1. Step 1 Analysis: Progress Towards the Emittance Paper
26/06/2012: CM33 Analysis Session
Step 1 Analysis: Progress Towards the Emittance Paper
CM33: Analysis Session
V. Blackmore

2. 26/06/2012: CM33 Analysis Session
The Cogs & Wheels
The meaning of “data”, “reconstruction” and “simulation”.
The reconstruction procedure.

3. What do I mean by “simulation”, “reconstruction” and “data”?
26/06/2012: CM33 Analysis Session
What do I mean by “simulation”, “reconstruction” and “data”?
Simulation
Data
Mark took a G4Beamline created beam and simulated its passage between TOF0 and TOF1 in G4MICE.
We know everything about this beam at TOF0 and TOF1: 𝑥, 𝑦, 𝑧, 𝑝 𝑥 , 𝑝 𝑦 , 𝑝 𝑧 ,𝑡
It does not include any detector effects (e.g. resolution).
Simulation is shown in red in subsequent plots.
Compiled from Step I data from 2010.
Know only 𝑥, 𝑦,𝑡 at TOF0 and TOF1.
Position determined from the time’s recorded by PMTs at each end of a slab, e.g.,
𝑥= 𝑐 𝑒𝑓𝑓 𝑡 𝐿 − 𝑡 𝑅 +∆ 2
Depends on slab calibration.
Data is shown in black in subsequent plots.
𝑡 𝑅 𝑥
𝑡 𝐿

4. What do I mean by “simulation”, “reconstruction” and “data”?
26/06/2012: CM33 Analysis Session
What do I mean by “simulation”, “reconstruction” and “data”?
Simulation
Data
Mark took a G4Beamline created beam and simulated its passage between TOF0 and TOF1 in G4MICE.
We know everything about this beam at TOF0 and TOF1: 𝑥, 𝑦, 𝑧, 𝑝 𝑥 , 𝑝 𝑦 , 𝑝 𝑧 ,𝑡
It does not include any detector effects (e.g. resolution).
Simulation is shown in red in subsequent plots.
Compiled from Step I data from 2010.
Know only 𝑥, 𝑦,𝑡 at TOF0 and TOF1.
Position determined from the time’s recorded by PMTs at each end of a slab, e.g.,
𝑥= 𝑐 𝑒𝑓𝑓 𝑡 𝐿 − 𝑡 𝑅 +∆ 2
Depends on slab calibration.
Data is shown in black in subsequent plots.
Reconstruction
‘Halfway house’
Derived from simulation.
Takes 𝑥, 𝑦,𝑡 and smears according to TOF resolution.
Should be comparable to data.
Reconstruction is shown in blue in subsequent plots.
𝑡 𝑅 𝑥
𝑡 𝐿

5. “Reconstructing” Simulation & Data
26/06/2012: CM33 Analysis Session
“Reconstructing” Simulation & Data
Transfer matrix
𝑥 1 𝑥′ 1 = 𝑀 11 𝑀 12 𝑀 21 𝑀 𝑥 0 𝑥′ 0
Marks thesis gives all the details.
First, assume the muon travels in a straight line and estimate momentum.
Then, assume linear beam transport, and track the muon through Q789, determining the angles 𝑥 ′ , 𝑦 ′ at TOF0 and TOF1.
Repeat to improve.
𝑥′ 0 𝑥′ 1 = 1 𝑀 − 𝑀 −1 𝑀 𝑥 0 𝑥 1
{ 𝑥 0,1 , 𝑦 0,1 , 𝑡}
{ 𝑥 ′ 0,1 , 𝑦′ 0,1 , 𝑝 𝑧 }
𝑀 𝑥 =𝑂 𝐹 9 𝑂 𝐷 8 𝑂 𝐹 7 𝑂 𝑀 𝑦 =𝑂 𝐷 9 𝑂 𝐹 8 𝑂 𝐷 7 𝑂

6. Reconstruction Accuracy
26/06/2012: CM33 Analysis Session
Reconstruction Accuracy
How well does the reconstruction work?
The emittances of the Step I data sets.
Improvements to make.

7. Reconstruction Accuracy
26/06/2012: CM33 Analysis Session
Reconstruction Accuracy
Mark has demonstrated how accurate his algorithm is at previous CMs if you need more detail.
Simulation vs. Reconstruction: Then…
… and now. ? ? ?
After recalculating with the appropriate variables.

8. Calculated Emittances in Data
26/06/2012: CM33 Analysis Session
Calculated Emittances in Data
Inc. cuts on TOF slabs,
𝑝 𝑧 , and 𝜒 2 <6

9. 26/06/2012: CM33 Analysis Session
Improvements
To better demonstrate agreement or disagreement between data and our expectations.
Option 1: Remove the effect of detector resolution from data, so we can directly compare with simulation.
Calculate the ‘resolution matrix’ from the difference between the covariance matrix describing reconstruction and simulation.
Ideally, then subtract this matrix from our data.
Problem 1a: Get undesirable negative elements of the resolution matrix.
Problem 1b: Simulations only exist for the ‘6mm’ beams.
Not clear what to do for the others.
Option 2: Remove the effect of dispersion from simulation, reconstruction and data.
Quote emittances as 𝜀 𝑥,𝑦 = 𝜖 𝑥,𝑦 + 𝐷 𝑥.𝑦 , where 𝜖 is the emittance with dispersion subtracted, and 𝐷 𝑥,𝑦 is the dispersion in that plane.
Problem 2: Differences in the simulation where there shouldn’t be differences!

10. Sanity Check Please! Next, to the attached pdf plots!
26/06/2012: CM33 Analysis Session
Sanity Check Please!
Next, to the attached pdf plots!
Red = simulation, blue = reconstruction, black = data.
All 1D histograms are normalised
Dispersion
𝑥 0 → 𝑥 1
𝜇 + and 𝜇 − simulation discrepancy