Symbolic Summation in Perturbative Quantum Field Theory

Project Lead

Project Duration

01/02/2008 - 31/01/2013

Publications

2018

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C.G. Raab, C.-S. Radu, C. Schneider

J. Math. Phys. 59(062305), pp. 1-55. 2018. ISSN 0022-2488. arXiv:1706.01299 [hep-th]. [url]
[bib]
@article{RISC5456,
author = {J. Ablinger and J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and C.G. Raab and C.-S. Radu and C. Schneider},
title = {{Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams}},
language = {english},
journal = {J. Math. Phys.},
volume = {59},
number = {062305},
pages = {1--55},
isbn_issn = {ISSN 0022-2488},
year = {2018},
note = {arXiv:1706.01299 [hep-th]},
refereed = {no},
length = {55},
url = {https://arxiv.org/abs/1706.01299}
}

Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions

J. Middeke, C. Schneider

In: Advances in Computer Algebra. WWCA 2016., C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 149-173. 2018. Springer, ISSN 2194-1009. arXiv:1705.00280 [cs.SC]. [url]
[bib]
@incollection{RISC5447,
author = {J. Middeke and C. Schneider},
title = {{Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {149--173},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.00280 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {24},
url = {https://arxiv.org/abs/1705.00280}
}

Representing (q-)hypergeometric products and mixed versions in difference rings

E.D. Ocansey, C. Schneider

In: Advances in Computer Algebra. WWCA 2016., C. Schneider, E. Zima (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 175-213. 2018. Springer, ISSN 2194-1009. arXiv:1705.01368 [cs.SC]. [url]
[bib]
@incollection{RISC5448,
author = {E.D. Ocansey and C. Schneider},
title = {{Representing (q-)hypergeometric products and mixed versions in difference rings}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics},
volume = {226},
pages = {175--213},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1705.01368 [cs.SC]},
editor = {C. Schneider and E. Zima},
refereed = {yes},
length = {36},
url = {https://arxiv.org/abs/1705.01368}
}

Refined Holonomic Summation Algorithms in Particle Physics

J. Blümlein, M. Round, C. Schneider

In: Advances in Computer Algebra. WWCA 2016., E. Zima, C. Schneider (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 51-91. 2018. Springer, ISSN 2194-1009. arXiv:1706.03677 [cs.SC]. [url]
[bib]
@incollection{RISC5462,
author = {J. Blümlein and M. Round and C. Schneider},
title = {{Refined Holonomic Summation Algorithms in Particle Physics}},
booktitle = {{ Advances in Computer Algebra. WWCA 2016.}},
language = {english},
series = {Springer Proceedings in Mathematics & Statistics },
volume = {226},
pages = {51--91},
publisher = {Springer},
isbn_issn = {ISSN 2194-1009},
year = {2018},
note = {arXiv:1706.03677 [cs.SC]},
editor = {E. Zima and C. Schneider},
refereed = {yes},
length = {39},
url = {https://arxiv.org/abs/1706.03677}
}

The two-mass contribution to the three-loop pure singlet operator matrix element

J. Ablinger, J. Blümlein, A. De Freitas, C. Schneider, K. Schönwald

Nucl. Phys. B(927), pp. 339-367. 2018. ISSN 0550-3213. arXiv:1711.06717 [hep-ph]. [url]
[bib]
@article{RISC5504,
author = {J. Ablinger and J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},
title = {{The two-mass contribution to the three-loop pure singlet operator matrix element}},
language = {english},
journal = {Nucl. Phys. B},
number = {927},
pages = {339--367},
isbn_issn = {ISSN 0550-3213},
year = {2018},
note = {arXiv:1711.06717 [hep-ph]},
refereed = {yes},
length = {29},
url = {https://arxiv.org/abs/1711.06717}
}

Algebraic independence of sequences generated by (cyclotomic) harmonic sums

J. Ablinger, C. Schneider

Annals of Combinatorics 22(2), pp. 213-244. 2018. ISSN: 0218-0006. arXiv:1510.03692 [cs.SC], doi 10.1007/s00026-018-0381-5. [url]
[bib]
@article{RISC5507,
author = {J. Ablinger and C. Schneider},
title = {{Algebraic independence of sequences generated by (cyclotomic) harmonic sums}},
language = {english},
journal = {Annals of Combinatorics},
volume = {22},
number = {2},
pages = {213--244},
isbn_issn = {ISSN: 0218-0006},
year = {2018},
note = {arXiv:1510.03692 [cs.SC], doi 10.1007/s00026-018-0381-5},
refereed = {yes},
length = {32},
url = {https://link.springer.com/journal/26/22/2/page/1}
}

