Abstract
The QED hadronic vacuum polarization function plays an important role in the determination of precision electroweak observables and of the anomalous magnetic moment of the muon. These contributions have been computed from data, by means of dispersion relations affecting the electron positron hadronic cross sections, or by first principle lattice-QCD computations in the Standard Model. Today there is a discrepancy between the two approaches for determining these contributions, which affects the comparison of the measurement of the anomalous magnetic moment of the muon with the theoretical predictions. In this article, we revisit the idea that this discrepancy may be explained by the presence of a new light gauge boson that couples to the first generation quark and leptons and has a mass below the GeV scale. We discuss the requirements for its consistency with observations and the phenomenological implications of such a gauge extension.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Muon g − 2 collaboration, Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46,ppm, Phys. Rev. Lett. 126 (2021) 141801 [arXiv:2104.03281] [INSPIRE].
Muon g − 2 collaboration, Measurement of the negative muon anomalous magnetic moment to 0.7 ppm, Phys. Rev. Lett. 92 (2004) 161802 [hep-ex/0401008] [INSPIRE].
T. Aoyama et al., The anomalous magnetic moment of the muon in the Standard Model, Phys. Rep. 887 (2020) 1 [arXiv:2006.04822] [INSPIRE].
Muon g − 2 collaboration, Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm, Phys. Rev. Lett. 131 (2023) 161802 [arXiv:2308.06230] [INSPIRE].
T. Moroi, The Muon anomalous magnetic dipole moment in the minimal supersymmetric standard model, Phys. Rev. D 53 (1996) 6565 [Erratum ibid. 56 (1997) 4424] [hep-ph/9512396] [INSPIRE].
A. Greljo, P. Stangl and A.E. Thomsen, A model of muon anomalies, Phys. Lett. B 820 (2021) 136554 [arXiv:2103.13991] [INSPIRE].
J.M. Yang and Y. Zhang, Low energy SUSY confronted with new measurements of W-boson mass and muon g − 2, Sci. Bull. 67 (2022) 1430 [arXiv:2204.04202] [INSPIRE].
S.P. Martin and J.D. Wells, Muon Anomalous Magnetic Dipole Moment in Supersymmetric Theories, Phys. Rev. D 64 (2001) 035003 [hep-ph/0103067] [INSPIRE].
J. Liu, C.E.M. Wagner and X.-P. Wang, A light complex scalar for the electron and muon anomalous magnetic moments, JHEP 03 (2019) 008 [arXiv:1810.11028] [INSPIRE].
S. Baum, M. Carena, N.R. Shah and C.E.M. Wagner, The tiny (g − 2) muon wobble from small-μ supersymmetry, JHEP 01 (2022) 025 [arXiv:2104.03302] [INSPIRE].
M. Chakraborti, S. Heinemeyer and I. Saha, Improved (g − 2)μ measurements and wino/higgsino dark matter, Eur. Phys. J. C 81 (2021) 1069 [arXiv:2103.13403] [INSPIRE].
P. Athron, C. Balázs, D.H.J. Jacob, W. Kotlarski, D. Stöckinger and H. Stöckinger-Kim, New physics explanations of aμ in light of the FNAL muon g − 2 measurement, JHEP 09 (2021) 080 [arXiv:2104.03691] [INSPIRE].
K.S. Babu, S. Jana and Vishnu P.K., Correlating W-Boson Mass Shift with Muon g − 2 in the Two Higgs Doublet Model, Phys. Rev. Lett. 129 (2022) 121803 [arXiv:2204.05303] [INSPIRE].
G. Arcadi, L. Calibbi, M. Fedele and F. Mescia, Muon g − 2 and B-anomalies from Dark Matter, Phys. Rev. Lett. 127 (2021) 061802 [arXiv:2104.03228] [INSPIRE].
F. Wang, L. Wu, Y. Xiao, J.M. Yang and Y. Zhang, GUT-scale constrained SUSY in light of new muon g − 2 measurement, Nucl. Phys. B 970 (2021) 115486 [arXiv:2104.03262] [INSPIRE].
S. Borsanyi et al., Leading hadronic contribution to the muon magnetic moment from lattice QCD, Nature 593 (2021) 51 [arXiv:2002.12347] [INSPIRE].
