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

Di Vita, Stefano; Laporta, Stefano; Mastrolia, Pierpaolo; Primo, Amedeo; Schubert, Ulrich

doi:10.1007/JHEP09(2018)016

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

Abstract

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 QCD corrections to top-pair production at hadron colliders. In particular our results, together with the planar master integrals recently computed, represent the complete set of functions needed for the evaluation of the photonic two-loop virtual next-to-next-to-leading order QED corrections to μe → μe and e⁺e^– → μ⁺μ^–.

Authors:

^[1]; Laporta, Stefano ^[2]; Mastrolia, Pierpaolo ^[2]; Primo, Amedeo ^[3]; Schubert, Ulrich ^[4]

INFN, Sezione di Milano, Milano (Italy)
Univ. di Padova, Padova (Italy); INFN, Sezione di Padova, Padova (Italy)
Univ. of Zurich, Zurich (Switzerland)
Argonne National Lab. (ANL), Argonne, IL (United States)

Publication Date:: Tue Sep 04 00:00:00 EDT 2018

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

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

OSTI Identifier:: 1494707

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: 2018; Journal Issue: 9; 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; NLO Computations

Citation Formats


                    Di Vita, Stefano, Laporta, Stefano, Mastrolia, Pierpaolo, Primo, Amedeo, and Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs.  United States: N. p., 2018. 
Web.  doi:10.1007/JHEP09(2018)016.

Copy to clipboard


                    Di Vita, Stefano, Laporta, Stefano, Mastrolia, Pierpaolo, Primo, Amedeo, & Schubert, Ulrich. Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs.  United States.  https://doi.org/10.1007/JHEP09(2018)016

Copy to clipboard


                    Di Vita, Stefano, Laporta, Stefano, Mastrolia, Pierpaolo, Primo, Amedeo, and Schubert, Ulrich. Tue .  
"Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs".  United States.  https://doi.org/10.1007/JHEP09(2018)016.  https://www.osti.gov/servlets/purl/1494707.

Copy to clipboard


                    
@article{osti_1494707,

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

  author       = {Di Vita, Stefano and Laporta, Stefano and Mastrolia, Pierpaolo and Primo, Amedeo and Schubert, Ulrich},

  abstractNote = {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 QCD corrections to top-pair production at hadron colliders. In particular our results, together with the planar master integrals recently computed, represent the complete set of functions needed for the evaluation of the photonic two-loop virtual next-to-next-to-leading order QED corrections to μe → μe and e+e– → μ+μ–.},

  doi          = {10.1007/JHEP09(2018)016},

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

  number       = 9,

  volume       = 2018,

  place        = {United States},

  year         = {Tue Sep 04 00:00:00 EDT 2018},

  month        = {Tue Sep 04 00:00:00 EDT 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP09(2018)016

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 42 works

Citation information provided by
Web of Science

Figures / Tables:

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

All figures and tables (4 total)

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

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Springer
DOI: 10.5167/uzh-41374

Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
text, January 2016

Bonciani, Roberto; Di Vita, Stefano; Mastrolia, Pierpaolo
arXiv
DOI: 10.48550/arxiv.1604.08581

QED vertex form factors at two loops
journal, January 2004

Bonciani, R.; Mastrolia, P.; Remiddi, E.
Nuclear Physics B, Vol. 676, Issue 1-2
DOI: 10.1016/j.nuclphysb.2003.10.031

Multiloop integrals in dimensional regularization made simple
text, January 2013

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

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

Abbiendi, G.; Calame, C. M. Carloni; Marconi, U.
The European Physical Journal C, Vol. 77, Issue 3
DOI: 10.1140/epjc/s10052-017-4633-z

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

Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
text, January 2009

Lee, R. N.
arXiv
DOI: 10.48550/arxiv.0911.0252

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Institute of Physics Publishing
DOI: 10.5167/uzh-30915

Chow polylogarithms and regulators
journal, January 1995

Goncharov, A. B.
Mathematical Research Letters, Vol. 2, Issue 1
DOI: 10.4310/MRL.1995.v2.n1.a9

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

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Journal of High Energy Physics, Vol. 2011, Issue 1
DOI: 10.1007/JHEP01(2011)102