The Heavy Quark Form Factors at Two Loops

J. Ablinger, A. Behring, J. Bluemlein, G. Falcioni, A. De Freitas, P. Marquard, N. Rana, C. Schneider

Physical Review D 97(094022), pp. 1-44. 2018. ISSN 1550-2368. arXiv:1712.09889 [hep-ph]. [url]
[bib]
@article{RISC5522,
author = {J. Ablinger and A. Behring and J. Bluemlein and G. Falcioni and A. De Freitas and P. Marquard and N. Rana and C. Schneider},
title = {{The Heavy Quark Form Factors at Two Loops}},
language = {english},
journal = {Physical Review D},
volume = {97},
number = {094022},
pages = {1--44},
isbn_issn = {ISSN 1550-2368},
year = {2018},
note = {arXiv:1712.09889 [hep-ph]},
refereed = {yes},
length = {131},
url = {https://doi.org/10.1103/PhysRevD.97.094022}
}

The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg, Q}^{(3)}$

J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald

Nucl. Phys. B 932, pp. 129-240. 2018. ISSN 0550-3213. arXiv:1804.02226 [hep-ph]. [url]
[bib]
@article{RISC5618,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
title = {{The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$}},
language = {english},
journal = {Nucl. Phys. B},
volume = {932},
pages = {129--240},
isbn_issn = {ISSN 0550-3213},
year = {2018},
note = {arXiv:1804.02226 [hep-ph]},
refereed = {yes},
length = {112},
url = {https://doi.org/10.1016/j.nuclphysb.2018.04.023}
}

The Variable Flavor Number Scheme at Next-to-Leading Order

J. Blümlein, A. De Freitas, C. Schneider, K. Schönwald

Physics Letters B 782, pp. 362-366. 2018. ISSN: 0370-2693. arXiv:1804.03129 [hep-ph]. [url]
[bib]
@article{RISC5619,
author = {J. Blümlein and A. De Freitas and C. Schneider and K. Schönwald},
title = {{The Variable Flavor Number Scheme at Next-to-Leading Order}},
language = {english},
journal = {Physics Letters B},
volume = {782},
pages = {362--366},
isbn_issn = {ISSN: 0370-2693},
year = {2018},
note = {arXiv:1804.03129 [hep-ph]},
refereed = {yes},
length = {10},
url = { https://doi.org/10.1016/j.physletb.2018.05.054}
}

Heavy Quark Form Factors at Three Loops in the Planar Limit

J. Ablinger, J. Blümlein, P. Marquard, N. Rana, C. Schneider

Physics Letters B 782, pp. 528-532. 2018. ISSN: 0370-2693. arXiv:1804.07313 [hep-ph]. [url]
[bib]
@article{RISC5689,
author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},
title = {{Heavy Quark Form Factors at Three Loops in the Planar Limit}},
language = {english},
journal = {Physics Letters B},
volume = {782},
pages = {528--532},
isbn_issn = {ISSN: 0370-2693},
year = {2018},
note = {arXiv:1804.07313 [hep-ph]},
refereed = {yes},
length = {9},
url = {https://doi.org/10.1016/j.physletb.2018.05.077}
}

Analytic Computing Methods for Precision Calculations in Quantum Field Theory

J. Blümlein, C. Schneider

INTERNATIONAL JOURNAL OF MODERN PHYSICS A (IJMPA) 33(1830015), pp. 1-35. 2018. ISSN: 1793-656X. [url]
[bib]
@article{RISC5698,
author = {J. Blümlein and C. Schneider},
title = {{Analytic Computing Methods for Precision Calculations in Quantum Field Theory}},
language = {english},
journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A (IJMPA)},
volume = {33},
number = {1830015},
pages = {1--35},
isbn_issn = {ISSN: 1793-656X},
year = {2018},
refereed = {yes},
length = {29},
url = {https://doi.org/10.1142/S0217751X18300156}
}

The ρ parameter at three loops and elliptic integrals

J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, P. Marquard, C. Schneider

In: Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018, , to appear in PoS , pp. 1-14. 2018. arXiv:1807.05287 [hep-ph].
[bib]
@inproceedings{RISC5722,
author = {J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and P. Marquard and C. Schneider},
title = {{The ρ parameter at three loops and elliptic integrals}},
booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018}},
language = {english},
series = {to appear in PoS},
pages = {1--14},
isbn_issn = {?},
year = {2018},
note = {arXiv:1807.05287 [hep-ph]},
editor = {?},
refereed = {yes},
length = {14}
}