C. Aubin, T. Blum, M. Golterman and S. Peris, Muon anomalous magnetic moment with staggered fermions: Is the lattice spacing small enough?, Phys. Rev. D 106 (2022) 054503 [arXiv:2204.12256] [INSPIRE].
M. Cè et al., Window observable for the hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD, Phys. Rev. D 106 (2022) 114502 [arXiv:2206.06582] [INSPIRE].
Extended Twisted Mass collaboration, Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions, Phys. Rev. D 107 (2023) 074506 [arXiv:2206.15084] [INSPIRE].
chiQCD collaboration, Muon g − 2 with overlap valence fermions, Phys. Rev. D 107 (2023) 034513 [arXiv:2204.01280] [INSPIRE].
RBC and UKQCD collaborations, Update of Euclidean windows of the hadronic vacuum polarization, Phys. Rev. D 108 (2023) 054507 [arXiv:2301.08696] [INSPIRE].
Fermilab Lattice et al. collaborations, Light-quark connected intermediate-window contributions to the muon g − 2 hadronic vacuum polarization from lattice QCD, Phys. Rev. D 107 (2023) 114514 [arXiv:2301.08274] [INSPIRE].
A. Keshavarzi, D. Nomura and T. Teubner, Muon g − 2 and α(\( {M}_Z^2 \)): a new data-based analysis, Phys. Rev. D 97 (2018) 114025 [arXiv:1802.02995] [INSPIRE].
A. Crivellin, M. Hoferichter, C.A. Manzari and M. Montull, Hadronic Vacuum Polarization: (g − 2)μ versus Global Electroweak Fits, Phys. Rev. Lett. 125 (2020) 091801 [arXiv:2003.04886] [INSPIRE].
L. Di Luzio, A. Masiero, P. Paradisi and M. Passera, New physics behind the new muon g − 2 puzzle?, Phys. Lett. B 829 (2022) 137037 [arXiv:2112.08312] [INSPIRE].
L. Darmé, G. Grilli di Cortona and E. Nardi, The muon g − 2 anomaly confronts new physics in e± and μ± final states scattering, JHEP 06 (2022) 122 [arXiv:2112.09139] [INSPIRE].
L. Darmé, G. Grilli di Cortona and E. Nardi, Indirect new physics effects on σhad confront the (g − 2)μ window discrepancies and the CMD-3 result, arXiv:2212.03877 [INSPIRE].
G.R. Farrar, The muon g − 2 and lattice QCD hadronic vacuum polarization may point to new, long-lived neutral hadrons, arXiv:2206.13460 [INSPIRE].
CMD-3 collaboration, Measurement of the e+e− → π+π− cross section from threshold to 1.2 GeV with the CMD-3 detector, arXiv:2302.08834 [INSPIRE].
A. Keshavarzi, W.J. Marciano, M. Passera and A. Sirlin, Muon g − 2 and ∆α connection, Phys. Rev. D 102 (2020) 033002 [arXiv:2006.12666] [INSPIRE].
V.M. Aul’chenko et al., Measurement of the e+e− → π+π− cross section with the CMD-2 detector in the 370–520 MeV c.m. energy range, JETP Lett. 84 (2006) 413 [hep-ex/0610016] [INSPIRE].
CMD-2 collaboration, High-statistics measurement of the pion form factor in the ρ-meson energy range with the CMD-2 detector, Phys. Lett. B 648 (2007) 28 [hep-ex/0610021] [INSPIRE].
M.N. Achasov et al., Update of the e+e− → π+π− cross-section measured by SND detector in the energy region 400 < \( \sqrt{s} \) < 1000 MeV, J. Exp. Theor. Phys. 103 (2006) 380 [hep-ex/0605013] [INSPIRE].
KLOE-2 collaboration, Combination of KLOE σ(e+e− → π+π−γ(γ)) measurements and determination of \( {a}_{\mu}^{\pi^{+}{\pi}^{-}} \) in the energy range 0.10 < s < 0.95 GeV2, JHEP 03 (2018) 173 [arXiv:1711.03085] [INSPIRE].
BaBar collaboration, Precise measurement of the e+e− → π+π−(γ) cross section with the Initial State Radiation method at BABAR, Phys. Rev. Lett. 103 (2009) 231801 [arXiv:0908.3589] [INSPIRE].
