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2021-03-19 scattering¶

The next referee's meeting to discuss LiH scattering analysis will take place on Friday 19th March at 09:30 GMT.

We will use the regular MICE Zoom meeting room:

[[computing-software:MICE_zoom_info|MICE Zoom Connection]] (login required)

Copy of the paper

Notes¶

Analysis update¶

John Nugent gave an update. Some items still outstanding.

ACTION: Add forward convolution uncertainty - JN made a simple toy model. Throws a couple of Gaussians and convolves them, with and without truncation that represents the channel acceptance/statistics. Systematic effect for a "worst case" is less than 1 % effect on the bin population even in the tails. 0.1 mrad on RMS, compared with 0.5 mrad systematic. JHC asks what happens to the probability (rather than fraction of each bin). JHC points out that the scattering distribution has large kurtosis and this needs to be represented. PS: we can do sum of two Gaussians. ACTION repeat with more realistic scattering distribution. ACTION show the probability as well as fraction of each bin.

Momentum calculation - JN showed results of toy MC. Noted that the momentum loss is 34 MeV/c for 170 MeV/c and 28 MeV/c particles which is consistent with the 6 MeV/c systematic correction. PS: why do we need to repeat with this less sophisticated formula that includes no stochastic effects? CR: you have a mapping from TOF12 to momentum based on MAUS. Can you please check that the TOF12 to momentum mapping in the toy MC is the same. JHC: ACTION Please put formula (1) onto the same plot as the toy MC; the difference should be the correction.

Momentum residual - JN showed the residual has mean consistent with 0 for empty and full, TOF01 vs TOF12 at 200 MeV/c. JHC can we see the residual as a function of momentum? JN will have a go at pulling the plots up while we go through the paper (Completed during the meeting, see below).

Acceptance distributions at other momenta - plots looked qualitatively similar at different momenta. JHC what were the values at theta= 0? CR we will look them up at the end (Completed during the meeting, see below). JHC are you happy that they are not symmetric. Esp 172 theta_X. PS yes it is a symmetric fit. The beam distribution was a bit asymmetric CR: this is a small effect compared to the other systematics.

Normalised residuals plots in forward convolution - JN showed the plots

Correlated errors - JN discussed his algorithm for calculating correlated errors still a work in process

Moliere checks - JHC has been looking at the Moliere calculation. Original did nit include scattering by electrons. Original fix is Z^2->Z(Z+1) which is incorrect because electrons are low mass and bound but okay for order of magnitude (hence stronger in low z). JHC followed a Gottschalk NIM paper. Ambiguity on sign of u_in where u_in is some constant. JHC showed results for u_in with both curves. Flipped sign appeared to reproduce the data better. Also checked effect for Li7 but small effect. PS: how does it compare with z(z+1)? JHC: roughly 20 % on central width. PS: muScat compared to Geant4.7 and to Z^2 Moliere and Z(Z+1) Moliere and conclude for lH2 neither is great. This is consistent with JHC's statements. ACTION JHC to compare with muScat. ACTION JHC to send new Moliere data. ACTION CR we should also write down what we did in an appendix to help others confused by sign of u_in.

JN - TOF01 vs TOF12 residual RMS 170 MeV/c is 5.808, 240 MeV/c is 10.39. CR: TOF resolution in momentum is worse and energy straggling is worse.

JN - momentum acceptance in the central bin is 98.8 % 200 MeV/c, 97.6 % 170 MeV/c. Consistent Order of Magnitude with Gaussian toy model calculation.

Paper¶

Title - ACTION remove MICE from title.

Abstract - ACTION remove sentence "MICE has measured emittance reduction". Would be helpful to indicate whether measurements agree with data in the final line of the abstract.

Section 1

Too much wording about MCS which is perhaps unnecessary. Specifically line 25-26. Bethe did not simplify Moliere theory. Moliere treated the nucleus. Bethe and others accounted for the electrons. Fano modified to account for inelastic cross-section of electrons i.e. "proper" correction for electrons. Condense to "we have measured something and compared it to G4 and Moliere modified by Fano". Remove the formulae beyond eqn (3). E.g. do we need Eqn (4) and (5)? PS it is what's inside G4. JHC: G4 does not do equation (4) and (5) really. We are in dangerous territory if we try to say what G4 does. E.g. what is the Urban model? What is Lewis model? JHC: please write down what is the G4 "data card" used but no more. CR: ACTION yes I can help with this.

