Advertisement

Journal of High Energy Physics

, 2019:30 | Cite as

On systematic and GR effects on muon g − 2 experiments

  • Alessio NotariEmail author
  • Daniele Bertacca
Open Access
Regular Article - Experimental Physics
  • 5 Downloads

Abstract

We derive in full generality the equations that govern the time dependence of the energy ℰ of the decay electrons in a muon g − 2 experiment. We include both electromagnetic and gravitational effects and we estimate possible systematics on the measurements of a ≡ (g − 2)/2, whose experimental uncertainty will soon reach ∆a/a ≈ 107. In addition to the standard modulation of ℰ when the motion is orthogonal to a constant magnetic field B, with angular frequency ωa = ea|B|/m, we study effects due to: (1) a non constant muon γ factor, in presence of electric fields E, (2) a correction due to a component of the muon velocity along B (the “pitch correction”), (3) corrections to the precession rate due to E fields, (4) non-trivial spacetime metrics. Oscillations along the radial and vertical directions of the muon lead to oscillations in ℰ with a relative size of order 106, for the BNL g − 2 experiment. We then find a subleading effect in the “pitch” correction, leading to a frequency shift of ∆ωaa\( \mathcal{O} \)(109) and subleading effects of about ∆ωaa few ×\( \mathcal{O} \)(108–109) due to E fields. Finally we show that GR effects are dominated by the Coriolis force, due to the Earth rotation with angular frequency ωT, leading to a correction of about ∆ωaa≈ ωT/(γωa) \( \mathcal{O} \) (1012). A similar correction might be more appreciable for future electron g − 2 experiments, being of order ∆ωaa,el≈ ωT/(ωa,el) 7 × 1013, compared to the present experimental uncertainty, ∆ael/ael 1010, and forecasted to reach soon ∆ael/ael 1011.

Keywords

Other experiments 

Notes

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

References

  1. [1]
    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].
  2. [2]
    Muon g-2 collaboration, Muon (g − 2) Technical Design Report, arXiv:1501.06858 [INSPIRE].
  3. [3]
    A. Keshavarzi, D. Nomura and T. Teubner, Muon g − 2 and \( \alpha \left({M}_Z^2\right) \): a new data-based analysis, Phys. Rev.D 97 (2018) 114025 [arXiv:1802.02995] [INSPIRE].
  4. [4]
    M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g − 2 and \( \alpha \left({m}_Z^2\right) \)using newest hadronic cross-section data, Eur. Phys. J.C 77 (2017) 827 [arXiv:1706.09436] [INSPIRE].
  5. [5]
    F. Jegerlehner, Muon g − 2 theory: The hadronic part, EPJ Web Conf.166 (2018) 00022 [arXiv:1705.00263] [INSPIRE].
  6. [6]
    J.P. Miller, E. de Rafael, B.L. Roberts and D. Stöckinger, Muon (g − 2): Experiment and Theory, Ann. Rev. Nucl. Part. Sci.62 (2012) 237 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    B.L. Roberts, Historical Introduction to Electric and Magnetic Moments, Adv. Ser. Direct. High Energy Phys.20 (2009) 1 [INSPIRE].CrossRefGoogle Scholar
  8. [8]
    T. Morishima, T. Futamase and H.M. Shimizu, Post-Newtonian effects of Dirac particle in curved spacetime — III: the muon g − 2 in the Earth’s gravity, arXiv:1801.10246 [INSPIRE].
  9. [9]
    M. Visser, Post-Newtonian particle physics in curved spacetime, arXiv:1802.00651 [INSPIRE].
  10. [10]
    P. Guzowski, The effect of Earth’s gravitational field on the muon magic momentum, arXiv:1802.01120 [INSPIRE].
  11. [11]
    H. Nikolic, Can effective muon g − 2 depend on the gravitational potential?, arXiv:1802.04025 [INSPIRE].
  12. [12]
    A. László and Z. Zimborás, Quantification of GR effects in muon g − 2, EDM and other spin precession experiments, Class. Quant. Grav.35 (2018) 175003 [arXiv:1803.01395] [INSPIRE].
  13. [13]
    D. Venhoek, Analyzing “magnetic moments in curved spacetime”: pitfalls in GR, arXiv:1804.09524 [INSPIRE].
  14. [14]
    J.P. Miller and B.L. Roberts, The Muon (g − 2) Spin Equations, the Magic γ, What’s small and what’s not, arXiv:1805.01944 [INSPIRE].
  15. [15]
    B.L. Roberts and W.J. Marciano, Lepton Dipole Moments, World Scientific (2009).
  16. [16]
    F.J.N. Farley, Pitch correction in (g − 2) experiments, Phys. Lett.B 42 (1972) 66 [INSPIRE].
  17. [17]
    J.H. Field and G. Fiorentini, Corrections to the g − 2 frequency in weak focusing storage devices due to betatron oscillations, Nuovo Cim.A 21 (1974) 297 [INSPIRE].
  18. [18]
    F. De Felice and D. Bini, Classical Measurements in Curved Space-Times, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2010).
  19. [19]
    V. Bargmann, L. Michel and V.L. Telegdi, Precession of the polarization of particles moving in a homogeneous electromagnetic field, Phys. Rev. Lett.2 (1959) 435 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    R.T. Jantzen, P. Carini and D. Bini, The Many faces of gravitoelectromagnetism, Annals Phys.215 (1992) 1 [gr-qc/0106043] [INSPIRE].
  21. [21]
    J.D. Jackson, Classical Electrodynamics, Wiley (1998).Google Scholar
  22. [22]
    D.F. Jackson Kimball et al., Overview of the Cosmic Axion Spin Precession Experiment (CASPEr), arXiv:1711.08999 [INSPIRE].
  23. [23]
    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].
  24. [24]
    S. Sturm, G. Werth and K. Blaum, Electron g-factor determinations in Penning traps, Annalen Phys.525 (2013) 620 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    G. Gabrielse, S.E. Fayer, T.G. Myers and X. Fan, Towards an Improved Test of the Standard Model’s Most Precise Prediction, arXiv:1904.06174 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Departament de Física Quàntica i Astrofiśıca & Institut de Ciéncies del Cosmos (ICCUB)Universitat de BarcelonaBarcelonaSpain
  2. 2.Dipartimento di Fisica ed AstronomiaUniversità di PadovaPadovaItaly
  3. 3.INFN, Sezione di PadovaPadovaItaly

Personalised recommendations