W.N. Cottingham, The neutron proton mass difference and electron scattering experiments, Ann. Phys. 25 (1963) 424 [INSPIRE].
J.F. Donoghue and A.F. Perez, The Electromagnetic mass differences of pions and kaons, Phys. Rev. D 55 (1997) 7075 [hep-ph/9611331] [INSPIRE].
D. Stamen, D. Hariharan, M. Hoferichter, B. Kubis and P. Stoffer, Kaon electromagnetic form factors in dispersion theory, Eur. Phys. J. C 82 (2022) 432 [arXiv:2202.11106] [INSPIRE].
A. Crivellin and M. Hoferichter, Width effects of broad new resonances in loop observables and application to (g − 2)μ, Phys. Rev. D 108 (2023) 013005 [arXiv:2211.12516] [INSPIRE].
BaBar collaboration, Search for a Dark Photon in e+e− Collisions at BaBar, Phys. Rev. Lett. 113 (2014) 201801 [arXiv:1406.2980] [INSPIRE].
H.B. O’Connell, B.C. Pearce, A.W. Thomas and A.G. Williams, ρ–ω mixing, vector meson dominance and the pion form-factor, Prog. Part. Nucl. Phys. 39 (1997) 201 [hep-ph/9501251] [INSPIRE].
M.N. Achasov et al., Study of the process e+e− → π+π−π0 in the energy region \( \sqrt{s} \) below 0.98 GeV, Phys. Rev. D 68 (2003) 052006 [hep-ex/0305049] [INSPIRE].
BABAR collaboration, Study of the process e+e− → π+π−π0 using initial state radiation with BABAR, Phys. Rev. D 104 (2021) 112003 [arXiv:2110.00520] [INSPIRE].
B.C. Odom, D. Hanneke, B. D’Urso and G. Gabrielse, New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron, Phys. Rev. Lett. 97 (2006) 030801 [INSPIRE].
M. Pospelov, Secluded U(1) below the weak scale, Phys. Rev. D 80 (2009) 095002 [arXiv:0811.1030] [INSPIRE].
T. Aoyama, T. Kinoshita and M. Nio, Theory of the Anomalous Magnetic Moment of the Electron, Atoms 7 (2019) 28 [INSPIRE].
S. Volkov, Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops, Phys. Rev. D 100 (2019) 096004 [arXiv:1909.08015] [INSPIRE].
X. Fan, T.G. Myers, B.A.D. Sukra and G. Gabrielse, Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130 (2023) 071801 [arXiv:2209.13084] [INSPIRE].
R.H. Parker, C. Yu, W. Zhong, B. Estey and H. Müller, Measurement of the fine-structure constant as a test of the Standard Model, Science 360 (2018) 191 [arXiv:1812.04130] [INSPIRE].
L. Morel, Z. Yao, P. Cladé and S. Guellati-Khélifa, Determination of the fine-structure constant with an accuracy of 81 parts per trillion, Nature 588 (2020) 61 [INSPIRE].
BaBar collaboration, Search for Invisible Decays of a Dark Photon Produced in e+e− Collisions at BaBar, Phys. Rev. Lett. 119 (2017) 131804 [arXiv:1702.03327] [INSPIRE].
Belle-II collaboration, Search for an Invisibly Decaying Z′ Boson at Belle II in e+e− → μ+μ−(e±μ∓) Plus Missing Energy Final States, Phys. Rev. Lett. 124 (2020) 141801 [arXiv:1912.11276] [INSPIRE].
ALEPH, DELPHI, L3, OPAL collaborations and LEP Electroweak Working Group, Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP, Phys. Rep. 532 (2013) 119 [arXiv:1302.3415] [INSPIRE].
G. Bellini et al., Precision measurement of the 7Be solar neutrino interaction rate in Borexino, Phys. Rev. Lett. 107 (2011) 141302 [arXiv:1104.1816] [INSPIRE].
TEXONO collaboration, Measurement of \( \overline{\nu} \)e-Electron Scattering Cross-Section with a CsI(Tl) Scintillating Crystal Array at the Kuo-Sheng Nuclear Power Reactor, Phys. Rev. D 81 (2010) 072001 [arXiv:0911.1597] [INSPIRE].
