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


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.


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© 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

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