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

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.  doi: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.  doi: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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DOI: 10.1007/JHEP01(2020)024

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

Abstract

Citation Formats

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

The elliptic dilogarithm for the sunset graph
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Numerical multi-loop integrals and applications
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SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop
journal, November 2015

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

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

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

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

Harmonic Polylogarithms
journal, February 2000

Numerical evaluation of multiple polylogarithms
journal, May 2005

Multiple polylogarithms, cyclotomy and modular complexes
journal, January 1998

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

Scalar one-loop integrals
journal, January 1979

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

FIESTA 2: Parallelizeable multiloop numerical calculations
journal, March 2011

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

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

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

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

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

Scalar two-loop integrals for gauge boson self-energy diagrams with a massless fermion loop
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FIESTA 3: Cluster-parallelizable multiloop numerical calculations in physical regions
journal, July 2014

MBnumerics: Numerical integration of Mellin-Barnes integrals in physical regions
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FIRE5: A C++ implementation of Feynman Integral REduction
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AMBRE—a Mathematica package for the construction of Mellin–Barnes representations for Feynman integrals
journal, December 2007

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