- Open Access
Complete two-loop unrenormalized electroweak corrections to
Phys. Rev. D 114, 013003 – Published 8 July, 2026
DOI: https://doi.org/10.1103/5ssz-gr6j
Abstract
We compute the complete two-loop unrenormalized electroweak corrections to the Higgsstrahlung process at future Higgs factories. Our result for a given center-of-mass energy is expressed as a piecewise function defined by several deeply expanded power series, which has high precision and can be further manipulated efficiently. We find that the finite part of the unrenormalized two-loop electroweak corrections can contribute a few thousandths, which might indicate their importance to match the precision of future Higgs factories. This work represents the first complete calculation of the unrenormalized two-loop electroweak corrections for processes with four external particles.
Physics Subject Headings (PhySH)
Article Text
References (54)
- G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
- S. Chatrchyan et al. (CMS Collaboration), Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012).
- H. Baer et al., The International Linear Collider Technical Design Report—Volume 2: Physics, arXiv:1306.6352.
- T. Behnke et al., The International Linear Collider Technical Design Report—Volume 1: Executive Summary, arXiv:1306.6327.
- P. Bambade et al., The international linear collider: A global project, arXiv:1903.01629.
- M. Dong et al. (CEPC Study Group), CEPC Conceptual Design Report: Volume 2—Physics & Detector, arXiv:1811.10545.
- CEPC Study Group, CEPC Conceptual Design Report: Volume 1—Accelerator, arXiv:1809.00285.
- M. Bicer et al. (TLEP Design Study Working Group), First look at the physics case of TLEP, J. High Energy Phys. 01 (2014) 164.
- A. Abada et al. (FCC Collaboration), FCC physics opportunities: Future circular collider conceptual design report Volume 1, Eur. Phys. J. C 79, 474 (2019).
- A. Abada et al. (FCC Collaboration), FCC-ee: The Lepton collider: Future circular collider conceptual design report Volume 2, Eur. Phys. J. Special Topics 228, 261 (2019).
- F. An et al., Precision Higgs physics at the CEPC, Chin. Phys. C 43, 043002 (2019).
- J. Fleischer and F. Jegerlehner, Radiative corrections to Higgs production by in the Weinberg-Salam model, Nucl. Phys. B216, 469 (1983).
- B. A. Kniehl, Radiative corrections for associated production at future colliders, Z. Phys. C 55, 605 (1992).
- A. Denner, J. Kublbeck, R. Mertig, and M. Bohm, Electroweak radiative corrections to H Z, Z. Phys. C 56, 261 (1992).
- Y. Gong, Z. Li, X. Xu, L. L. Yang, and X. Zhao, Mixed QCD-EW corrections for Higgs boson production at colliders, Phys. Rev. D 95, 093003 (2017).
- Q.-F. Sun, F. Feng, Y. Jia, and W.-L. Sang, Mixed electroweak-QCD corrections to at Higgs factories, Phys. Rev. D 96, 051301 (2017).
- W. Chen, F. Feng, Y. Jia, and W.-L. Sang, Mixed electroweak-QCD corrections to at CEPC with finite-width effect, Chin. Phys. C 43, 013108 (2019).
- C. Ma, Y. Wang, X. Xu, L. L. Yang, and B. Zhou, Mixed QCD-EW corrections for Higgs leptonic decay via vertex, J. High Energy Phys. 09 (2021) 114.
- Q. Song and A. Freitas, On the evaluation of two-loop electroweak box diagrams for production, J. High Energy Phys. 04 (2021) 179.
- X. Liu and Y.-Q. Ma, Multiloop corrections for collider processes using auxiliary mass flow, Phys. Rev. D 105, L051503 (2022).
- Z. Li, Y. Wang, and Q.-f. Wu, Categorization of two-loop Feynman diagrams in the correction to , Chin. Phys. C 45, 053102 (2021).
- S. Weinzierl, Feynman Integrals. A Comprehensive Treatment for Students and Researchers, UNITEXT for Physics (Springer, New York, 2022).