Status of R(s) measurements by energy scan method
journal, January 2018

Ignatov, Fedor
EPJ Web of Conferences, Vol. 179
DOI: 10.1051/epjconf/201817901005

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

Czakon, Michal; Mitov, Alexander
Journal of High Energy Physics, Vol. 2012, Issue 12
DOI: 10.1007/JHEP12(2012)054

Three-loop master integrals for ladder-box diagrams with one massive leg
text, January 2014

Di Vita, Stefano; Mastrolia, Pierpaolo; Schubert, Ulrich
arXiv
DOI: 10.48550/arxiv.1408.3107

A quasi-finite basis for multi-loop Feynman integrals
text, January 2014

von Manteuffel, Andreas; Panzer, Erik; Schabinger, Robert M.
arXiv
DOI: 10.48550/arxiv.1411.7392

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Springer
DOI: 10.5167/uzh-90656

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Institute of Physics Publishing
DOI: 10.5167/uzh-13578

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

Laporta, S.
International Journal of Modern Physics A, Vol. 15, Issue 32
DOI: 10.1142/S0217751X00002159

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Journal of High Energy Physics, Vol. 2009, Issue 08
DOI: 10.1088/1126-6708/2009/08/067

Harmonic Polylogarithms
text, January 1999

Remiddi, E.; Vermaseren, J. A. M.
arXiv
DOI: 10.48550/arxiv.hep-ph/9905237

Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs
journal, November 2017

Mastrolia, Pierpaolo; Passera, Massimo; Primo, Amedeo
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/JHEP11(2017)198

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

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Journal of High Energy Physics, Vol. 2008, Issue 07
DOI: 10.1088/1126-6708/2008/07/129

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

Czakon, Michal; Mitov, Alexander
arXiv
DOI: 10.48550/arxiv.1207.0236

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
arXiv
DOI: 10.48550/arxiv.1309.4450

Magnus and Dyson Series for Master Integrals
text, January 2014

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

A non-planar two-loop three-point function beyond multiple polylogarithms
text, January 2017

Manteuffel, A. Von; Tancredi, L.
Karlsruhe
DOI: 10.5445/ir/1000072078

A non-planar two-loop three-point function beyond multiple polylogarithms
text, January 2017

Manteuffel, A. Von; Tancredi, L.
Karlsruhe
DOI: 10.5445/ir/1000072078#verlagsausgabe

Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to
journal, May 2010

Lee, R. N.
Nuclear Physics B, Vol. 830, Issue 3
DOI: 10.1016/j.nuclphysb.2009.12.025

Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
text, January 2008

Czakon, M.
arXiv
DOI: 10.48550/arxiv.0803.1400

A systematic and efficient method to compute multi-loop master integrals
journal, April 2018

Liu, Xiao; Ma, Yan-Qing; Wang, Chen-Yu
Physics Letters B, Vol. 779
DOI: 10.1016/j.physletb.2018.02.026

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

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

Borowka, S.; Heinrich, G.; Jones, S. P.
Computer Physics Communications, Vol. 196
DOI: 10.1016/j.cpc.2015.05.022

Magnus and Dyson series for Master Integrals
journal, March 2014

Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)082

Harmonic Polylogarithms
journal, February 2000

Remiddi, E.; Vermaseren, J. A. M.
International Journal of Modern Physics A, Vol. 15, Issue 05
DOI: 10.1142/S0217751X00000367

Two-loop correction to Bhabha scattering
journal, February 2001

Bern, Z.; Dixon, L.; Ghinculov, A.
Physical Review D, Vol. 63, Issue 5
DOI: 10.1103/PhysRevD.63.053007

Numerical evaluation of multiple polylogarithms
journal, May 2005

Vollinga, Jens; Weinzierl, Stefan
Computer Physics Communications, Vol. 167, Issue 3
DOI: 10.1016/j.cpc.2004.12.009

Massive planar and non-planar double box integrals for light N f contributions to $ gg\to t\overline{t} $
journal, October 2013

von Manteuffel, Andreas; Studerus, Cedric
Journal of High Energy Physics, Vol. 2013, Issue 10
DOI: 10.1007/JHEP10(2013)037