JHC: cooling expression eqn (6) (cooling eqn) should move up the paper to highlight the importance of scattering. Need to move the following paragraph up as well to keep consistency/flow of the paper. MB: please fix "m" -> "m_\mu".

PS: need to fix the momentum range of the bins. JN: you are correct, it is 160 to 255.

Section 2

MB: is fig. 1 to scale? CR: yes it was generated from MAUS geometry. The line break indicates that it is discontinuous. PS: do we need the date? CR: ACTION no. Let's take it off. JHC: ACTION Add some dimensions to the text. With respect to position of upstream measurement plane, the absorber and downstream measurement plane. Distance between TOFs. Fiducial radius of the tracker (150 mm).

JHC: what is the point of referencing the detectors in the text? CR: they explain the diagram.

JHC: ACTION say right handed coordinate system, +y is up, +z is beam direction. Don't quote east and west.

JHC: ACTION mention aluminium windows in the tracker volume, explain tracker helium. Absorber was under vacuum. Mention Parylene coating on LiH absorber.

MB: ACTION need short sentence describing the tracker - what is "station 5" CR: ACTION record spatial resolution, reference scattering budget in the table

JHC: ACTION most expressions (8) - (14) are not necessary. Why not use space angles? Say we use projected distributions where the projected distribution is in coordinate system of the reference particle. Mention the angular distribution of the incident beam. PS: ACTION we will keep eqn (9) and (10) and put them in an appendix/supplementary information.

JHC: later on maybe we should show the theta scat 3D space angle CR: it might just confuse things. JHC: at least explain that we use projected angles because of the trouble with deconvolution. PS: we can look at the 3D data distribution vs G4. CR: let's not add more work! ACTION We will have a look at it and add it to the note. If it causes trouble it doesn't go in the paper.

JHC: ACTION again, please give a bit more details on dimensions. Table 1 - please discuss in the text a bit more the effect of scattering and how it contributes to the "angle". "Total" should be "Expected" total. Note Al window has a thickness that varies with radius.

Section 3

JHC:ACTION Say that the positron contamination is excluded from the sample. JN: it happens naturally by the momentum selection cuts. PS: "Positrons are identified by having TOF01 less than 26 ns" note they are used in the analysis as part of the TOF normalisation.

JHC: what is significance of 3 mm emittance. CR: it was only 3 mm nominal. PS: it is to highlight that it was not a pencil beam. JHC: we need to describe the beam - indicate size and divergence. PS: ACTION could you please provide RMS width and divergence of each beam.

JHC: do we need table 2? CR: we could put absolute numbers into table 3 to give an indication of stats PS: ACTION I am happy to remove table 2.

MB: why are the first three rows the same in Table 3? JN: it comes before the momentum selection CR: ACTION you should merge the top 3 columns then.

JHC: line 100 - ACTION 90 mm is not the active radius of the tracker but rather a fiducial selection. MB: ACTION please define station 5 (in apparatus description section).

JHC: line 102 - ACTION please write that the data is binned by tof in 200 ps bins (not momentum).

JHC: we add the samples together, then chop each one into TOF bins? JN: yes. CR: ACTION you should call them samples, not beams. JHC: say early on "all of the beams were combined, and then we selected samples from the combined distributions"

JHC: ACTION please move the TOF distribution plot up to the selection section

CR: other papers we have shown the distributions for all the cuts. JHC, PS: I don't think that is necessary. PS: I will move fig. 5(a) and (b) up to Section 3. JHC: you can't move fig. 5(b) without discussing momentum reconstruction. CR: reader does not need to know necessarily the details of momentum recon JHC: can you show the same samples on the same plot JN: I will have to think about it. (Note: we were leaning towards leaving fig. 5(b) and only moving figure 5(a)).

JHC: fig. 5(a) where are the pions? PS: it is a muon beam, pions are strongly suppressed. CR: you don't really mention the transport line at all. PS: I could add it. CR: it's not a big effect probably not worth discussion.

