Computer Algebra for Multi-Loop Feynman Integrals

Project Lead

Project Duration

01/09/2021 - 31/08/2025

Publications

2022

[Schneider]

New 2– and 3–loop heavy flavor corrections to unpolarized and polarized deep-inelastic scattering

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

SciPost Phys. Proc.(8), pp. 137.1-137.15. 2022. ISSN 2666-4003. DIS2021, arXiv:2107.09350 [hep-ph]. [doi]
[bib]
@article{RISC6497,
author = {J. Ablinger and J. Blümlein and A. De Freitas and M. Saragnese and C. Schneider and K. Schönwald},
title = {{New 2– and 3–loop heavy flavor corrections to unpolarized and polarized deep-inelastic scattering}},
language = {english},
abstract = {A survey is given on the new 2-- and 3--loop results for the heavy flavor contributions to deep--inelastic scattering in the unpolarized and the polarized case. We also discuss related new mathematical aspectsapplied in these calculations.},
journal = {SciPost Phys. Proc.},
number = {8},
pages = {137.1--137.15},
isbn_issn = {ISSN 2666-4003},
year = {2022},
note = {DIS2021, arXiv:2107.09350 [hep-ph]},
refereed = {yes},
length = {15},
url = {https://www.doi.org/10.21468/SciPostPhysProc.8.137}
}
[Schneider]

The 3-loop anomalous dimensions from off-shell operator matrix elements

J. Blümlein, P. Marquard, C. Schneider, K. Schönwald

In: To appear in Proc. of Loops and Legs in Quantum Field Theory - LL 2022, P. Marquard, M. Steinhauser (ed.)PoS (LL2022) 048, pp. 1-12. July 2022. ISSN 1824-8039. arXiv:2207.07943 [hep-ph]. [doi]
[bib]
@inproceedings{RISC6528,
author = {J. Blümlein and P. Marquard and C. Schneider and K. Schönwald},
title = {{The 3-loop anomalous dimensions from off-shell operator matrix elements}},
booktitle = {{To appear in Proc. of Loops and Legs in Quantum Field Theory - LL 2022}},
language = {english},
abstract = {We report on the calculation of the three--loop polarized and unpolarized flavor non--singlet and the polarized singlet anomalous dimensions using massless off--shell operator matrix elements in a gauge--variant framework. We also reconsider the unpolarized two--loop singlet anomalous dimensions and correct errors in the foregoing literature.},
number = {PoS (LL2022) 048},
pages = {1--12},
isbn_issn = {ISSN 1824-8039},
year = {2022},
month = {July},
note = { arXiv:2207.07943 [hep-ph]},
editor = {P. Marquard and M. Steinhauser},
refereed = {no},
keywords = {hypergeometric series, Appell-series, symbolic summation, coupled systems, partial linear difference equations},
length = {12},
url = {https://doi.org/10.48550/arXiv.2207.08524}
}
[Schneider]

Error bounds for the asymptotic expansion of the partition function

Koustav Banerjee, Peter Paule, Cristian-Silviu Radu, Carsten Schneider

Technical report no. 22-13 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). September 2022. arXiv:2209.07887 [math.NT]. Licensed under CC BY 4.0 International. [doi] [pdf]
[bib]
@techreport{RISC6620,
author = {Koustav Banerjee and Peter Paule and Cristian-Silviu Radu and Carsten Schneider},
title = {{Error bounds for the asymptotic expansion of the partition function}},
language = {english},
abstract = {Asymptotic study on the partition function $p(n)$ began with the work of Hardy and Ramanujan. Later Rademacher obtained a convergent series for $p(n)$ and an error bound was given by Lehmer. Despite having this, a full asymptotic expansion for $p(n)$ with an explicit error bound is not known. Recently O'Sullivan studied the asymptotic expansion of $p^{k}(n)$-partitions into $k$th powers, initiated by Wright, and consequently obtained an asymptotic expansion for $p(n)$ along with a concise description of the coefficients involved in the expansion but without any estimation of the error term. Here we consider a detailed and comprehensive analysis on an estimation of the error term obtained by truncating the asymptotic expansion for $p(n)$ at any positive integer $n$. This gives rise to an infinite family of inequalities for $p(n)$ which finally answers to a question proposed by Chen. Our error term estimation predominantly relies on applications of algorithmic methods from symbolic summation. },
number = {22-13},
year = {2022},
month = {September},
note = {arXiv:2209.07887 [math.NT]},
keywords = {partition function, asymptotic expansion, error bounds, symbolic summation},
length = {43},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

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