1. π +  e + ν e Calibration: Corrected Results and Degrader vs. No Degrader James Mott Mu2e Software & Simulations Meeting 02/04/15

2. Reminder: Pion Calibration 22 One idea is to calibrate the tracker momentum scale using positive pion decay to a positron: π +  e + ν e If the pion is stopped in the target, then this produces a mono-energetic e + source at 69.8 MeV for the tracker Using a peak for energy scale may provide a better handle (smaller systematics?) than using the DIO tail BUT only ~10 -6 π stops per POT and Br(π +  e + ν e )~10 -4 mean that the signal we’re looking for is very small

3. Reminder: Previous Results (& Mea Culpa) 33 At the last collaboration meeting, I presented a feasibility study for finding this small signal. The day after, I found a bug where I was correcting for the efficiency of a stopped particle decay to a tracker/calo hit twice. I corrected the results which Dave then showed in his summary talk. I don’t think that any main conclusions drawn have changed, but the S/B has reduced from 10 to 4. Here, I’ll quickly re-run over the main details of the previous talk and show the updated result. Then I’ll show the same results if the degrader is removed…

4. Emma Barnes did a lot of work to study the feasibility of using this channel for calibration (see DocDB 3681 & 2884). She concluded that with some changes to the B-field, beam intensity and adding a pion degrader, a peak should be visible: We want to validate this result by reproducing it in the Offline software framework and then build on it from there. Recap: Emma’s work 44 Momentum / MeV

5. Changes from nominal running conditions: 55 For this calibration, there are significant changes to the default setup: Rotate collimator at centre of transport solenoid to accept positive particles (and remove negative ones) Reduce B-field to 70% (using Mau9 special fields) Add 3.5 mm pion degrader to entrance of DS Reduce beam intensity by factor of 50 These last three changes were all recommended by Emma after considering many different configurations For now, we’re taking them as the optimal configuration.

6. What samples do we want to simulate? 66 To make a realistic representation of the calibration I’ve made the following samples of events: Stopped π +  e + in target (S) & degrader (BG) Stopped π +  μ +  e + in target & degrader (both BG) In-flight π +  μ +  e + and π +  e + (both BG) Stopped μ +  e + in target, degrader & other places (needed for event mixing) In-flight μ +  e + (BG and event mixing) Beam flash: all in-flight particles except μ + & π + (mixing) I’ll use colour-coding in the next few slides…

7. Simulation stage 1: 77 As a starting point, I take previously generated samples of protons-on-target (‘beam’ and ‘pions’ samples): Particles go from POT to middle of transport solenoid (TS3) ‘beam’ has full physics on (2 x 10 9 POT) ‘pions’ has pion decay switched off to increase number that make it through (5 x 10 9 POT) Geant4 killer volumes p

8. Simulation stage 2: 88 Take the output from stage one (at TS3 vacuum) and pass these to the detector solenoid (DS). Rotated TS3 collimator 180° to accept positive particles. Special downstream transport solenoid field used to avoid discontinuity due to DS @ 70% In ‘pions’ sample, decay still switched off.

9. Take particles entering DS and track until they stop. Keep pion decay switched off and also turn off muon decay. Separate out those that stop in the target, degrader and elsewhere dividing into pions, muons and other particles. Store input information and stopping information for pions and muons. These Ntuples become the input for the next stage. Simulation stage 3: 99 DS field @ 70%

10. Simulation stage 4: Pions & Beam Flash 10 Take particles divided by type and with stopping info and make hits in tracker/calorimeter for use in reconstruction. For pions, turn on decay and force either e + or μ + (and weight event based on proper time). Target/degrader stops: sample position/time distributions Non-stops (in flights): sample input distributions For beam flash, run through input particle distributions from beam sample once

11. Simulation stage 4: Muons 11 Take particles divided by type and with stopping info and make hits in tracker/calorimeter for use in reconstruction. For in-flight muons, take target & other stops: Force decay randomly along exponential distribution truncated at proper stopping time (weight accordingly) For stopped muons, place at location/time from beam sample. Weight as (1 – in-flight weight) or ~98%. Finally apply filter at 150 ns to keep output files small

