Abstract
The anomalous magnetic moments of the electron and the muon are interesting observables, since they can be measured with great precision and their values can be computed with excellent accuracy within the Standard Model (SM). The current experimental measurement of this quantities show a deviation of a few standard deviations with respect to the SM prediction, which may be a hint of new physics. The fact that the electron and the muon masses differ by two orders of magnitude and the deviations have opposite signs makes it difficult to find a common origin of these anomalies. In this work we introduce a complex singlet scalar charged under a Peccei-Quinn-like (PQ) global symmetry together with the electron transforming chirally under the same symmetry. In this realization, the CP-odd scalar couples to electron only, while the CP-even part can couple to muons and electrons simultaneously. In addition, the CP-odd scalar can naturally be much lighter than the CP-even scalar, as a pseudo-Goldstone boson of the PQ-like symmetry, leading to an explanation of the suppression of the electron anomalous magnetic moment with respect to the SM prediction due to the CP-odd Higgs effect dominance, as well as an enhancement of the muon one induced by the CP-even component.
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Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
J.S. Schwinger, On quantum electrodynamics and the magnetic moment of the electron, Phys. Rev. 73 (1948) 416 [INSPIRE].
C.M. Sommerfield, Magnetic dipole moment of the electron, Phys. Rev. 107 (1957) 328 [INSPIRE].
A. Petermann, Fourth order magnetic moment of the electron, Helv. Phys. Acta 30 (1957) 407 [INSPIRE].
T. Kinoshita and W.B. Lindquist, Eighth order anomalous magnetic moment of the electron, Phys. Rev. Lett. 47 (1981) 1573 [INSPIRE].
T. Kinoshita, B. Nizic and Y. Okamoto, Eighth order QED contribution to the anomalous magnetic moment of the muon, Phys. Rev. D 41 (1990) 593 [INSPIRE].
S. Laporta and E. Remiddi, The analytical value of the electron (g − 2) at order α 3 in QED, Phys. Lett. B 379 (1996) 283 [hep-ph/9602417] [INSPIRE].
G. Degrassi and G.F. Giudice, QED logarithms in the electroweak corrections to the muon anomalous magnetic moment, Phys. Rev. D 58 (1998) 053007 [hep-ph/9803384] [INSPIRE].
T. Kinoshita and M. Nio, Improved α 4 term of the muon anomalous magnetic moment, Phys. Rev. D 70 (2004) 113001 [hep-ph/0402206] [INSPIRE].
T. Kinoshita and M. Nio, The tenth-order QED contribution to the lepton g − 2: evaluation of dominant α 5 terms of muon g − 2, Phys. Rev. D 73 (2006) 053007 [hep-ph/0512330] [INSPIRE].
M. Passera, Precise mass-dependent QED contributions to leptonic g − 2 at order α 2 and α 3, Phys. Rev. D 75 (2007) 013002 [hep-ph/0606174] [INSPIRE].
A.L. Kataev, Reconsidered estimates of the 10th order QED contributions to the muon anomaly, Phys. Rev. D 74 (2006) 073011 [hep-ph/0608120] [INSPIRE].
T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron, Phys. Rev. D 77 (2008) 053012 [arXiv:0712.2607] [INSPIRE].
T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Tenth-order QED contribution to the electron g − 2 and an improved value of the fine structure constant, Phys. Rev. Lett. 109 (2012) 111807 [arXiv:1205.5368] [INSPIRE].
T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Complete tenth-order QED contribution to the muon g − 2, Phys. Rev. Lett. 109 (2012) 111808 [arXiv:1205.5370] [INSPIRE].
S. Laporta, High-precision calculation of the 4-loop contribution to the electron g − 2 in QED, Phys. Lett. B 772 (2017) 232 [arXiv:1704.06996] [INSPIRE].
T. Aoyama, T. Kinoshita and M. Nio, Revised and improved value of the QED tenth-order electron anomalous magnetic moment, Phys. Rev. D 97 (2018) 036001 [arXiv:1712.06060] [INSPIRE].
S. Volkov, New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED, Phys. Rev. D 96 (2017) 096018 [arXiv:1705.05800] [INSPIRE].
S. Volkov, Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment, Phys. Rev. D 98 (2018) 076018 [arXiv:1807.05281] [INSPIRE].