MB: ACTION please cite the MAUS JINST paper ref [28] - R. Asfandiyarov et al 2019 JINST 14 T04005

JHC: overflow bin statement must be later in the paper, in the analysis section. PS: I prefer it here. CR: in the emittance paper we talk about upstream and downstream samples. JHC: ACTION use wording like "We select on the upstream tracks and the downstream distributions are whatever they are" PS: the acceptance plots which show efficiency reflects the fact that we do have events that go into the overflow bin.

JHC: line 117-120: fig. 4 shows a mysterious asymmetry vs theta x and theta y. Can we remove fig 4 and explain the alignment procedure in the text. Then we don't need to list the numbers in the text. ACTION Just mention that the alignment is done and it is small.

JHC: line 116: how can fig. 3 be squared with the scattering in the absorber. A better plot is the position of the vertex where scattering occurred. JN: well, 36 mm (RMS) is a reasonably small distance, it shows that they likely scattered in the absorber JHC: what about the ones that are 200 (or 300) mm apart? CR: it means it scattered not in the absorber. JHC/CR: ACTION we decide to remove fig. 3 and remove the statement saying fig. 3 demonstrates scattering consistent with absorber scattering. JN will make a plot showing z position of closest approach between the tracks for the MICE note and we will decide whether we should include it.

PS: so we remove paragraph line 115-120? Or abbreviate heavily? JHC: yes.

JHC: Line 122. ACTION This says the same thing as line 102. PS: yes we will move this up when we move fig. 5(a) up.

JHC: be careful, p_mu recon is also near here. Need to make a separation between sample selection which is TOF01 and momentum reconstruction, which is different.

JHC: ACTION propose using subheadings like "selection" and "reconstruction" in section 3.

JHC: line 128 - you mean "TOF samples" not "beam settings". not THE three different beam settings as there are 11 or so settings. ACTION please fix the wording

PS: ACTION we also need to rehash table 4 - "172" is no longer "172". JHC: just call them TOF bins. CR: need to redo the table headings in table 3 as well

JHC: table 4 what is the standard deviation? it is the RMS width of the bin. Fig. 6 what is the true momentum distribution width? CR: fig 5(d) has the momentum residual. JN: we chose the bin width to be wider than the TOF resolution. PS: the RMS in table 4 is the RMS of fig. 6. PS: we could include residuals from all 3 settings. JN: the paper would start getting quite long. JHC: the point is table 4 shows the momentum spread of the reconstructed muons, not the momentum spread of the true muons. E.g. It may lead to a misleading Moliere calculation for someone. PS: ACTION we could include the residual width on the table. JHC: yes please also make sure the s.d. includes measurement errors. Call residual width "momentum resolution". PS: I will also reference fig. 6 from tab. 4

JHC: ACTION table 4 caption needs a bit of reworking

JHC: do the figures change for no absorber? JN: yes, e.g. the TOF bins change. CR: should we list both. JHC: ACTION yes, list the tof bins in table 4 for empty and full datasets. CR: It is good, it exposes some of the limitations (and hence the systematic error). JHC: do they have the same momentum JN: yes more or less.

Fig. 7 JHC: (a) and (b) show distributions of position upstream. It may be more useful to show distributions of angles upstream and downstream. JN: it exposes the angle offset. JHC: you can correct for it. JN: the plots are offset after accounting for the 6 mrad correction. CR: <theta^u_y - theta^d_y> = <theta^u_y> - <theta^d_y>. If upstream distribution is offset then both distributions are offset (or there is a bug). PS: the position distribution feeds into the fiducial. JHC: so does the angular distribution. We should include the angular spread. ACTION make a Table including RMS x, x', y, y' upstream and downstream. PS: keep fig. 7(a) and (b). Shows the asymmetry and good reproduction in MC. JHC: ACTION show (c) and (d) for the three samples. Should show good agreement between MC and data.

PS: suggest 7 x, y, x', y' for 200 beam, subtract off x' y' means so that MC and data are both central. Another plot showing theta_x, theta_y for the three settings. CR, JHC: agree. JHC: and table of chi^2. Worth comment in the text that Geant is in good agreement with the data.

JHC: do we need empty theta_x, theta_y? JN: there isn't an MC data comparison. JHC: there should be one. ACTION add empty theta_x, theta_y.