12. Bookkeeping & mixing: 12 SampleN Gen (10 6 )Records* / μBunch** π+ Target e+e+ 2.55.8 x 10 -5 μ+e+μ+e+ 5008.8 x 10 -2 π+ Degrader e+e+ 52.7 x 10 -5 μ+e+μ+e+ 15004.4 x 10 -2 π+ In-flight e+e+ 2.57.6 x 10 -6 μ+e+μ+e+ 109.5 x 10 -3 Beam Flash -626193 μ+ Target -1047.0 μ+ Degrader -1073.7 μ+ Other -1014.6 μ+ In-flight t DS < 1501001.58 150 – 20012500.66 t DS > 20012500.10 * Record is any event which leaves a hit in the tracker or calorimeter ** Weights taken into account. 1 μBunch = 630k POT (50x reduction) Background Mix Overlay on BG mix

13. Cut-set C (recommended for tracking) contains the following: Which selection cuts to use?: 13 ParameterCut-set C ValueSame for π + ? Why not? Fit StatusSuccessful fitY- No. Active HitsN > 25Y- Fit Consistencyχ 2 consistency > 2 x 10 -3 Y- Mom. Errσ p < 250 keV/cY- Track t 0 Errσ t < 0.9 nsY- Pitch45° < θ < 60°Y- Track t 0 700 < t 0 < 1695 nsN Pions have all decayed by then (use 300 < t 0 < 500 ns) Min Trans. Rad.-80 mm < d 0 < 105 mmN d 0 signed by angular mom. Max Trans. Rad.450 mm < d 0 + 2/ω < 680 mmY

14. Momentum distribution: After all cuts 14 In-flight μ + (BG) Target π +  e + (Sig) 67.5 – 70.0 MeV: S = 1.9 x 10 -12 / POT B = 4.6 x 10 -13 / POT S/B = 4.1 150 < t DS < 200 ns t DS > 200 ns Target π +  μ +  e + (BG)

15. With/without mixing cross-check: 15 See same relative fractions in individual and mixed samples. See similar reductions in reconstruction efficiency when overlaid on BG mix (75 – 90%) I think this result is therefore now correctly scaled… With Background Mixing No Background Mixing Cross-check scaling against reconstructed distribution of single records…

16. Effect of correcting mistake: 16 We now have a factor 1.7 more signal events. Unfortunately we also have 3.5 times more background events. S/B has reduced from 10 to 4.1, but we have more events in total. WRONG! Corrected version Previous version

17. Updated expected signal rates: 17 With these cuts, we expect 2.3 x 10 -12 reconstructed π +  e + events per POT Reduced beam intensity by 50 means ~6 x 10 5 POT/μBunch or ~1 x 10 11 POT/sec Therefore we expect reconstructed pions at ~0.23 Hz 24 hours:~19,900 evts (cf. 11,200 before) 3 days:~59,700 evts (cf. 33,600 before) These seem like large enough numbers from a statistical point of view. But further studies on systematics are needed to understand how events we’ll actually need.

18. Why use a degrader? 18 Increase no. of stopped π + s Since relativistic π + s are less likely to decay on the way, but also less likely to stop Also reduces BG from late (low energy) in-flight muons More closely reproduce stopped muon distribution: Z (mm) μ + Target Stops No Degrader π + Target Stops 3.5 mm Degrader π + Target Stops No Degrader

19. Why wouldn’t we use a degrader? 19 From an engineering point of view, an automatically removable degrader is a pain (or so we keep being told!). Indeed, at the moment, there is no design for this system. We therefore need to be sure that we definitely need a degrader for this calibration. Our gut feeling has always been that this was likely to be essential for this calibration channel. But to answer the question more thoroughly, I’ve re-run the whole simulation chain without the degrader...