P.J. Mohr and B.N. Taylor, CODATA recommended values of the fundamental physical constants: 1998, Rev. Mod. Phys. 72 (2000) 351 [INSPIRE].
A. Czarnecki and W.J. Marciano, Lepton anomalous magnetic moments: a theory update, Nucl. Phys. Proc. Suppl. 76 (1999) 245 [hep-ph/9810512] [INSPIRE].
F. Jegerlehner, Hadronic contributions to electroweak parameter shifts: a detailed analysis, Z. Phys. C 32 (1986) 195 [INSPIRE].
B.W. Lynn, G. Penso and C. Verzegnassi, Strong interaction contributions to one loop leptonic process, Phys. Rev. D 35 (1987) 42 [INSPIRE].
M.L. Swartz, Reevaluation of the hadronic contribution to α(M 2 Z ), Phys. Rev. D 53 (1996) 5268 [hep-ph/9411353] [INSPIRE].
A.D. Martin and D. Zeppenfeld, A determination of the QED coupling at the Z pole, Phys. Lett. B 345 (1995) 558 [hep-ph/9411377] [INSPIRE].
S. Eidelman and F. Jegerlehner, Hadronic contributions to g − 2 of the leptons and to the effective fine structure constant α(M 2 Z ), Z. Phys. C 67 (1995) 585 [hep-ph/9502298] [INSPIRE].
B. Krause, Higher order hadronic contributions to the anomalous magnetic moment of leptons, Phys. Lett. B 390 (1997) 392 [hep-ph/9607259] [INSPIRE].
M. Davier and A. Hocker, New results on the hadronic contributions to α(M 2 Z ) and to (g − 2)μ, Phys. Lett. B 435 (1998) 427 [hep-ph/9805470] [INSPIRE].
F. Jegerlehner, Hadronic effects in (g − 2)μ and alpha QED(M Z): status and perspectives, in Radiative corrections: application of quantum field theory to phenomenology. Proceedings, 4th International Symposium, RADCOR’98, Barcelona, Spain, 8–12 September 1998, pg. 75 [hep-ph/9901386] [INSPIRE].
F. Jegerlehner, Theoretical precision in estimates of the hadronic contributions to (g − 2)μ and α QED(M Z), Nucl. Phys. Proc. Suppl. 126 (2004) 325 [hep-ph/0310234] [INSPIRE].
K. Melnikov and A. Vainshtein, Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited, Phys. Rev. D 70 (2004) 113006 [hep-ph/0312226] [INSPIRE].
J.F. de Troconiz and F.J. Yndurain, The hadronic contributions to the anomalous magnetic moment of the muon, Phys. Rev. D 71 (2005) 073008 [hep-ph/0402285] [INSPIRE].
J. Bijnens and J. Prades, The hadronic light-by-light contribution to the muon anomalous magnetic moment: where do we stand?, Mod. Phys. Lett. A 22 (2007) 767 [hep-ph/0702170] [INSPIRE].
M. Davier, The hadronic contribution to (g − 2)μ, Nucl. Phys. Proc. Suppl. 169 (2007) 288 [hep-ph/0701163] [INSPIRE].
A. Czarnecki, B. Krause and W.J. Marciano, Electroweak fermion loop contributions to the muon anomalous magnetic moment, Phys. Rev. D 52 (1995) R2619 [hep-ph/9506256] [INSPIRE].
A. Czarnecki, B. Krause and W.J. Marciano, Electroweak corrections to the muon anomalous magnetic moment, Phys. Rev. Lett. 76 (1996) 3267 [hep-ph/9512369] [INSPIRE].
A. Czarnecki and B. Krause, Electroweak corrections to the muon anomalous magnetic moment, Nucl. Phys. Proc. Suppl. 51C (1996) 148 [hep-ph/9606393] [INSPIRE].
A. Czarnecki, W.J. Marciano and A. Vainshtein, Refinements in electroweak contributions to the muon anomalous magnetic moment, Phys. Rev. D 67 (2003) 073006 [Erratum ibid. D 73 (2006) 119901] [hep-ph/0212229] [INSPIRE].
S. Heinemeyer, D. Stöckinger and G. Weiglein, Electroweak and supersymmetric two-loop corrections to (g − 2)μ, Nucl. Phys. B 699 (2004) 103 [hep-ph/0405255] [INSPIRE].
