White Paper (2025)
White Paper (2025)
arXiv link:
https://arxiv.org/abs/2505.21476
Publication information:
Submitted for publication in Physics Reports
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About
The full list of authors of the White Paper is listed in the arXiv submission.
Section Authors
The major sections of the White Paper were written and edited by the section authors listed at the top of each section:
- Section 2: Data-driven calculations of HVP
R. Aliberti, G. Benton, D. Boito, M. Bruno, C. M. Carloni Calame, V. Cirigliano, G. Colangelo, L. Cotrozzi, M. Cottini, M. Davier, A. Denig, V. Druzhinin, M. Golterman, A. Hoecker, M. Hoferichter, B.-L. Hoid, S. Holz, F. Ignatov, A. Keshavarzi, B. Kubis, A. Kupich, S. Laporta, T. Leplumey, Q. Liu, I. Logashenko, G. López Castro, A.-M. Lutz, B. Malaescu, K. Maltman, A. Miranda, S. E. M¨uller, A. Nesterenko, D. Nomura, M. Passera, S. Peris, F. Piccinini, R. Pilato, L. Polat, P. Roig, J. Ruiz de Elvira, A. Signer, P. Stoffer, T. Teubner, G. Toledo, Y. Ulrich, G. Venanzoni, A. Wright, E. Zaid, Z. Zhang - Section 3: Lattice QCD calculations of HVP
T. Blum, M. Bruno, M. Cè, D. Clarke, M. Della Morte, C. DeTar, A. X. El-Khadra, R. Frezzotti, G. Gagliardi, A. Gérardin, D. Giusti, S. Gottlieb, V. Gülpers, S. Kuberski, S. Lahert, C. Lehner, L. Lellouch, M. K. Marinković, H. Meyer, E. Neil, J. Parrino, A. Portelli, J. Sitison, J. T. Tsang, R. Van de Water, G. Wang, H. Wittig - Section 4: Interplay of lattice-QCD and data-driven evaluations of HVP
D. Boito, A. X. El-Khadra, M. Golterman, M. Hoferichter, C. Lehner, L. Lellouch, T. Leplumey, B. Malaescu - Section 5: Data-driven and analytic approaches to HLbL
J. Bijnens, L. Cappiello, G. Eichmann, C. S. Fischer, S. Gonzàlez-Solís, N. Hermansson-Truedsson, M. Hoferichter, B.-L. Hoid, S. Holz, B. Kubis, A. Kupść, P. Masjuan, M. Procura, A. Rebhan, C. F. Redmer, A. Rodríguez-Sánchez, P. Roig, P. Sánchez-Puertas, P. Stoffer, M. Zillinger - Section 6: Lattice approaches to HLbL
X. Feng, A. Gérardin, L. Jin, T. Lin, H. Meyer - Section 7: The QED contributions to $a_\mu$
T. Aoyama, M. Hayakawa, M. Nio, S. Volkov - Section 8: The electroweak contributions to $a_\mu$
D. Stöckinger, H. Stöckinger-Kim
Coordinators
This review is organized in four main chapters, the writing of which was delegated to four corresponding working groups. The Coordinators of the working groups are:
- Data-Driven HVP:
Vincenzo Cirigliano, Achim Denig, Fedor Ignatov, Bogdan Malaescu - Lattice HVP:
Steven Gottlieb, Antonin Portelli - Analytic HLbL:
Johan (Hans) Bijnens, Anton Rebhan - Lattice HLbL:
Luchang Jin, Harvey Meyer
In addition, sections on the QED and EW contributions are coordinated by Makiko Nio and Dominik Stöckinger, respectively.
Editorial Board
The writing of the updated White Paper by the section authors was coordinated by the steering committee, which also performed the final assembly into one document:
- Gilberto Colangelo (University of Bern)
- Michel Davier (University of Paris-Saclay and CNRS, Orsay)
- Aida X. El-Khadra (University of Illinois Urbana-Champaign)
- Martin Hoferichter (University of Bern)
- Christoph Lehner (University of Regensburg)
- Laurent Lellouch (Aix-Marseille University)
- Tsutomu Mibe (KEK)
- Lee Roberts (Boston University)
- Thomas Teubner (University of Liverpool)
- Hartmut Wittig (University of Mainz)
Summary Table
Summary of the contributions to $a_\mu$. After the experimental
number from E989 and E821, the first block gives the main results for
the hadronic contributions from Secs. 2-6, as well as the combined result for
HLbL scattering from phenomenology and lattice QCD constructed
in Sec. 9.
The second block summarizes the quantities entering our recommended SM value, in particular, the total HVP contribution, evaluated from lattice QCD calculations and $e^+e^-$ and $\tau$ data, and the total HLbL number.
The construction of the total HVP and HLbL contributions takes into account correlations among the terms at different orders, and the final rounding includes subleading digits at intermediate stages.
In the Citation Refs. column the references upon which the
corresponding results are based are listed as downloadable
bib files together with the citation commands.
| Contribution | Section | Equation | Value x 1011 | Citation Refs |
|---|---|---|---|---|
| Experimental average (E821+E989) | Eq. (9.5) | 116 592 071.5(14.5) | bib, cite | |
| HVP LO (lattice) | Sec. 3.6.1 | Eq. (3.37) | 7132(61) | bib, cite |
| HVP LO ($e^+e^-, \tau$) | Sec. 2 | Table 5 | Estimates not provided at this point | bib, cite |
| HVP NLO ($e^+e^-$) | Sec. 2.9 | Eq. (2.47) | -99.6(1.3) | bib, cite |
| HVP NNLO ($e^+e^-$) | Sec. 2.9 | Eq. (2.48) | 12.4(1) | bib, cite |
| HLbL (phenomenology) | Sec. 5.10 | Eq. (5.69) | 103.3(8.8) | bib, cite |
| HLbL NLO (phenomenology) | Sec. 5.10 | Eq. (5.70) | 2.6(6) | bib, cite |
| HLbL (lattice) | Sec. 6.2.8 | Eq. (6.34) | 122.5(9.0) | bib, cite |
| HLbL (phenomenology + lattice) | Sec. 9 | Eq. (9.2) | 112.6(9.6) | bib, cite |
| QED | Sec. 7.5 | Eq. (7.27) | 116 584 718.8(2) | bib, cite |
| EW | Sec. 8 | Eq. (8.12) | 154.4(4) | bib, cite |
| HVP LO (lattice) + HVP N(N)LO($e^+e^-$) | Sec. 9 | Eq. (9.1) | 7045(61) | bib, cite |
| HLbL (phenomenology + lattice + NLO) | Sec. 9 | Eq. (9.3) | 115.5(9.9) | bib, cite |
| Total SM Value | Sec. 9 | Eq. (9.4) | 116 592 033(62) | bib, cite |
| Difference: $\Delta a_\mu\colon= a_\mu^{\text{exp}}-a_\mu^{\text{SM}}$ | Sec. 9 | Eq. (9.6) | 38(63) |
Summary Plots
Figure 40: Summary of various determinations of $a_{\mu}^{\text{HVP, LO}}$ propagated to $a_{\mu}^{\text{SM}}$. The red band denotes the experimental world average, the grey band indicates the WP20 result based on $e^+e^-$ experiments above the first dashed line, and the blue band denotes the final WP25 result.
Figure 82: Summary of HLbL evaluations, from data-driven methods (green), lattice QCD (blue), and combinations (black).
Figure 83: Summary of the current SM prediction for $a_{\mu}$ in comparison to experiment (red band and data points). The final WP25 prediction is denoted in black and via the blue band.