- Open Access
theory at six loops
Phys. Rev. D 112, 016028 – Published 31 July, 2025
DOI: https://doi.org/10.1103/sp5q-km2c
Abstract
We present the renormalization functions of dimensionally regularized theory in six dimensions up to loop order six in the minimal subtraction scheme.
Physics Subject Headings (PhySH)
See Also
theory at seven loops
Phys. Rev. D 107, 036002 (2023)
Article Text
Supplemental Material
References (44)
- J. C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
- J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, International Series of Monographs on Physics 113, (Clarendon Press, Oxford, 2002).
- K. G. Chetyrkin and F. V. Tkachov, Integration by parts: The algorithm to calculate -functions in 4 loops, Nucl. Phys. B192, 159 (1981).
- F. V. Tkachov, A theorem on analytical calculability of 4-loop renormalization group functions, Phys. Lett. 100B, 65 (1981).
- K. G. Chetyrkin and V. A. Smirnov, -operation corrected, Phys. Lett. 144B, 419 (1984).
- K. G. Chetyrkin and F. V. Tkachov, Infrared -operation and ultraviolet counterterms in the MS-scheme, Phys. Lett. 114B, 340 (1982).
- M. V. Kompaniets and E. Panzer, Minimally subtracted six loop renormalization of -symmetric theory and critical exponents, Phys. Rev. D 96, 036016 (2017).
- P. A. Baikov, K. G. Chetyrkin, and J. H. Kühn, Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators, J. High Energy Phys. 04 (2017) 119.
- P. A. Baikov, K. G. Chetyrkin, and J. H. Kühn, Five-loop running of the QCD coupling constant, Phys. Rev. Lett. 118, 082002 (2017).
- P. A. Baikov, K. G. Chetyrkin, J. H. Kühn, and J. Rittinger, Vector correlator in massless QCD at order and the QED -function at five Loop, J. High Energy Phys. 07 (2012) 017.
- M. Borinsky, J. A. Gracey, M. V. Kompaniets, and O. Schnetz, Five loop renormalization of theory with applications to the Lee-Yang edge singularity and percolation theory, Phys. Rev. D 103, 116024 (2021).
- K. G. Chetyrkin, G. Falcioni, F. Herzog, and J. A. M. Vermaseren, Five-loop renormalisation of QCD in covariant gauges, J. High Energy Phys. 10 (2017) 179.
- F. Herzog, B. Ruijl, T. Ueda, J. A. M. Vermaseren, and A. Vogt, The five-loop beta function of Yang-Mills theory with fermions, J. High Energy Phys. 02 (2017) 090.
- F. Herzog, S. Moch, B. Ruijl, T. Ueda, J. A. M. Vermaseren, and A. Vogt, Five-loop contributions to low- non-singlet anomalous dimensions in QCD, Phys. Lett. B 790, 436 (2019).
- A. L. Kataev and S. A. Larin, Analytical five-loop expressions for the renormalization group QED -function in different renormalization schemes, JETP Lett. 96, 61 (2012).
- M. V. Kompaniets and A. Pikelner, Critical exponents from five-loop scalar theory renormalization near six-dimensions, Phys. Lett. B 817, 136331 (2021).
- T. Luthe, A. Maier, P. Marquard, and Y. Schröder, Five-loop quark mass and field anomalous dimensions for a general gauge group, J. High Energy Phys. 01 (2017) 081.
- T. Luthe, A. Maier, P. Marquard, and Y. Schröder, Complete renormalization of QCD at five loops, J. High Energy Phys. 03 (2017) 020.
- T. Luthe, A. Maier, P. Marquard, and Y. Schröder, The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge, J. High Energy Phys. 10 (2017) 166.
- O. Schnetz, Graphical functions and single-valued multiple polylogarithms, Commun. Number Theory Phys. 8, 589 (2014).
- M. Golz, E. Panzer, and O. Schnetz, Graphical functions in parametric space, Lett. Math. Phys. 107, 1177 (2017).
- O. Schnetz, Generalized single-valued hyperlogarithms, arXiv:2111.11246.
- F. C. S. Brown, Feynman amplitudes, coaction principle, and cosmic Galois group, Commun. Num. Theor. Phys. 11, 453 (2017).
- F. C. S. Brown, Notes on motivic periods, Commun. Num. Theor. Phys. 11, 557 (2017).
- E. Panzer and O. Schnetz, The Galois coaction on periods, Commun. Num. Theor. Phys. 11, 657 (2017).
- S. Caron-Huot, L. J. Dixon, F. Dulat, M. von Hippel, A. J. McLeod, and G. Papathanasiou, The cosmic Galois group and extended Steinmann relations for planar SYM amplitudes, J. High Energy Phys. 09 (2019) 061.
- O. Schnetz, The Galois coaction on the electron anomalous magnetic moment, Commun. Num. Theor. Phys. 12, 335 (2018).
- M. Borinsky and O. Schnetz, Graphical functions in even dimensions, Commun. Num. Theor. Phys. 16, 515 (2022).
- M. Borinsky and O. Schnetz, Recursive computation of Feynman periods, J. High Energy Phys. 08 (2022) 291.
- O. Schnetz, hyperlogprocedures, Version 0.8, maple package available on the homepage of the author at https://www.physik.uni-hamburg.de/th2/ag-moch/personen/schnetz-oliver.html (2025).
- O. Schnetz, theory at seven loops, Phys. Rev. D 107, 036002 (2023).
- O. Schnetz, Loop calculations with graphical functions, in talk presented at RadCor, Crieff, UK (2023).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/sp5q-km2c for renormalization functions in theory and in theory.
- O. Schnetz, Graphical functions with spin, J. High Energy Phys. 06 (2025) 053.
- O. Schnetz, Numbers and functions in quantum field theory, Phys. Rev. D 97, 085018 (2018).
- M. d’Eramo, L. Peliti, and G. Parisi, Theoretical predictions for critical exponents at the -point of Bose liquids, Lett. Nuovo Cimento 2, 878 (1971).
- S. Jeffries and K. A. Yeats, A degree preserving delta wye transformation with applications to 6-regular graphs and Feynman periods, Ann. Inst. Henri Poincaré D 11, 641 (2024).
- D. I. Kazakov, The method of uniqueness, a new powerful technique for multiloop calculations, Phys. Lett. 133B, 406 (1983).
- G. Parisi, On self-consistency conditions in conformal covariant field theory, Lett. Nuovo Cimento 4, 777 (1972).
- S. Laporta, High-precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15, 5087 (2000).
- S. Laporta and E. Remiddi, The analytical value of the electron () at order in QED, Phys. Lett. B 379, 283 (1996).
- S. Weinzierl, Feynman Integrals (Springer Nature, Cham, Switzerland, 2022).
- D. J. Broadhurst and D. Kreimer, Knots and numbers in theory to 7 loops and beyond, Int. J. Mod. Phys. C 06, 519 (1995).
- O. Schnetz, Quantum periods: A census of transcendentals, Commun. Num. Theor. Phys. 4, 1 (2010).