Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants. (English) Zbl 1380.81438

Summary: We present analytical results at four-loop level for the renormalization constants and anomalous dimensions of an extended QCD model with one coupling constant and an arbitrary number of fermion representations. One example of such a model is the QCD plus gluinos sector of a supersymmetric theory where the gluinos are Majorana fermions in the adjoint representation of the gauge group.
The renormalization constants of the gauge boson (gluon), ghost and fermion fields are analytically computed as well as those for the ghost-gluon vertex, the fermion-gluon vertex and the fermion mass. All other renormalization constants can be derived from these. Some of these results were already produced in Feynman gauge for the computation of the \(\beta\)-function of this model, which was recently published [M. F. Zoller, “Four-loop QCD \(\beta\)-function with different fermion representations of the gauge group”, J. High Energy Phys. 2016, No. 10, Paper No. 118, 8 p. (2016; doi:10.1007/JHEP10(2016)118)]. Here we present results for an arbitrary \(\xi\)-parameter.


81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory


Full Text: DOI arXiv


[1] Zoller, MF, Four-loop QCD β-function with different fermion representations of the gauge group, JHEP, 10, 118, (2016)
[2] K.G. Chetyrkin, Four-loop renormalization of QCD: Full set of renormalization constants and anomalous dimensions, Nucl. Phys.B 710 (2005) 499 [hep-ph/0405193] [INSPIRE]. · Zbl 1115.81399
[3] T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The Four loop β-function in quantum chromodynamics, Phys. Lett.B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].
[4] M. Czakon, The Four-loop QCD β-function and anomalous dimensions, Nucl. Phys.B 710 (2005) 485 [hep-ph/0411261] [INSPIRE]. · Zbl 1115.81400
[5] J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett.B 405 (1997) 327 [hep-ph/9703284] [INSPIRE]. · Zbl 1377.81237
[6] K.G. Chetyrkin, Quark mass anomalous dimension to\( \mathcal{O}\left({α}_S^4\right) \), Phys. Lett.B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].
[7] K.G. Chetyrkin and A. Retey, Renormalization and running of quark mass and field in the regularization invariant and MS-bar schemes at three loops and four loops, Nucl. Phys.B 583 (2000) 3 [hep-ph/9910332] [INSPIRE]. · Zbl 1245.81033
[8] Baikov, PA; Chetyrkin, KG; Kühn, JH, Five-loop running of the QCD coupling constant, Phys. Rev. Lett., 118, (2017)
[9] Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, JAM; Vogt, A., The five-loop β-function of Yang-Mills theory with fermions, JHEP, 02, 090, (2017) · Zbl 1377.81103
[10] Luthe, T.; Maier, A.; Marquard, P.; Schröder, Y., Towards the five-loop β-function for a general gauge group, JHEP, 07, 127, (2016) · Zbl 1390.81644
[11] H. Suman and K. Schilling, First lattice study of ghost propagators in SU(2) and SU(3) gauge theories, Phys. Lett.B 373 (1996) 314 [hep-lat/9512003] [INSPIRE].
[12] D. Becirevic et al., Asymptotic scaling of the gluon propagator on the lattice, Phys. Rev.D 61 (2000) 114508 [hep-ph/9910204] [INSPIRE]. · Zbl 0782.68091
[13] D. Becirevic et al., Asymptotic behavior of the gluon propagator from lattice QCD, Phys. Rev.D 60 (1999) 094509 [hep-ph/9903364] [INSPIRE].
[14] D. Becirevic et al., Gluon propagator, triple gluon vertex and the QCD coupling constant, Nucl. Phys. Proc. Suppl.83 (2000) 159 [hep-lat/9908056] [INSPIRE].
[15] Smekal, L.; Maltman, K.; Sternbeck, A., The strong coupling and its running to four loops in a minimal MOM scheme, Phys. Lett., B 681, 336, (2009)
[16] ETM collaboration, B. Blossier et al., \(α\)_{\(S\)}from Lattice QCD: progresses and perspectives for a realistic full-QCD determination of the running Strong coupling, PoS(ICHEP 2010)372 [arXiv:1012.3135] [INSPIRE].
[17] B. Blossier et al., RI/MOM renormalization constants (\(N\)_{\(f\)} = 4) and the strong coupling constant (\(N\)_{\(f\)} = 2 + 1 + 1) from twisted-mass QCD, PoS(LATTICE 2011)223 [arXiv:1111.3023] [INSPIRE].
