Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 44 min ago
PreprintCC BY 4.0arXiv

Holonomic techniques for massive 3-loop form factors: the gluonic case

  • J. Blümlein
  • A. De Freitas
  • P. Marquard
  • J. Obrovsky
  • C. Schneider
Open at sourcePDFDOICite

Abstract

Massive three-loop form factors for vector, axial-vector, scalar, and pseudoscalar currents are vital for precision collider phenomenology. Extending the quarkonic framework to the more complex gluonic case, in Ref. (arXiv:2609.22034 [hep-ph]) we computed these contributions widely using advanced computer algebra, automated guessing, and large-scale PSLQ searches. Here, we outline the core strategy of the large-moment method and illustrate its main challenges, including solving record-sized recurrences and differential equations. Our high-precision evaluation provides an exact analytic representation around s=0 in terms of MZVs. We achieved a complete analytic series expansion around s=±∞ for the first time, which depends on MZVs and three constants out of higher number spaces, along with reliable analytic continuations across s ∈ (−∞, ∞), serving as a landmark benchmark for modern symbolic computation.

Related

  1. Analytic results on the massive three-loop form factors: gluonic contributions
    J. Blümlein, A. De Freitas, P. Marquard +2
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  2. Polyakov-loop potential of accelerated gluonic matter and thermodynamic subtleties
    Hao-Lei Chen, Kenji Fukushima, Yu-Han Gao +3
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
  3. New results for the 4-loop massive cusp anomalous dimension
    Nikolaos Kidonakis
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  4. Bonanno–Reuter regular black hole: Quasi-resonances, grey-body factors and absorption cross-sections of a massive scalar field
    Zainab Malik
    Annals of PhysicsPeer-reviewedLicence not statedFull text7 citedHigh-energy & particle physicsOpenAlex
  5. Exact spin form factors and correlations at a massive Kramers-Wannier interface
    Zoltan Bajnok, Yizhuang Liu
    arXivPreprintCC0Full textHigh-energy & particle physicsStatistical & nonlinear physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{blumlein2026holonomic,
  title = {{Holonomic techniques for massive 3-loop form factors: the gluonic case}},
  author = {J. Blümlein and A. De Freitas and P. Marquard and J. Obrovsky and C. Schneider},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24279},
  eprint = {2609.24279},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24279},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Holonomic techniques for massive 3-loop form factors: the gluonic case
AU  - J. Blümlein
AU  - A. De Freitas
AU  - P. Marquard
AU  - J. Obrovsky
AU  - C. Schneider
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24279
UR  - https://arxiv.org/abs/2609.24279
AB  - Massive three-loop form factors for vector, axial-vector, scalar, and pseudoscalar currents are vital for precision collider phenomenology. Extending the quarkonic framework to the more complex gluonic case, in Ref. (arXiv:2609.22034 [hep-ph]) we computed these contributions widely using advanced computer algebra, automated guessing, and large-scale PSLQ searches. Here, we outline the core strategy of the large-moment method and illustrate its main challenges, including solving record-sized recurrences and differential equations. Our high-precision evaluation provides an exact analytic representation around s=0 in terms of MZVs. We achieved a complete analytic series expansion around s=±∞ for the first time, which depends on MZVs and three constants out of higher number spaces, along with reliable analytic continuations across s ∈ (−∞, ∞), serving as a landmark benchmark for modern symbolic computation.
ER  -