T. Gribouk and A. Czarnecki, Electroweak interactions and the muon g − 2: bosonic two-loop effects, Phys. Rev. D 72 (2005) 053016 [hep-ph/0509205] [INSPIRE].
J. Bijnens, E. Pallante and J. Prades, Analysis of the hadronic light by light contributions to the muon g − 2, Nucl. Phys. B 474 (1996) 379 [hep-ph/9511388] [INSPIRE].
M. Hayakawa and T. Kinoshita, Pseudoscalar pole terms in the hadronic light by light scattering contribution to muon g − 2, Phys. Rev. D 57 (1998) 465 [Erratum ibid. D 66 (2002) 019902] [hep-ph/9708227] [INSPIRE].
M. Knecht and A. Nyffeler, Hadronic light by light corrections to the muon g − 2: the pion pole contribution, Phys. Rev. D 65 (2002) 073034 [hep-ph/0111058] [INSPIRE].
M. Knecht, A. Nyffeler, M. Perrottet and E. de Rafael, Hadronic light by light scattering contribution to the muon g − 2: an effective field theory approach, Phys. Rev. Lett. 88 (2002) 071802 [hep-ph/0111059] [INSPIRE].
M.J. Ramsey-Musolf and M.B. Wise, Hadronic light by light contribution to muon g − 2 in chiral perturbation theory, Phys. Rev. Lett. 89 (2002) 041601 [hep-ph/0201297] [INSPIRE].
J. Prades, E. de Rafael and A. Vainshtein, The hadronic light-by-light scattering contribution to the muon and electron anomalous magnetic moments, Adv. Ser. Direct. High Energy Phys. 20 (2009) 303 [arXiv:0901.0306] [INSPIRE].
A.L. Kataev, Analytical eighth-order light-by-light QED contributions from leptons with heavier masses to the anomalous magnetic moment of electron, Phys. Rev. D 86 (2012) 013010 [arXiv:1205.6191] [INSPIRE].
A. Kurz, T. Liu, P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order, Phys. Rev. D 92 (2015) 073019 [arXiv:1508.00901] [INSPIRE].
G. Colangelo, M. Hoferichter, M. Procura and P. Stoffer, Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon, Phys. Rev. Lett. 118 (2017) 232001 [arXiv:1701.06554] [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].
T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Tenth-order electron anomalous magnetic moment — contribution of diagrams without closed lepton loops, Phys. Rev. D 91 (2015) 033006 [Erratum ibid. D 96 (2017) 019901] [arXiv:1412.8284] [INSPIRE].
P.J. Mohr, D.B. Newell and B.N. Taylor, CODATA recommended values of the fundamental physical constants: 2014, Rev. Mod. Phys. 88 (2016) 035009 [arXiv:1507.07956] [INSPIRE].
F. Jegerlehner, The muon g − 2 in progress, Acta Phys. Polon. B 49 (2018) 1157 [arXiv:1804.07409] [INSPIRE].
H. Davoudiasl and W.J. Marciano, Tale of two anomalies, Phys. Rev. D 98 (2018) 075011 [arXiv:1806.10252] [INSPIRE].
D. Hanneke, S. Fogwell and G. Gabrielse, New measurement of the electron magnetic moment and the fine structure constant, Phys. Rev. Lett. 100 (2008) 120801 [arXiv:0801.1134] [INSPIRE].
D. Hanneke, S.F. Hoogerheide and G. Gabrielse, Cavity control of a single-electron quantum cyclotron: measuring the electron magnetic moment, Phys. Rev. A 83 (2011) 052122 [arXiv:1009.4831] [INSPIRE].
RBC and UKQCD collaborations, Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 121 (2018) 022003 [arXiv:1801.07224] [INSPIRE].
Muon g-2 collaboration, Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].
G.F. Giudice, P. Paradisi and M. Passera, Testing new physics with the electron g − 2, JHEP 11 (2012) 113 [arXiv:1208.6583] [INSPIRE].
F. Abu-Ajamieh, Probing scalar and pseudoscalar solutions of the g − 2 anomaly, arXiv:1810.08891 [INSPIRE].
A. Crivellin, M. Hoferichter and P. Schmidt-Wellenburg, Combined explanations of (g − 2)μ,e and implications for a large muon EDM, Phys. Rev. D 98 (2018) 113002 [arXiv:1807.11484] [INSPIRE].