[18] Bornyakov, VG; Ilgenfritz, EM; Litwinski, C.; Mitrjushkin, VK; Muller-Preussker, M., Landau gauge ghost propagator and running coupling in SU(2) lattice gauge theory, Phys. Rev., D 92, (2015)
[19] L. Clavelli, P.W. Coulter and L.R. Surguladze, Gluino contribution to the three loop β-function in the minimal supersymmetric standard model, Phys. Rev.D 55 (1997) 4268 [hep-ph/9611355] [INSPIRE].
[20] Denner, A.; Eck, H.; Hahn, O.; Kublbeck, J., Feynman rules for fermion number violating interactions, Nucl. Phys., B 387, 467, (1992)
[21] Nogueira, P., Automatic Feynman graph generation, J. Comput. Phys., 105, 279, (1993) · Zbl 0782.68091
[22] T. Seidensticker, Automatic application of successive asymptotic expansions of Feynman diagrams, hep-ph/9905298 [INSPIRE].
[23] R. Harlander, T. Seidensticker and M. Steinhauser, Complete corrections of O(αα_{\(s\)}) to the decay of the Z boson into bottom quarks, Phys. Lett.B 426 (1998) 125 [hep-ph/9712228] [INSPIRE].
[24] M. Misiak and M. Münz, Two loop mixing of dimension five flavor changing operators, Phys. Lett.B 344 (1995) 308 [hep-ph/9409454] [INSPIRE].
[25] K.G. Chetyrkin, M. Misiak and M. Münz, β-functions and anomalous dimensions up to three loops, Nucl. Phys.B 518 (1998) 473 [hep-ph/9711266] [INSPIRE]. · Zbl 0945.81064
[26] Y. Schröder, Automatic reduction of four loop bubbles, Nucl. Phys. Proc. Suppl.116 (2003) 402 [hep-ph/0211288] [INSPIRE].
[27] F. Di Renzo, A. Mantovi, V. Miccio and Y. Schröder, 3-D lattice QCD free energy to four loops, JHEP05 (2004) 006 [hep-lat/0404003] [INSPIRE].
[28] Chetyrkin, KG; Zoller, MF, Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the standard model, JHEP, 06, 033, (2012)
[29] Zoller, MF, Top-Yukawa effects on the β-function of the strong coupling in the SM at four-loop level, JHEP, 02, 095, (2016)
[30] Chetyrkin, KG; Zoller, MF, Leading QCD-induced four-loop contributions to the β-function of the Higgs self-coupling in the SM and vacuum stability, JHEP, 06, 175, (2016)
[31] M.F. Zoller, Three-loop β-function for the Higgs self-coupling, PoS(LL2014)014 [arXiv:1407.6608] [INSPIRE].
[32] J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
[33] M. Tentyukov and J.A.M. Vermaseren, The Multithreaded version of FORM, Comput. Phys. Commun.181 (2010) 1419 [hep-ph/0702279] [INSPIRE].
[34] M. Steinhauser, MATAD: A program package for the computation of MAssive TADpoles, Comput. Phys. Commun.134 (2001) 335 [hep-ph/0009029] [INSPIRE]. · Zbl 0978.81058
[35] Smirnov, AV, Algorithm FIRE — Feynman integral reduction, JHEP, 10, 107, (2008) · Zbl 1245.81033
[36] Smirnov, AV, FIRE5: a C++ implementation of Feynman integral reduction, Comput. Phys. Commun., 189, 182, (2015) · Zbl 1344.81030
[37] Luthe, T.; Maier, A.; Marquard, P.; Schröder, Y., Complete renormalization of QCD at five loops, JHEP, 03, 020, (2017) · Zbl 1377.81237
[38] Vladimirov, AA, Method for computing renormalization group functions in dimensional renormalization scheme, Theor. Math. Phys., 43, 417, (1980)
[39] Chetyrkin, KG; Smirnov, VA, R\^{}{*} operation corrected, Phys. Lett., B 144, 419, (1984)
[40] K.G. Chetyrkin, Combinatorics of R-, R\^{}{−1}- and R\^{}{*}-operations and asymptotic expansions of Feynman integrals in the limit of large momenta and masses, arXiv:1701.08627 [INSPIRE]. · Zbl 1344.81030
[41] P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Massless Propagators, R(\(s\)) and Multiloop QCD, Nucl. Part. Phys. Proc.261-262 (2015) 3 [arXiv:1501.06739] [INSPIRE]. · Zbl 1390.81644
[42] Davydychev, AI; Tausk, JB, Two loop selfenergy diagrams with different masses and the momentum expansion, Nucl. Phys., B 397, 123, (1993)
[43] S.A. Larin, F.V. Tkachov and J.A.M. Vermaseren, The FORM version of MINCER, NIKHEF-H-91-18 [INSPIRE].
[44] T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys.A 14 (1999) 41 [hep-ph/9802376] [INSPIRE]. · Zbl 0924.22017
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