Section 4

Section 4.1
JHC: Moliere has disappeared from fig. 8. Forwards convolution is best done with Geant. Why not just use fig. 7 if you dont have moliere? PS: fig. 8 you are demonstrating that empty + G4 is consistent with data. Fig. 7 demonstrates G4 a priori is consistent with data. JHC: but the agreement in fig. 8 is worse than the agreement a priori. Why not just use the full MC? JN: we can include Moliere as well. PS: overlaying moliere and geant is difficult to read. Should we do another set of plots including moliere? JHC: what is the point? PS: fig. 8 shows forwards convolution works. This justifies the concept of deconvolution. JHC: there is a disagreement with Geant. PS: table 6 shows the chi2 is not so bad. JN: we isolate the scattering in G4 from the rest of G4. JHC: then we should compare G4 forwards convolution and G4 JHC: the forwards convolution is not as good as the full MC. PS: there is a systematic uncertainty associated with the convolution method.

CR: is there anything technically wrong with the plots? JHC: Eq. 16 is wrong. what is theta_max and theta_min. JN: I will check. Theta max and theta min come from the distribution I used in the forwards convolution. JHC: What does the chi2 wording in eq 17 mean? Where is the acceptance correction done? Strange statement about iterative stuff that I don't understand. JHC: what is the conclusion drawn from fig. 8. PS's conclusion is that the forwards convolution of empty is reasonably consistent with full. Given that G4 is consistent with data, one may conclude that forwards convolution is a useful technique. JN will try again to put Moliere on the paper.

JHC, CR, JN, PS: ACTION Agree that we include fig. 8 with Moliere, Full, G4 convolved, NO empty, change the titles, check and fix the convolution routines as necessary.

JHC: would be interesting to see if G4 and Moliere agree independent of data. ACTION Put it in the MICE note. Do the new calculation. Possibly in an appendix of the paper.

Section 4.2
JHC: ACTION Please add a bit more explanation on the end. How does xi, xi' refer to the figures. PS: okay, why not just reference the paper. JHC: yes, but you need to at least say what you use as inputs and how you decide it converged. PS: say what the deconvolution does (in words) and how it goes about its business. JN: the code is included in ROOT so it is reasonably well known.

Section 4.3
JHC: what does "the effect of additional material in the scattering model" mean? PS: we adjust the systematic in the density. JN: we don't do that anymore. ACTION Need to get rid of the sentence. Instead we quote error on the absorber thickness. JN: put it in the apparatus description section PS: it is there, but we don't quote effect on radiation length or scattering. CR: ACTION put the radiation length and "expected scattering width" in apparatus section, remove it from 4.3.

JHC: ACTION variations should be uncertainties

JHC: what does variations in the time of flight due to the resolution and momentum calibration mean? JN: it means TOF resolution and momentum reconstruction uncertainty. ACTION Momentum "estimation" would be better, rather than calibration.

JHC: TOF is not a systematic effect in scattering, it is momentum resolution. JN: we treat it as a scattering uncertainty. PS: it changes the scattering width so it is systematic on scattering width. JN: I will make a TOF MC truth distribution plot to help us see through this.

CR: you are discussing two different things. JN/PS are talking about measurement of thetax for 200 MeV/c. JHC is talking about measurement of thetax for the sample. JN: we need to do measurement of thetax for 200 because that is the momentum of the Moliere. JN: but we have MC distributions at 200 for doing the deconvolution. JHC: put the finite momentum width in the MC distributions.

JHC: ACTION line 177 to 185 is repeated immediately afterwards. Please remove repetition.

JHC: ACTION eqn (20) should be corrected.

JHC: is sigma signed quantity? PS: ACTION I will check with JN.

JHC: I don't understand what "imposed" means on line 155. ACTION Please clarify.

JHC: theta0,x is not really the RMS? It's a Gaussian fit? PS: no, he does use the widths. I will check with JN. JHC: but widths in table 7 is not the same thing. PS: the systematics are RMS widths, table 7 is the gaussian fit width. PS: they should be theta_0,x theta_0,y. PDG says Gaussian fit to central 98 %. JHC: but what did you do? PS: Gaussian fit in +/- 45 mrad. JHC: you should say that in the paper. PS: yes. CR: it is on line 220. JHC: it is not directly comparable with PDG. PS: we would have to check. CR: looking at fig. 7 it looks like about 99.something %. JHC: worth investing a bit of effort CR: looks like it might be possible. ACTION Need to check.

Arrange a meeting for 3 weeks time. Propose Friday 9th in the afternoon.