Author:
Notari Alessio,Bertacca Daniele
Abstract
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 ≈ 10
−7. In addition to the standard modulation of ℰ when the motion is orthogonal to a constant magnetic field B, with angular frequency ω
a
= 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 10
−6, for the BNL g − 2 experiment. We then find a subleading effect in the “pitch” correction, leading to a frequency shift of ∆ω
a
/ω
a
≈
$$ \mathcal{O} $$
O
(10
−9) and subleading effects of about ∆ω
a
/ω
a
≈ few ×
$$ \mathcal{O} $$
O
(10
−8–10
−9) due to E fields. Finally we show that GR effects are dominated by the Coriolis force, due to the Earth rotation with angular frequency ω
T
, leading to a correction of about ∆ω
a
/ω
a
≈ ω
T
/(γω
a
) ≈
$$ \mathcal{O} $$
O
(10
−12). A similar correction might be more appreciable for future electron g − 2 experiments, being of order ∆ω
a
/ω
a
,
el
≈ ω
T
/(ω
a
,
el) ≈ 7 × 10
−13, compared to the present experimental uncertainty, ∆a
el
/a
el
≈ 10
−10, and forecasted to reach soon ∆a
el
/a
el
≈ 10
−11.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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