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

The Anomalous Magnetic Moment of the Muon
book, January 2017

Jegerlehner, Friedrich
Springer Tracts in Modern Physics
DOI: 10.1007/978-3-319-63577-4

Two-loop form factors in QED
journal, August 2003

Mastrolia, P.; Remiddi, E.
Nuclear Physics B, Vol. 664, Issue 1-2
DOI: 10.1016/S0550-3213(03)00405-X

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

Di Vita, Stefano; Mastrolia, Pierpaolo; Schubert, Ulrich
Journal of High Energy Physics, Vol. 2014, Issue 9
DOI: 10.1007/JHEP09(2014)148

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

Bonciani, Roberto; Di Vita, Stefano; Mastrolia, Pierpaolo
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)091

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

Carloni Calame, C. M.; Passera, M.; Trentadue, L.
Physics Letters B, Vol. 746
DOI: 10.1016/j.physletb.2015.05.020

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

Bonciani, R.; Ferroglia, A.; Gehrmann, T.
Journal of High Energy Physics, Vol. 2013, Issue 12
DOI: 10.1007/JHEP12(2013)038

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

NLO electroweak radiative corrections for four-fermionic process at Belle II
text, January 2017

Aleksejevs, A.; Barkanova, S.; Zykunov, V.
arXiv
DOI: 10.48550/arxiv.1701.07047

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

Di Vita, Stefano; Mastrolia, Pierpaolo; Primo, Amedeo
Journal of High Energy Physics, Vol. 2017, Issue 4
DOI: 10.1007/JHEP04(2017)008

LiteRed 1.4: a powerful tool for reduction of multiloop integrals
journal, June 2014

Lee, Roman N.
Journal of Physics: Conference Series, Vol. 523
DOI: 10.1088/1742-6596/523/1/012059

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

Czakon, M.
Physics Letters B, Vol. 664, Issue 4-5
DOI: 10.1016/j.physletb.2008.05.028

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

Czakon, Michal; Mitov, Alexander
Journal of High Energy Physics, Vol. 2013, Issue 1
DOI: 10.1007/JHEP01(2013)080

Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language
journal, January 2002

Bauer, Christian; Frink, Alexander; Kreckel, Richard
Journal of Symbolic Computation, Vol. 33, Issue 1
DOI: 10.1006/jsco.2001.0494

A quasi-finite basis for multi-loop Feynman integrals
journal, February 2015

von Manteuffel, Andreas; Panzer, Erik; Schabinger, Robert M.
Journal of High Energy Physics, Vol. 2015, Issue 2
DOI: 10.1007/JHEP02(2015)120

Numerical evaluation of harmonic polylogarithms
journal, November 2001

Gehrmann, T.; Remiddi, E.
Computer Physics Communications, Vol. 141, Issue 2
DOI: 10.1016/S0010-4655(01)00411-8

NLO electroweak radiative corrections for four-fermionic process at Belle II
journal, January 2017

Aleksejevs, Aleksandrs; Barkanova, Svetlana; Zykunov, Vladimir
EPJ Web of Conferences, Vol. 138
DOI: 10.1051/epjconf/201713806001

NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction
text, January 2012

Czakon, Michal; Mitov, Alexander
arXiv
DOI: 10.48550/arxiv.1210.6832

Magnus and Dyson series for Master Integrals
text, January 2014

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

Vertex diagrams for the QED form factors at the 2-loop level
journal, June 2003

Bonciani, R.; Mastrolia, P.; Remiddi, E.
Nuclear Physics B, Vol. 661, Issue 1-2
DOI: 10.1016/S0550-3213(03)00299-2

On μe-scattering at NNLO in QED
journal, January 2018

Mastrolia, P.; Passera, M.; Primo, A.
EPJ Web of Conferences, Vol. 179
DOI: 10.1051/epjconf/201817901014

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:

Muon-electron scattering at NLO
journal, February 2019

Alacevich, Massimo; Carloni Calame, Carlo M.; Chiesa, Mauro
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)155

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

Di Vita, Stefano; Gehrmann, Thomas; Laporta, Stefano
Springer
DOI: 10.5167/uzh-172528

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

Di Vita, Stefano; Gehrmann, Thomas; Laporta, Stefano
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)117