20. Bookkeeping & Mixing: With/without Degrader 20 SampleRecords / μBunch 3.5 mm DegraderNo DegraderRatio π+ Target e+e+ 5.8 x 10 -5 2.1 x 10 -5 0.36 μ+e+μ+e+ 8.8 x 10 -2 3.1 x 10 -2 0.35 π+ Degrader e+e+ 2.7 x 10 -5 -- μ+e+μ+e+ 4.4 x 10 -2 -- π+ In-flight e+e+ 7.6 x 10 -6 1.6 x 10 -5 2.1 μ+e+μ+e+ 9.5 x 10 -3 1.8 x 10 -2 1.9 Beam Flash -1932071.07 μ+ Target -47.0115.12.45 μ+ Degrader -73.7- μ+ Other -14.627.61.90 μ+ In-flight t DS < 1501.581.070.68 150 – 2000.661.582.40 t DS > 2000.102.4924.9 Background Mix Overlay on BG mix

21. Cut Selection: After All Cuts 21 67.5 – 70.0 MeV: S = 2.4 x 10 -12 / POT B = 1.2 x 10 -11 / POT S/B = 0.2 (cf. 4.1 before) In-flight μ + (BG) Target π +  e + (Sig) 150 < t DS < 200 ns t DS > 200 ns

22. Do we really need a degrader? 22 Signal to background ratio is 20 times worse without degrader. We would therefore have to run for much longer to get the same level of accuracy on the peak position. We are also much more sensitive to the shape of the background in this configuration – this could be a big problem. So it looks like the degrader is necessary if we want to use this calibration technique, but this should be confirmed with a quick study of the accuracy for the two different cases.

23. Where next? 23 It seems that extracting a pion calibration signal is feasible if we have a degrader and that we get a reasonable S/B. We still need to understand if we will have enough events to identify systematic effects. It takes about 6 weeks to run through this simulation (all told), so if we want to generate higher stats, we’ll need to improve the yield for the background. In the meantime, we can work with what we’ve got so far and different signal-only samples (which are quick to make). Unfortunately, I now have to go back full-time on g-2, so I’m going to slowly hand this work over to others at BU

24. Backup Slides 24

25. Reminder: Emma’s Result 25 On top of this, the signal peak was added with a simple Gaussian at 69.8 MeV with the expected resolution, rather than an anti-symmetric tail. The normalisation for the signal peak came from her simulations and should be a lot more accurate than the normalisation on the background. Emma found it difficult to generate enough statistics for the background (as I have also). When she applied timing cuts on her in-flight backgrounds, she had very few events remaining (O(π)). As a result, to generate this plot, she used the number of events that passed her cuts and normalised with an earlier time cut. I think this is normalised to 24 hrs running (~6 x 10 15 POT)

26. After All Cuts: Compare to Emma’s Result 26 But with our higher statistics, we can now produce a more accurate version of the background shape. We find it’s smaller and flatter than in Emma’s best guess. Mostly expect observed differences between distributions. See energy tail and overall energy loss shift in my result which weren’t in Emma’s. Normalised to 24 hrs (~6 x 10 15 POT)

27. Cuts directly from cut-set C (& momentum > 62 MeV): Cut Selection: Cut-set C Keepers 27 t 0 (ns) N hits, χ 2, σ p σ t and ϑ cuts applied Distributions dominated by in-flight muons entering DS before 200ns

28. Remove early muons with cut on entry time into tracker: Cut Selection: t 0 Cut 28 Now clearly see signal 300 < t0 < 500 ns Emma found this to be optimal and I’ve not got enough background statistics to re-do it t 0 / ns

29. Check whether Cut-set C min/max radius cuts are OK: Cut Selection: Min. & Max. Radius Cuts 29 Cut-set C (with min transverse radius sign change) looks OK

30. After All Cuts: Fit Momentum Log 30

31. After All Cuts: Fit Momentum Error 31

32. After All Cuts: t 0 32

33. After All Cuts: t 0 Error 33

34. After All Cuts: Chi-Squared 34

35. After All Cuts: Event Weight 35

36. After All Cuts: Active Hits 36

37. After All Cuts: Fit Consistency 37

38. After All Cuts: Pitch 38

39. After All Cuts: Track Origin x 39

40. After All Cuts: Track Origin y 40

41. After All Cuts: Track Origin z 41