English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We review the spin equations for the muon in the 1.45~T muon storage ring atBrookhaven National Laboratory, which has subsequently been relocated toFermilab. Muons are stored in a uniform 1.45~T magnetic field, and verticalfocusing is provided by four sets of electrostatic quadrupoles placedsymmetrically around the storage ring. The storage ring is operated at the"magic $\gamma = 29.3$" so that the effect of the motional magnetic fieldcancels for muons at the magic momentum. We point out the relative sizes of thevarious terms in the spin equations, and show that for experiments that use themagic $\gamma$ and electric quadrupole focusing to store the muon beam, anyproposed effect that multiplies either the motional magnetic field $\vec \beta\times \vec E$ or the muon pitching motion $\vec \beta \cdot \vec B$ term, willbe smaller by three or more orders of magnitude, relative to the spinprecession from the storage ring magnetic field. We use a recently proposedGeneral Relativity correction as an example, to demonstrate the smallness ofany such contribution, and point out that the revised preprint from theseauthors still contains a conceptual error, that significantly overestimates themagnitude of their proposed correction. We have prepared this document in thehope that future authors will find it useful, should they wish to proposecorrections 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 smallcorrections due to the presence of the radial electric field and the verticalpitching motion of themuons (betatron motion) in the storage ring are takeninto account.

The Muon $(g-2)$ Spin Equations, the Magic $\gamma$, What's small and what's not