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

Fael, Matteo
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)027

Explicit form of the R-ratio of electron-positron annihilation into hadrons
text, January 2019

Nesterenko, A. V.
arXiv
DOI: 10.48550/arxiv.1902.06504

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

Mandal, Manoj K.; Zhao, Xiaoran
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)190

Determining arbitrary Feynman integrals by vacuum integrals
journal, April 2019

Liu, Xiao; Ma, Yan-Qing
Physical Review D, Vol. 99, Issue 7
DOI: 10.1103/physrevd.99.071501

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

Nesterenko, A. V.
Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 11
DOI: 10.1088/1361-6471/ab433e

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

Fael, M.; Passera, M.
Physical Review Letters, Vol. 122, Issue 19
DOI: 10.1103/physrevlett.122.192001

Determine Arbitrary Feynman Integrals by Vacuum Integrals
text, January 2018

Liu, Xiao; Ma, Yan-Qing
arXiv
DOI: 10.48550/arxiv.1801.10523

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

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

Journal Article Mastrolia, Pierpaolo ; Passera, Massimo ; Primo, Amedeo ; ... - Journal of High Energy Physics (Online)

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 tomore »« less
Cited by 46
https://doi.org/10.1007/JHEP11(2017)198

Full Text Available
Topics in perturbative quantum field theory: eighth order QED contribution to the anomalous magnetic moment of the muon and next to leading order QCD correction to. gamma gamma -->. M/sup +/M/sup -/(M =. pi. , K)

Thesis/Dissertation Nizic, B

In Part I the evaluation of the complete eighth order QED contribution to the difference of the anomalous magnetic moments of the muon and the electron, (a/sub ..mu../ - a/sub e/, arising from 469 Feynman diagrams is presented. The result is 140.7(4.5)(..cap alpha../..pi..). The theoretical error represents the estimated accuracy of the required numerical integration. The light-by-light QED contribution to (a/sub ..mu../ - a/sub e/) has also been improved. With these results the difference a/sub ..mu../ - a/sub e/ through eighth order in QED is (a/sub ..mu../ - a/sub e/)/sup QED/ = 619,551(21) x 10/sup -11/. Adding to the presentmore »« less
Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

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

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 particularmore » case of our general solution.« less
Cited by 55
https://doi.org/10.1007/JHEP05(2014)090

Full Text Available
Two-Loop Correction to Bhabha Scattering

Technical Report Dixon, Lance

We present the two-loop virtual QED corrections to e{sup +}e{sup -} {yields} {mu}{sup +} {mu}{sup -} and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at e{sup +}e{sup -} colliders. The calculation also tests methods that may be applied to analogous QCD processes.
https://doi.org/10.2172/784733

Full Text Available
Two-loop correction to Bhabha scattering

Journal Article Bern, Z ; Dixon, L ; Ghinculov, A - Physical Review D

We present the two-loop virtual QED corrections to e{sup +}e{sup -}{yields}{mu}{sup +}{mu}{sup -} and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at e{sup +}e{sup -} colliders. The calculation also tests methods that may be applied to analogous QCD processes.
https://doi.org/10.1103/PhysRevD.63.053007

Similar Records

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

Abstract

Citation Formats

Figures / Tables:

Magnus and Dyson Series for Master Integrals conference, August 2014

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

Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering text, January 2016

QED vertex form factors at two loops journal, January 2004

Multiloop integrals in dimensional regularization made simple text, January 2013

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

Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D text, January 2009

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

Chow polylogarithms and regulators journal, January 1995

Multiloop Integrals in Dimensional Regularization Made Simple journal, June 2013

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

Status of R(s) measurements by energy scan method journal, January 2018

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

Three-loop master integrals for ladder-box diagrams with one massive leg text, January 2014

A quasi-finite basis for multi-loop Feynman integrals text, January 2014

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

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

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

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

Harmonic Polylogarithms text, January 1999

Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs journal, November 2017

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

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

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

Magnus and Dyson Series for Master Integrals text, January 2014

A non-planar two-loop three-point function beyond multiple polylogarithms text, January 2017

A non-planar two-loop three-point function beyond multiple polylogarithms text, January 2017

Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to journal, May 2010

Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD text, January 2008

A systematic and efficient method to compute multi-loop master integrals journal, April 2018

