Muon spin asymmetry

[Tom-Willemsen]

This is somewhat similar to neutron polarization, but looking at forwards/back-scattering detector banks rather than spin-up/spin-down periods.

Discussed 10/07/2025 01:13:19

Description

• Measure arrays of detector counts against time on forward detectors, F, and backwards detectors, B.
  • The detectors included in F and B must be configurable by the scientists.
• Rebin the F and B arrays to reduce noise, using a scientist-provided set of time bins
• Compute the array $\huge a = \frac{F-αB}{F+αB}$
  • $a$ is the asymmetry
  • $α$ is a scientist-provided scalar constant
  • Propagating uncertainties correctly (the existing polarisation function will need to be modified to include an $α$ term, which may be 1.
  • This results in an array of asymmetry $a$ against time
• Fit the array of $a$ against time using one of the following models:
  • $\huge a = B + A_0 cos({ω_0} {t} + {φ_0}) e^{-λ_0 t}$
  • $\huge a = B + A_0 cos({ω_0} {t} + {φ_0}) e^{-λ_0 t} + A_1 cos({ω_1} {t} + {φ_1}) e^{-λ_1 t}$
  • This results in a number of fitting parameters (e.g. $B$, $A_0$, $ω_0$, $φ_0$, $λ_0$), with uncertainties
  • These fitting parameters are the "result" from counting a single scan point - similar to how intensity is the "result" from a standard normalizing reducer.
  • The scientists will provide initial guesses for all fit parameters, as constants.
  • General constraints: $A_n >= 0$ and $ω_n >= 0$
• Scan across an x-variable (e.g. magnet current), for $N$ points. At each scan point the above fit is performed and a fit parameter is returned.
• The scan plots x (e.g. magnet current) against y (e.g. $A_0$ fit parameter above).
• A fit is also done at this higher level. This will be a Gaussian or another peak-like shape. The Gaussian may be either positive (looking for a maximum) or negative (looking for a minimum). This will use our standard LiveFit infrastructure and models, which are sufficient.

Acceptance criteria

• Implement a SimpleDae reducer which takes as arguments lists of forwards and backwards detectors, calculates the fitted quantities as described above, and exposes them from the reducer (along with their associated uncertainties)