless two-loop four-point functions
journal, September 2002

Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution
text, January 2013

Two-loop master integrals for $ q\overline{q}\to VV $ : the planar topologies
journal, August 2013

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

Two-loop master integrals for $ q\overline{q}\to VV $ : the planar topologies
text, January 2013

Analytic results for two-loop master integrals for Bhabha scattering I
text, January 2013

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

NNLO QCD corrections to jet production at hadron colliders from gluon scattering
text, January 2014

Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators
journal, January 2000

Magnus and Dyson Series for Master Integrals
text, January 2014

Expansion by regions: revealing potential and Glauber regions automatically
journal, September 2012

Second-order QCD corrections to jet production at hadron colliders: the all-gluon contribution
text, January 2013

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

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

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

Algorithm FIRE—Feynman Integral REduction
journal, October 2008

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

Three-mass triangle integrals and single-valued polylogarithms
text, January 2012

Asymptotic expansion of Feynman integrals near threshold
journal, June 1998

Three-mass triangle integrals and single-valued polylogarithms
journal, November 2012

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
text, January 2000

Second-Order QCD Corrections to Jet Production at Hadron Colliders: The All-Gluon Contribution
journal, April 2013

Magnus and Dyson series for Master Integrals
text, January 2014

Helicity amplitudes for O(αs) production of W+W−, W±Z, ZZ, W±γ, or Zγ pairs at hadron colliders
journal, October 1998

Differential equations for Feynman graph amplitudes
journal, December 1997

Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion
text, January 2015

Next-to-leading order QCD corrections to the decay width H → Zγ
text, January 2015

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
text, January 2019

$W^{+} W^{-}$ Production at Hadron Colliders in Next to Next to Leading Order QCD
journal, November 2014

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
journal, September 2014

Analytic result for the nonplanar hexa-box integrals
text, January 2019

W+W- production at Hadron Colliders in next to next to leading order QCD
text, January 2014

Analytic result for the nonplanar hexa-box integrals
text, January 2018

Analytic result for the nonplanar hexa-box integrals
journal, March 2019

Two-loop doubly massive four-point amplitude involving a half-BPS and Konishi operator
journal, May 2019

On the status of expansion by regions
journal, February 2019

Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
text, January 2015

Systematic approximation of multi-scale Feynman integrals
text, January 2018

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
journal, September 2019

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron
text, January 2016

Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
text, January 2014

Systematic approximation of multi-scale Feynman integrals
text, January 2018

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron
text, January 2016

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence
journal, December 2016

The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons
text, January 2015

Pentagon functions for massless planar scattering amplitudes
text, January 2018

Systematic approximation of multi-scale Feynman integrals
journal, August 2018

The two-loop helicity amplitudes for q q ¯ ′ → V 1 V 2 → 4 $$ q\overline{q}^{\prime}\to {V}_1{V}_2\to 4 $$ leptons
journal, September 2015

Transforming differential equations of multi-loop Feynman integrals into canonical form
text, January 2016

Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence
text, January 2016