- J. L. Bourjaily et al., Functions beyond multiple polylogarithms for precision collider physics, arXiv:2203.07088.
- P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105, 279 (1993).
- P. Nogueira, Feynman graph generation and propagator mixing, I, Comput. Phys. Commun. 269, 108103 (2021).
- T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140, 418 (2001).
- F. Jegerlehner, Facts of life with , Eur. Phys. J. C 18, 673 (2001).
- D. Kreimer, The problem and anomalies: A clifford algebra approach, Phys. Lett. B 237, 59 (1990).
- J. G. Korner, D. Kreimer, and K. Schilcher, A Practicable scheme in dimensional regularization, Z. Phys. C 54, 503 (1992).
- D. Kreimer, The role of gamma(5) in dimensional regularization, arXiv:hep-ph/9401354.
- L. Chen, An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting , J. High Energy Phys. 11 (2023) 30.
- K. G. Chetyrkin and F. V. Tkachov, Integration by parts: The algorithm to calculate beta functions in 4 loops, Nucl. Phys. B192, 159 (1981).
- R. N. Lee, LiteRed 1.4: A powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523, 012059 (2014).
- T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs, J. High Energy Phys. 07 (2019) 031.
- S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15, 5087 (2000).
- X. Liu and Y.-Q. Ma, Determining arbitrary Feynman integrals by vacuum integrals, Phys. Rev. D 99, 071501 (2019).
- X. Guan, X. Liu, and Y.-Q. Ma, Complete reduction of two-loop five-light-parton scattering amplitudes, Chin. Phys. C 44, 093106 (2020).
- A. V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation, Phys. Lett. B 254, 158 (1991).
- M. Caffo, H. Czyz, M. Gunia, and E. Remiddi, BOKASUN: A Fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams, Comput. Phys. Commun. 180, 427 (2009).
- M. Czakon, Tops from light quarks: Full mass dependence at two-loops in QCD, Phys. Lett. B 664, 307 (2008).
- X. Liu, Y.-Q. Ma, and C.-Y. Wang, A systematic and efficient method to compute multi-loop master integrals, Phys. Lett. B 779, 353 (2018).
- X. Liu, Y.-Q. Ma, W. Tao, and P. Zhang, Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow, Chin. Phys. C 45, 013115 (2021).
- Z.-F. Liu and Y.-Q. Ma, Feynman integrals are completely determined by linear algebra, Phys. Rev. Lett. 129, 222001 (2022).
- X. Liu and Y.-Q. Ma, AMFlow: A Mathematica package for Feynman integrals computation via Auxiliary Mass Flow, Comput. Phys. Commun. 283, 108565 (2023).
- M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions, Comput. Phys. Commun. 269, 108125 (2021).
- T. Armadillo, R. Bonciani, S. Devoto, N. Rana, and A. Vicini, Evaluation of Feynman integrals with arbitrary complex masses via series expansions, Comput. Phys. Commun. 282, 108545 (2023).
- R. M. Prisco, J. Ronca, and F. Tramontano, LINE: Loop integrals numerical evaluation, J. High Energy Phys. 07 (2025) 219.
- P. Zhang, C.-Y. Wang, X. Liu, Y.-Q. Ma, C. Meng, and K.-T. Chao, Semi-analytical calculation of gluon fragmentation into quarkonia at next-to-leading order, J. High Energy Phys. 04 (2019) 116.
- R. L. Workman (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
- A. Freitas, W. Hollik, W. Walter, and G. Weiglein, Complete fermionic two-loop results for the MW–MZ interdependence, Phys. Lett. B 495, 338 (2000).
- A. Freitas and Q. Song, Two-loop electroweak corrections with Fermion loops to , Phys. Rev. Lett. 130, 031801 (2023).
- D. Binosi and L. Theussl, JaxoDraw: A graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161, 76 (2004).
- M. Beneke and V. A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B522, 321 (1998).
- V. A. Smirnov, Problems of the strategy of regions, Phys. Lett. B 465, 226 (1999).