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RICH CK Theta Resolution Optimisation

This MR introduces an overhaul of how in the RICH I compute the expected Cherenkov Thats resolution values for each track and mass hypothesis.

The procedure used so far has been to attempt to compute the resolution analytically for each track/hypo combination, from first principles, by computing a number of contributions to the resolution and adding these in quadrature. This is implemented in

https://gitlab.cern.ch/lhcb/Rec/-/blob/master/Rich/RichFutureRecTrackAlgorithms/src/RichTrackFunctionalCherenkovResolutions.cpp

This procedure is OK, but I have always know the values to not be 100% perfect. However, I have never really known for sure how good, or not, these values are.

This MR first introduces a new set of monitors, and some helper scripts, which allow me to better study this resolution. With this I can produce plots like

Rich1Gas-Long-pion-VPtot

The green curve shows the compute values, and the purple the results deduced from fits to the data. In general, for Long tracks, the computed values are not too bad, but tend to over estimate things at lower P. For RICH2, things are a bit worse

Rich2Gas-Long-kaon-VPtot

Using the results from the fits, I then computed parameterisations which I then use with a new implementation of the algorithm to compute the CK resolutions, that directly uses these values.

I have also (re)optimised a bit some of the selections cuts used in the photon reconstruction. I noticed a small bug in a local coordinate correction scale factor that was causing the required windows to be slightly larger than they otherwise would have needed to be. Previously the tuning of the various 'N-Sigma' cuts in the photon selection was a bit ad-hoc. I've added some new monitors that let me precisely study the selection offs. as a function of P, that lets me optimise things a bit more precisely.

Effs-Rich1Gas-Long-kaon

I also add tunings for each track type and resolution method (previously would just do it for Long tracks, and use the same tunings across the board). With this I get slightly better PID performance

CKRes-Optimisation

but with a slightly reduce CPU cost (e..g. 6.5 -> 5.9 ms/event for Long track sequence) due to the reduction in the number of fake photons due to the improved (pre) selection cuts.

Should be tested and applied together with Moore!668 (merged)

Ref updates will be needed in Brunel and Moore.

FYI @bmalecki @seaso

edit(acasaisv): Reference upates MRs, Moore!688 (merged), Brunel!1098 (merged)

Edited by Adrian Casais Vidal

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