The muon (g-2) spin equations, the magic γ, what’s small and what’s not
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Published version
Date
2018
DOI
Authors
Miller, James P.
Roberts, B. Lee
Version
Published version
OA Version
Citation
James P Miller, B Lee Roberts. 2018. "The Muon $(g-2)$ Spin Equations, the Magic γ, What’s small and what’s not." arXiv:1805.01944v2.
Abstract
We review the spin equations for the muon in the 1.45 T muon (g — 2) storage ring, now relocated
to Fermilab. Muons are stored in a uniform 1.45 T magnetic field, and vertical focusing is provided by
four sets of electrostatic quadrupoles placed symmetrically around the storage ring. The storage ring is
operated at a Lorentz factor centered on the "magic 𝛄 = 29:3"; the effect of the electric field on the muon
spin precession cancels for muons at the magic momentum. We point out the relative sizes of the various
terms in the spin equations, and show that for experiments that use the magic 𝛄 and electric quadrupole
focusing to store the muon beam, any proposed effect that multiplies either the motional magnetic field
β × 𝐸 or the muon pitching motion β • 𝐵 term, will be smaller by three or more orders of magnitude,
relative to the spin precession due to the storage ring magnetic field. We use a recently proposed General
Relativity correction [1] as an example, to demonstrate the smallness of any such contribution, and
point out that their revised preprint [7] still contains a conceptual error, that signi cantly overestimates
the magnitude of their proposed correction. We have prepared this document in the hope that future
authors will nd it useful, should they wish to propose corrections from some additional term added to
the Thomas equation, Eq. 13, below. Our goal is to clarify how the experiment is done, and how the
small corrections due to the presence of the radial electric field and the vertical pitching motion of the
muons (betatron motion) in the storage ring are taken into account.