Add BRF / beam jitter to the MC

[S81D]

For both the NC and stroboscopic analyses, correctly modeling the spill structure of the BNB is important to ensure any selection cuts / Data and MC comparison is accurate.

The observed bunch width in ANNIE can be broken down into:

$\sigma_{Data} = \sqrt{ <\sigma_{TOF}>^2 + <\sigma_{PMT}>^2 + <\sigma_{BNB}>^2 + <\sigma_{BRF}>^2}$

What is already included in the MC:

• $\sigma_{BNB}$ (Intrinsic BNB bunch width, based on observations from MicroBooNE)
• $\sigma_{PMT}$ (PMT timing jitter, based on 2023 laser calibration data - this is implemented in PMTWaveformSim)
• $\sigma_{TOF}$ (Simulation handles this, no corrections for the reconstructed vertex are being applied here)

What was remaining (that is now included) was the beam timing jitter / the uncertainty in the BRF fitting (which we use to improve the bunch reconstruction in the data). This term was determined by comparing the observed bunch width in the MC and data for muon events (CCinc and throughgoing muons for FY22 and FY23). Since the current version of the simulation already includes:

$\sigma_{MC} = \sqrt{ <\sigma_{TOF}>^2 + <\sigma_{PMT}>^2 + <\sigma_{BNB}>^2 }$

The final term can be extracted based on the remaining discrepancy. More details can be found here.

Describe your changes

Checklist before submitting your PR

• This PR implements a single change (one new/modified Tool, or a set of changes to implement one new/modified feature)
• This PR alters the minimum number of files to affect this change
• [N/A] If this PR includes a new Tool, a README and minimal demonstration ToolChain is provided
• [N/A] If a new Tool/ToolChain requires model or configuration files, their paths are not hard-coded, and means of generating those files is described in the readme, with examples provided on /pnfs/annie/persistent
• For every new usage, there is a reason the data must be on the heap
• For every new there is a delete, unless I explicitly know why (e.g. ROOT or a BoostStore takes ownership)

Additional Material

The default value set in the README was the weighted average observed for CCinc and throughgoing muons in FY22 and FY23 data. If using newer data (FY24 and later) a similar analysis is needed to verify if the beam timing uncertainties have changed.

[jminock]

Looks good!