TEXONO collaboration, A Search of Neutrino Magnetic Moments with a High-Purity Germanium Detector at the Kuo-Sheng Nuclear Power Station, Phys. Rev. D 75 (2007) 012001 [hep-ex/0605006] [INSPIRE].
CHARM-II collaboration, Precision measurement of electroweak parameters from the scattering of muon-neutrinos on electrons, Phys. Lett. B 335 (1994) 246 [INSPIRE].
S. Bilmis, I. Turan, T.M. Aliev, M. Deniz, L. Singh and H.T. Wong, Constraints on Dark Photon from Neutrino-Electron Scattering Experiments, Phys. Rev. D 92 (2015) 033009 [arXiv:1502.07763] [INSPIRE].
BaBar collaboration, Search for B → K(*)\( \nu \overline{\nu} \) and invisible quarkonium decays, Phys. Rev. D 87 (2013) 112005 [arXiv:1303.7465] [INSPIRE].
E949 collaboration, New measurement of the K+ → π+\( \nu \overline{\nu} \) branching ratio, Phys. Rev. Lett. 101 (2008) 191802 [arXiv:0808.2459] [INSPIRE].
HFLAV collaboration, Averages of b-hadron and c-hadron Properties at the End of 2007, arXiv:0808.1297 [INSPIRE].
G. Gagliardi, R. Frezzotti, V. Lubicz, G. Martinelli, F. Sanfilippo and S. Simula, Lattice determination of the pion mass difference \( {M}_{\pi^{+}}-{M}_{\pi^0} \) at order \( \mathcal{O} \)(αem) and \( \mathcal{O} \)((md − mu)2) including disconnected diagrams, PoS LATTICE2021 (2022) 255 [arXiv:2112.01066] [INSPIRE].
Z.-F. Cui, D. Binosi, C.D. Roberts and S.M. Schmidt, Pion charge radius from pion+electron elastic scattering data, Phys. Lett. B 822 (2021) 136631 [arXiv:2108.04948] [INSPIRE].
A1 collaboration, A Measurement of the axial form-factor of the nucleon by the p(e, e′π+)n reaction at W = 1125 MeV, Phys. Lett. B 468 (1999) 20 [nucl-ex/9911003] [INSPIRE].
P. Baillon et al., Study of π+π− scattering in π−p → π+π−X0 via a Chew-Low extrapolation, Phys. Lett. B 38 (1972) 555 [INSPIRE].
S.D. Protopopescu et al., ππ Partial Wave Analysis from Reactions π+p → π+π−∆++ and π+p → K+K−∆++ at 7.1 GeV/c, Phys. Rev. D 7 (1973) 1279 [INSPIRE].
S.-s. Fang, B. Kubis and A. Kupsc, What can we learn about light-meson interactions at electron-positron colliders?, Prog. Part. Nucl. Phys. 120 (2021) 103884 [arXiv:2102.05922] [INSPIRE].
J.J. Sakurai, Eight Ways of Determining the ρ-Meson Coupling Constant, Phys. Rev. Lett. 17 (1966) 1021 [INSPIRE].
S.G. Karshenboim, D. McKeen and M. Pospelov, Constraints on muon-specific dark forces, Phys. Rev. D 90 (2014) 073004 [Addendum ibid. 90 (2014) 079905] [arXiv:1401.6154] [INSPIRE].
Acknowledgments
C.W. would like to thank the Aspen Center for Physics, which is supported by National Science Foundation grant No. PHY-1607611, where part of this work has been done. We would like to thank R. Boughezal, G. Bodwin, T. Hobbs, F. Petriello and, in particular, F. Herren and R. van de Water for useful discussions and comments. We would also like to thank M. Hoferichter, A. Crivellin, and L. Darmé for interesting comments. C.W. has been partially supported by the U.S. Department of Energy under contracts No. DEAC02-06CH11357 at Argonne National Laboratory. The work of C.W. and N.C. at the University of Chicago has also been supported by the DOE grant DE-SC0013642.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2305.02354
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Coyle, N.M., Wagner, C.E.M. Resolving the muon g − 2 tension through Z′-induced modifications to σhad. J. High Energ. Phys. 2023, 71 (2023). https://doi.org/10.1007/JHEP12(2023)071
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2023)071