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

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

Magnus and Dyson series for Master Integrals journal, March 2014

Harmonic Polylogarithms journal, February 2000

Two-loop correction to Bhabha scattering journal, February 2001

Numerical evaluation of multiple polylogarithms journal, May 2005

Massive planar and non-planar double box integrals for light N f contributions to $ gg\to t\overline{t} $ journal, October 2013

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

The Anomalous Magnetic Moment of the Muon book, January 2017

Two-loop form factors in QED journal, August 2003

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

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

NLO electroweak radiative corrections for four-fermionic process at Belle II text, January 2017

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

LiteRed 1.4: a powerful tool for reduction of multiloop integrals journal, June 2014

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

Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language journal, January 2002

A quasi-finite basis for multi-loop Feynman integrals journal, February 2015

Numerical evaluation of harmonic polylogarithms journal, November 2001

NLO electroweak radiative corrections for four-fermionic process at Belle II journal, January 2017

NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction text, January 2012

Magnus and Dyson series for Master Integrals text, January 2014

Vertex diagrams for the QED form factors at the 2-loop level journal, June 2003

On μe-scattering at NNLO in QED journal, January 2018

Differential equations for Feynman graph amplitudes journal, December 1997

Muon-electron scattering at NLO journal, February 2019

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

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

Explicit form of the R-ratio of electron-positron annihilation into hadrons text, January 2019

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

Determining arbitrary Feynman integrals by vacuum integrals journal, April 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

Determine Arbitrary Feynman Integrals by Vacuum Integrals text, January 2018

Magnus and Dyson Series for Master Integrals
conference, August 2014

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

Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
text, January 2016

QED vertex form factors at two loops
journal, January 2004

Multiloop integrals in dimensional regularization made simple
text, January 2013

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

Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
text, January 2009

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

Chow polylogarithms and regulators
journal, January 1995

Multiloop Integrals in Dimensional Regularization Made Simple
journal, June 2013

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

Status of R(s) measurements by energy scan method
journal, January 2018

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

Three-loop master integrals for ladder-box diagrams with one massive leg
text, January 2014

A quasi-finite basis for multi-loop Feynman integrals
text, January 2014

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

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

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

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

Harmonic Polylogarithms
text, January 1999

Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs
journal, November 2017

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

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

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

Magnus and Dyson Series for Master Integrals
text, January 2014

A non-planar two-loop three-point function beyond multiple polylogarithms
text, January 2017

A non-planar two-loop three-point function beyond multiple polylogarithms
text, January 2017

Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to
journal, May 2010

Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
text, January 2008

A systematic and efficient method to compute multi-loop master integrals
journal, April 2018

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

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

Magnus and Dyson series for Master Integrals
journal, March 2014

Harmonic Polylogarithms
journal, February 2000

Two-loop correction to Bhabha scattering
journal, February 2001

Numerical evaluation of multiple polylogarithms
journal, May 2005

Massive planar and non-planar double box integrals for light N f contributions to $ gg\to t\overline{t} $
journal, October 2013

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

The Anomalous Magnetic Moment of the Muon
book, January 2017

Two-loop form factors in QED
journal, August 2003

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

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

NLO electroweak radiative corrections for four-fermionic process at Belle II
text, January 2017

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

LiteRed 1.4: a powerful tool for reduction of multiloop integrals
journal, June 2014

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

Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language
journal, January 2002

A quasi-finite basis for multi-loop Feynman integrals
journal, February 2015

Numerical evaluation of harmonic polylogarithms
journal, November 2001

NLO electroweak radiative corrections for four-fermionic process at Belle II
journal, January 2017

NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction
text, January 2012

Magnus and Dyson series for Master Integrals
text, January 2014

Vertex diagrams for the QED form factors at the 2-loop level
journal, June 2003

On μe-scattering at NNLO in QED
journal, January 2018

Differential equations for Feynman graph amplitudes
journal, December 1997

Muon-electron scattering at NLO
journal, February 2019

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

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

Explicit form of the R-ratio of electron-positron annihilation into hadrons
text, January 2019

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

Determining arbitrary Feynman integrals by vacuum integrals
journal, April 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

Determine Arbitrary Feynman Integrals by Vacuum Integrals
text, January 2018