TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses

Bauberger, Stefan; Freitas, Ayres; Wiegand, Daniel

doi:10.1007/JHEP01(2020)024

Title: TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses

Abstract

We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C. The set of master integrals under consideration was found with self-energy diagrams containing two closed fermion loops in mind. Two techniques are employed in deriving the expressions for the finite pieces that are then numerically integrated: (a) Sub-loop dispersion relations in the case of topologies containing sub-bubbles, and (b) a modification of the procedure suggested by Ghinculov for integrals with only sub-loop triangles.

Authors:

Bauberger, Stefan ^[1]; Freitas, Ayres ^[2]; Wiegand, Daniel ^[3]

Munich School of Philosophy, Munich (Germany)
Univ. of Pittsburgh, PA (United States). Pittsburgh Particle-physics Astro-physics & Cosmology Center (PITT-PACC)
Argonne National Lab. (ANL), Argonne, IL (United States); Northwestern Univ., Evanston, IL (United States)

Publication Date:: 2020-01-07

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

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

OSTI Identifier:: 1597274

Grant/Contract Number:: AC02-06CH11357; PHY-1820760; FG02-91ER40684

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; Higgs Physics; Quark Masses and SM Parameters

Citation Formats


                    Bauberger, Stefan, Freitas, Ayres, and Wiegand, Daniel. TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses.  United States: N. p., 2020. 
Web.  doi:10.1007/JHEP01(2020)024.

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                    Bauberger, Stefan, Freitas, Ayres, & Wiegand, Daniel. TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses.  United States.  https://doi.org/10.1007/JHEP01(2020)024

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                    Bauberger, Stefan, Freitas, Ayres, and Wiegand, Daniel. Tue .  
"TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses".  United States.  https://doi.org/10.1007/JHEP01(2020)024.  https://www.osti.gov/servlets/purl/1597274.

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@article{osti_1597274,

  title        = {TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses},

  author       = {Bauberger, Stefan and Freitas, Ayres and Wiegand, Daniel},

  abstractNote = {We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C. The set of master integrals under consideration was found with self-energy diagrams containing two closed fermion loops in mind. Two techniques are employed in deriving the expressions for the finite pieces that are then numerically integrated: (a) Sub-loop dispersion relations in the case of topologies containing sub-bubbles, and (b) a modification of the procedure suggested by Ghinculov for integrals with only sub-loop triangles.},

  doi          = {10.1007/JHEP01(2020)024},

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

  number       = 1,

  volume       = 2020,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

Copy to clipboard

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Works referenced in this record:

The elliptic dilogarithm for the sunset graph
journal, March 2015

Bloch, Spencer; Vanhove, Pierre
Journal of Number Theory, Vol. 148
DOI: 10.1016/j.jnt.2014.09.032

Numerical multi-loop integrals and applications
journal, September 2016

Freitas, A.
Progress in Particle and Nuclear Physics, Vol. 90
DOI: 10.1016/j.ppnp.2016.06.004

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

The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
journal, October 2014

Adams, Luise; Bogner, Christian; Weinzierl, Stefan
Journal of Mathematical Physics, Vol. 55, Issue 10
DOI: 10.1063/1.4896563

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms
journal, March 2018

Bourjaily, Jacob L.; McLeod, Andrew J.; Spradlin, Marcus
Physical Review Letters, Vol. 120, Issue 12
DOI: 10.1103/PhysRevLett.120.121603

Feynman integrals and iterated integrals of modular forms
journal, January 2018

Adams, Luise; Weinzierl, Stefan
Communications in Number Theory and Physics, Vol. 12, Issue 2
DOI: 10.4310/CNTP.2018.v12.n2.a1

Three-loop vacuum integrals with arbitrary masses
journal, November 2016

Freitas, Ayres
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/JHEP11(2016)145

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

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

Multiple polylogarithms, cyclotomy and modular complexes
journal, January 1998

Goncharov, A. B.
Mathematical Research Letters, Vol. 5, Issue 4
DOI: 10.4310/MRL.1998.v5.n4.a7

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

Scalar one-loop integrals
journal, January 1979

't Hooft, G.; Veltman, M.
Nuclear Physics B, Vol. 153
DOI: 10.1016/0550-3213(79)90605-9

Two-loop self-energy diagrams with different masses and the momentum expansion
journal, May 1993

Davydychev, A. I.; Tausk, J. B.
Nuclear Physics B, Vol. 397, Issue 1-2
DOI: 10.1016/0550-3213(93)90338-P

FIESTA 2: Parallelizeable multiloop numerical calculations
journal, March 2011

Smirnov, A. V.; Smirnov, V. A.; Tentyukov, M.
Computer Physics Communications, Vol. 182, Issue 3
DOI: 10.1016/j.cpc.2010.11.025

Simple one-dimensional integral representations for two-loop self-energies: the master diagram
journal, July 1995

Bauberger, S.; Böhm, M.
Nuclear Physics B, Vol. 445, Issue 1
DOI: 10.1016/0550-3213(95)00199-3

FIESTA4: Optimized Feynman integral calculations with GPU support
journal, July 2016

Smirnov, A. V.
Computer Physics Communications, Vol. 204
DOI: 10.1016/j.cpc.2016.03.013

SecDec: A general program for sector decomposition
journal, July 2011

Carter, Jonathon; Heinrich, Gudrun
Computer Physics Communications, Vol. 182, Issue 7
DOI: 10.1016/j.cpc.2011.03.026

Analytical and numerical methods for massive two-loop self-energy diagrams
journal, January 1995

Bauberger, S.; Berends, F. A.; Böhm, M.
Nuclear Physics B, Vol. 434, Issue 1-2
DOI: 10.1016/0550-3213(94)00475-T

Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
journal, May 2009

Smirnov, A. V.; Tentyukov, M. N.
Computer Physics Communications, Vol. 180, Issue 5
DOI: 10.1016/j.cpc.2008.11.006

Scalar two-loop integrals for gauge boson self-energy diagrams with a massless fermion loop
journal, January 1994

Scharf, R.; Tausk, J. B.
Nuclear Physics B, Vol. 412, Issue 3
DOI: 10.1016/0550-3213(94)90391-3

FIESTA 3: Cluster-parallelizable multiloop numerical calculations in physical regions
journal, July 2014

Smirnov, A. V.
Computer Physics Communications, Vol. 185, Issue 7
DOI: 10.1016/j.cpc.2014.03.015

MBnumerics: Numerical integration of Mellin-Barnes integrals in physical regions
conference, October 2018

Usovitsch, Johann; Dubovyk, Ievgen; Riemann, Tord
Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)
DOI: 10.22323/1.303.0046

FIRE5: A C++ implementation of Feynman Integral REduction
journal, April 2015

Smirnov, A. V.
Computer Physics Communications, Vol. 189
DOI: 10.1016/j.cpc.2014.11.024

AMBRE—a Mathematica package for the construction of Mellin–Barnes representations for Feynman integrals
journal, December 2007

Gluza, J.; Kajda, K.; Riemann, T.
Computer Physics Communications, Vol. 177, Issue 11
DOI: 10.1016/j.cpc.2007.07.001

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
journal, January 2011

Gluza, J.; Kajda, K.; Riemann, T.
The European Physical Journal C, Vol. 71, Issue 1
DOI: 10.1140/epjc/s10052-010-1516-y

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Title: TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses

Abstract

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