T. Kinoshita and W.J. Marciano, Theory of the muon anomalous magnetic moment, Adv. Ser. Direct. High Energy Phys. 7 (1990) 419 [INSPIRE].
Y.-F. Zhou and Y.-L. Wu, Lepton flavor changing scalar interactions and muon g − 2, Eur. Phys. J. C 27 (2003) 577 [hep-ph/0110302] [INSPIRE].
V. Barger, C.-W. Chiang, W.-Y. Keung and D. Marfatia, Proton size anomaly, Phys. Rev. Lett. 106 (2011) 153001 [arXiv:1011.3519] [INSPIRE].
D. Tucker-Smith and I. Yavin, Muonic hydrogen and MeV forces, Phys. Rev. D 83 (2011) 101702 [arXiv:1011.4922] [INSPIRE].
C.-Y. Chen, H. Davoudiasl, W.J. Marciano and C. Zhang, Implications of a light “dark Higgs” solution to the g μ − 2 discrepancy, Phys. Rev. D 93 (2016) 035006 [arXiv:1511.04715] [INSPIRE].
Y.-S. Liu, D. McKeen and G.A. Miller, Electrophobic scalar boson and muonic puzzles, Phys. Rev. Lett. 117 (2016) 101801 [arXiv:1605.04612] [INSPIRE].
B. Batell, N. Lange, D. McKeen, M. Pospelov and A. Ritz, Muon anomalous magnetic moment through the leptonic Higgs portal, Phys. Rev. D 95 (2017) 075003 [arXiv:1606.04943] [INSPIRE].
W.J. Marciano, A. Masiero, P. Paradisi and M. Passera, Contributions of axionlike particles to lepton dipole moments, Phys. Rev. D 94 (2016) 115033 [arXiv:1607.01022] [INSPIRE].
L. Wang, J.M. Yang and Y. Zhang, Probing a pseudoscalar at the LHC in light of R(D (*)) and muon g − 2 excesses, Nucl. Phys. B 924 (2017) 47 [arXiv:1610.05681] [INSPIRE].
R. Jackiw and S. Weinberg, Weak interaction corrections to the muon magnetic moment and to muonic atom energy levels, Phys. Rev. D 5 (1972) 2396 [INSPIRE].
J.P. Leveille, The second order weak correction to (g − 2) of the muon in arbitrary gauge models, Nucl. Phys. B 137 (1978) 63 [INSPIRE].
J.D. Bjorken et al., Search for neutral metastable penetrating particles produced in the SLAC beam dump, Phys. Rev. D 38 (1988) 3375 [INSPIRE].
E.M. Riordan et al., A search for short lived axions in an electron beam dump experiment, Phys. Rev. Lett. 59 (1987) 755 [INSPIRE].
M. Davier and H. Nguyen Ngoc, An unambiguous search for a light Higgs boson, Phys. Lett. B 229 (1989) 150 [INSPIRE].
M. Battaglieri et al., The heavy photon search test detector, Nucl. Instrum. Meth. A 777 (2015) 91 [arXiv:1406.6115] [INSPIRE].
BaBar collaboration, Search for a dark photon in e + e − collisions at BaBar, Phys. Rev. Lett. 113 (2014) 201801 [arXiv:1406.2980] [INSPIRE].
S. Knapen, T. Lin and K.M. Zurek, Light dark matter: models and constraints, Phys. Rev. D 96 (2017) 115021 [arXiv:1709.07882] [INSPIRE].
Belle-II collaboration, Belle II technical design report, arXiv:1011.0352 [INSPIRE].
Belle II collaboration, The Belle II physics book, arXiv:1808.10567 [INSPIRE].
A. Anastasi et al., Limit on the production of a low-mass vector boson in e + e − → Uγ, U → e + e − with the KLOE experiment, Phys. Lett. B 750 (2015) 633 [arXiv:1509.00740] [INSPIRE].
D.S.M. Alves and N. Weiner, A viable QCD axion in the MeV mass range, JHEP 07 (2018) 092 [arXiv:1710.03764] [INSPIRE].
BaBar collaboration, Search for a muonic dark force at BaBar, Phys. Rev. D 94 (2016) 011102 [arXiv:1606.03501] [INSPIRE].
B. Batell, A. Freitas, A. Ismail and D. Mckeen, Flavor-specific scalar mediators, Phys. Rev. D 98 (2018) 055026 [arXiv:1712.10022] [INSPIRE].
