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General
This meeting was for the most part dedicated to discussing the need for and the similarities and differences between the JPP and AANET shower fitters. The JPP section, on the JShower reconstruction chain, was presented by Bouke and by Brían, while the section on AANET, particularly AAShowerFit, was presented by Thijs.
A great deal of discussion took place during all three presentations and several suggestions for potential improvements in the reconstruction chains were put forward, which can be found in each resective section below.
Bouke - JShowerPrefit until JShowerEnergyFit
DISCLAIMER: As I presented this part myself, I was not able to write along with the full discussions that took place. So the minutes here are less extensive. For details I refer to the presentation slides. The action points discussed during the meeting can be found below.
Action points:
Brían - JShowerDirectionfit & JShowerFit
One of the strenghts of the Jpp reconstruction chains is their modularity. In other words, it is possible to play with the chain ordering and even to combine them with track reconstruction applications. Some things that may merit better documentation:
Thijs - AAShowerFit
AAShowerFit consists of a vertex determination exclusively based on timing information and a direction and energy fit based on amplitude information (and hopefully soon using also timing information, once Jordan's efforts bear fruit!).
Vertex fit
Hit selection: merge hits within 350 ns and look at local coincidences.
Brían: why is the hit window 350 ns?
Thijs: That's something to look up!
The hit time residuals are then minimized using the sum over sqrt(1 + dti^2), with dti the hit time residual of the i-th PMT, as an M-estimator.
Bouke: Why do we use sqrt(1+x^2) as M-estimator?
Thijs: To minimize the influence of outliers
Maarten: What do you use as input for your M-estimator?
Thijs: Hit with highest amplitude is starting point of M-estimator
Maarten: Can we use a Lorentzian M-estimator instead? Seems to reduce influence of outliers the most in e.g. position calibration.
Maarten: Suggestion --> introduce L2-logic, cluster logic and 4D-fit. If we can move the limits of applicability of AAShowerFit to lower energies, then we should do it!
The vertex fit performs well above 10 TeV. Below that, the distance residual shoots up.
Maarten: I would like to suggest to try to also reconstruct events originating very far away (even far beyond the actual size of the detector), using e.g. plain wave approximations for the incoming light wavefront.
Direction and energy fit
The hit counting for the direction and energy fit does not involve the ToT at this time.
Maarten: ToT can actually be used as a probe for the distance of an event. Very high ToT <--> very close hit.
Aart: Treating ToT in a mathematical way might be difficult (e.g. what how do you treat the statistics of high ToT due to simultaneous background hits).
Alls hits with residuals between -100 and +900 ns w.r.t. the vertex fit result are taken into account. The fit then minimizes a likelihood determined as the product of the hit- and no-hit-probabilities over all selected PMTs. The corresponding PDF is determined from MC.
Since the vertex is fixed, the distance and hit incidence angle can be pre-computed. So every PMT gets a 1D likelihood, where only Z is varied.
Furthermore, only the no-hits surrounding a sphere around the vertex have to be taken into account.
Bouke: How is the sphere's radius determined?
Aart: Sphere radius is dependent on energy. Size was determined as function of energy in MC-studies.
All of this results in a shower direction resolution below 2 degrees at energies above 100 TeV.
But there is still room for improvement! For example, so far no analytical shower elongation included yet in PDFs.
Aart: Shower elongation is included via MC PDFs, but these PDFs were created using 1 PeV showers, so the reconstruction might be somewhat biased.
Maarten: First try to include timing information, then include shower elongation, not the other way around. And also try to include PMT effects (time slewing!).
Maarten: Using absolute spherical geometry theta and phi angles can be a little awkward. Formulas become a lot cleaner if you use shower direction estimate as z-axis and define the corresponding direction cosines.
Maarten: On the longer term, need to include detector information, i.e. the rates and non-working PMTs and HRV PMTs. Is this on the agenda?
Aart: Certainly. Will soon be in the position where we can implement this. Also need to include rate information in the files.
Bouke: I will try to collect all the action points addressed today, such that we can set up a plan to look at them.
Aart: One additional point: can we try to run AAShowerFit on ORCA data?
Action points:
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Normal rounds
Jordan
Looking into likelihood parameter landscape surrounding the shower maximum.
Color coding of plots:
Position parameters indeed give maximum likelihood around true position.
Same for energy.
Very different behaviour in my plot for direction!
This may be caused by a difference in the calculation of the direction longitudinal angle.
Result: promille level difference in angle.
Maarten: Mathematically these two should not differ of course. But there may be some inaccuracy in the rotation matrix (jpp side) or a large numerical error in the evaluation of the acos for cosines bigger than 1 or smaller than -1 (aanet side).
Aart: Could also be an issue related to shower maximum or elongation.
Brían: What's the further plan?
Aart: We achieved an improvement for the vertex reconstruction using first hit arrival time PDFs. This is not too interesting, except for the tau reconstruction that Thijs is working on. But we are now also looking into whether we can achieve similar improvements for the direction reconstruction.
Brían:
The extremely low first hit probabilities presented last time, turned out to be related to the hit topology. I had been looking at PMTs far away from the vertex, but where the muon passes extremely closely to the PMT (~ 1m closest distance of approach).
When shifted away 60 m from the muon track, we see first hit probabilities which are around O(0.1) and the second peak disappears.
Maarten: We see the tails of the distribution here, because we miss the main peak in the PDF! As soon as you have passed this peak or are slightly before this peak, then the first hit probability goes to zero.
Ronald: Did you calculate the no-hit probability before the first hit?
Brían: Yes. This is the variable V.
Maarten: If you zoom in on the region around 200 ns (first peak in the PDF) and make the binning finer and finer, then the first peak will likely explode. It should be almost like a Dirac-delta, if you position the PMT (almost) right on top of the muon-track, then you are blinded by the light. So the first hit probability and the arrival time distribution are not actually shaped the same way!