Two-mass three-loop effects in deep-inelastic scattering

J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald

In: submitted, , pp. 1-8. 2018. arXiv:1807.07855 [hep-ph]. [url]
[bib]
@inproceedings{RISC5728,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald},
title = {{Two-mass three-loop effects in deep-inelastic scattering}},
booktitle = {{submitted}},
language = {english},
pages = {1--8},
isbn_issn = {?},
year = {2018},
note = {arXiv:1807.07855 [hep-ph]},
editor = {?},
refereed = {yes},
length = {8},
url = {https://arxiv.org/abs/1807.07855}
}

2017

Discovering and Proving Infinite Binomial Sums Identities

J. Ablinger

Experimental Mathematics 26(1), pp. 62-71. 2017. ISSN 1058-6458. 10.1080/10586458.2015.1116028. [url]
[bib]
@article{RISC5159,
author = {J. Ablinger},
title = {{Discovering and Proving Infinite Binomial Sums Identities}},
language = {english},
journal = {Experimental Mathematics},
volume = {26},
number = {1},
pages = {62--71},
isbn_issn = {ISSN 1058-6458},
year = {2017},
note = {10.1080/10586458.2015.1116028},
refereed = {yes},
length = {10},
url = {http://arxiv.org/abs/1507.01703}
}

Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm

J. Ablinger

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang and C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-8. 2017. ISSN 1824-8039. arXiv:1801.01039 [cs.SC]. [url]
[bib]
@inproceedings{RISC5527,
author = {J. Ablinger},
title = {{Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 069},
pages = {1--8},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = {arXiv:1801.01039 [cs.SC]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {8},
url = {https://pos.sissa.it/290/001/pdf}
}

Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses

J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, C. Schneider, F. Wißbrock

Nucl. Phys. B. 921, pp. 585-688. 2017. ISSN 0550-3213. arXiv:1705.07030 [hep-ph]. [url]
[bib]
@article{RISC5451,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Hasselhuhn and C. Schneider and F. Wißbrock},
title = {{Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses}},
language = {english},
journal = {Nucl. Phys. B.},
volume = {921},
pages = {585--688},
isbn_issn = {ISSN 0550-3213},
year = {2017},
note = {arXiv:1705.07030 [hep-ph]},
refereed = {yes},
length = {99},
url = {https://arxiv.org/abs/1705.07030}
}

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C.G. Raab, C.-S. Radu, C. Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-13. 2017. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [url]
[bib]
@inproceedings{RISC5350,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},
title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 069},
pages = {1--13},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = {arXiv:1711.09742 [hep-ph]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {13},
url = {https://pos.sissa.it/290/069/pdf}
}

Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects

C. Schneider

J. Symb. Comput. 80(3), pp. 616-664. 2017. ISSN 0747-7171. arXiv:1603.04285 [cs.SC]. [url]
[bib]
@article{RISC5270,
author = {C. Schneider},
title = {{Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects}},
language = {english},
journal = {J. Symb. Comput.},
volume = {80},
number = {3},
pages = {616--664},
isbn_issn = {ISSN 0747-7171},
year = {2017},
note = {arXiv:1603.04285 [cs.SC]},
refereed = {yes},
length = {54},
url = {http://arxiv.org/abs/1603.04285}
}

Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm

C. Schneider, R. Sulzgruber

Electron. J. Combin. 24(2), pp. 1-33. 2017. ISSN: 1077-8926. #P2.28, arXiv:1606.07597. [url]
[bib]
@article{RISC5318,
author = {C. Schneider and R. Sulzgruber},
title = {{Asymptotic and exact results on the complexity of the Novelli--Pak--Stoyanovskii algorithm}},
language = {english},
journal = {Electron. J. Combin. },
volume = {24},
number = {2},
pages = {1--33},
isbn_issn = {ISSN: 1077-8926},
year = {2017},
note = {#P2.28, arXiv:1606.07597},
refereed = {yes},
length = {25},
url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p28}
}

The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory

J. Blümlein, C. Schneider

Physics Letters B 771, pp. 31-36. 2017. ISSN 0370-2693. arXiv:1701.04614 [hep-ph]. [url]
[bib]
@article{RISC5402,
author = {J. Blümlein and C. Schneider},
title = {{The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory}},
language = {english},
journal = {Physics Letters B},
volume = {771},
pages = {31--36},
isbn_issn = {ISSN 0370-2693},
year = {2017},
note = {arXiv:1701.04614 [hep-ph]},
refereed = {yes},
length = {6},
url = {https://doi.org/10.1016/j.physletb.2017.05.001}
}

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