ATLAS collaboration, Measurements of four-lepton production at the Z resonance in pp collisions at \( \sqrt{s}=7 \) and 8 TeV with ATLAS, Phys. Rev. Lett. 112 (2014) 231806 [arXiv:1403.5657] [INSPIRE].
CMS collaboration, Search for an L μ − L τ gauge boson using Z → 4μ events in proton-proton collisions at \( \sqrt{s}=13 \) TeV, submitted to Phys. Lett. B (2018) [arXiv:1808.03684] [INSPIRE].
G. Marques-Tavares and M. Teo, Light axions with large hadronic couplings, JHEP 05 (2018) 180 [arXiv:1803.07575] [INSPIRE].
S.M. Barr and A. Zee, Electric dipole moment of the electron and of the neutron, Phys. Rev. Lett. 65 (1990) 21 [Erratum ibid. 65 (1990) 2920] [INSPIRE].
G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].
D. Liu, J. Liu, C.E.M. Wagner and X.-P. Wang, Bottom-quark forward-backward asymmetry, dark matter and the LHC, Phys. Rev. D 97 (2018) 055021 [arXiv:1712.05802] [INSPIRE].
BaBar collaboration, Search for low-mass dark-sector Higgs bosons, Phys. Rev. Lett. 108 (2012) 211801 [arXiv:1202.1313] [INSPIRE].
BaBar collaboration, Search for a narrow resonance in e + e − to four lepton final states, in Proceedings, 24th International Symposium on Lepton-Photon Interactions at High Energy (LP09), Hamburg, Germany, 17–22 August 2009 [arXiv:0908.2821] [INSPIRE].
N. Arkani-Hamed and N. Weiner, LHC signals for a superunified theory of dark matter, JHEP 12 (2008) 104 [arXiv:0810.0714] [INSPIRE].
M. Baumgart, C. Cheung, J.T. Ruderman, L.-T. Wang and I. Yavin, Non-Abelian dark sectors and their collider signatures, JHEP 04 (2009) 014 [arXiv:0901.0283] [INSPIRE].
Y. Bai and Z. Han, Measuring the dark force at the LHC, Phys. Rev. Lett. 103 (2009) 051801 [arXiv:0902.0006] [INSPIRE].
A. Katz and R. Sundrum, Breaking the dark force, JHEP 06 (2009) 003 [arXiv:0902.3271] [INSPIRE].
M. Lindner, M. Platscher and F.S. Queiroz, A call for new physics: the muon anomalous magnetic moment and lepton flavor violation, Phys. Rept. 731 (2018) 1 [arXiv:1610.06587] [INSPIRE].
R.S. Chivukula and H. Georgi, Composite technicolor Standard Model, Phys. Lett. B 188 (1987) 99 [INSPIRE].
G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].
S. Pascoli, S.T. Petcov and A. Riotto, Leptogenesis and low energy CP-violation in neutrino physics, Nucl. Phys. B 774 (2007) 1 [hep-ph/0611338] [INSPIRE].
S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
E. Akhmedov, A. Kartavtsev, M. Lindner, L. Michaels and J. Smirnov, Improving electro-weak fits with TeV-scale sterile neutrinos, JHEP 05 (2013) 081 [arXiv:1302.1872] [INSPIRE].
Z.-Z. Xing and Z.-H. Zhao, A review of μ-τ flavor symmetry in neutrino physics, Rept. Prog. Phys. 79 (2016) 076201 [arXiv:1512.04207] [INSPIRE].
A.J. Krasznahorkay et al., Observation of anomalous internal pair creation in 8 Be: a possible indication of a light, neutral boson, Phys. Rev. Lett. 116 (2016) 042501 [arXiv:1504.01527] [INSPIRE].
U. Ellwanger and S. Moretti, Possible explanation of the electron positron anomaly at 17 MeV in 8 Be transitions through a light pseudoscalar, JHEP 11 (2016) 039 [arXiv:1609.01669] [INSPIRE].
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Liu, J., Wagner, C.E.M. & Wang, XP. A light complex scalar for the electron and muon anomalous magnetic moments. J. High Energ. Phys. 2019, 8 (2019). https://doi.org/10.1007/JHEP03(2019)008
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DOI: https://doi.org/10.1007/JHEP03(2019)008