## Support #1789

### Field Off Multiple Scattering Measurement

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**Description**

Aim to measure multiple scattering in Liquid Hydrogen with the cooling channel magnets off.

**Files**

#### Updated by Nugent, John about 7 years ago

Hi Chris,

I have uploaded a figure showing the multiple scattering for two data samples. I am working with some (3, 240) MC data that I have. I cut on the P of the beam of which the mean value is 229 MeV/c. I am looking to see how strongly correlated the multiple scattering angle is with P. In this "worst case" scenario all particle with P below 229 MeV/c are in the P_Low figure and all particles with P above 229 MeV/c are in the P_High figure. Our TOFs have considerably better resolution than this case so here we are considering the two furthest apart distributions in P. As you can see in P_Low.pdf the two distributions have very similar means and RMS values. I also calculated the

Kolmogorov -> 0.31

Chi^2 -> 136.56

P value -> 0.74

NDF -> 148

The Kolmogorov test works best for unbinned data so I am not sure how relevant this value is here however the P value seems quite high which is again encouraging.

My first impression from this is that the multiple scattering angle measured is not strongly dependant on the P of the distribution. I would therefore be inclined to fit over the entire dataset without cutting to strongly in P to measure the scattering angle. With the numbers that I provided you previously this means that we would have a dataset comparable in size to that of MuScat in data.

Based on these numbers we have more than enough statistics to fight statistical errors on a bin by bin bases. My next task is to work through the systematic errors that I discussed in my talk last week. I will produce plots similar to the one I have just uploaded for the various systematics and document there impact. I am hoping that I will get through this tomorrow. With this information I am hoping to show that with a data set of the size we previously discussed a measurement of multiple scattering will be possible.

Cheers,

John

#### Updated by Nugent, John about 7 years ago

**File**Intsect_scat.pdf Intsect_scat.pdf added**File**PID_scat.pdf PID_scat.pdf added

I have uploaded plots for the PID & track projection.

1) PID

I cut all particle which are not muons in MC and look at the change in the scattering distribution. The mean and RMS are very similar to the uncut distribution and the

Kolmogorov -> 1

Chi2 -> 12.54

P -> 1

2) Projected tracks

I project tracks from the tracker volumes to the absorber and cut on the distance between the upstream and downstream projected tracks in the transverse direction. Again the mean and RMS are similar to the scenario with less stringent projection cuts the

`Kolmogorov -> 1`

Chi2 -> 21.06

P -> 1

3) Misalignment

Obviously I am still working on the misalignment so I do not have final numbers for this. However for the internal tracker alignment that I have done with Millepede I can say that the RMS of the residual plots was ~0.5 mm. This crudely corresponds to a 0.1 degree smearing for the scattering angle plots which have an RMS of ~1.7. So a small increase in the width of these plots.

4) Windows

I do not have any MC without the windows yet so I have no numbers for this particular error

5) Resolution of trackers

I am working my way through the MuScat deconvolution calculation for our trackers and I will post similar plots once I have them.

6) Residual fields

From a back of the envelope calculation we can see rho = P/(0.3*B) = 10^4 -> theta = 1/rho = 10^-4 rad -> delta_r = 0.3 mm in 3 m. This behaviour is slightly smaller than the misalignment contribution. I also ran a quick MC simulation with the residual field map provided by Holger however the population in the plots was to small to give an answer so I am currently re-running it to generate larger statistics.

All of these studies assume the worst case i.e. we don't cut any pions out with our PID detectors, the residual fields are maximal so they are conservative estimates. However from these figures we should be able to make a measurement with reasonable systematics. The largest effect is the misalignment and even this manageable.

I am still working on unpacking the tracker resolution is there anything else that I have missed Chris?

Cheers,

John

#### Updated by Rogers, Chris about 7 years ago

Response to comment #1:

I am comparing your fig P_Low.pdf with fig. 22 in MuScat paper.

My first impression from this is that the multiple scattering angle measured is not strongly dependant on the P of the distribution.

You do not have sufficient statistical significance to make this claim. In order to make such a claim with the statistical significance of MuScat, surely you need a sample with at least the same statistics? Specifically, your error bars are much larger than those in fig. 22.

Why not use equation 32.15 from pdg thus avoiding any arguments about statistics.

As an aside, your x' distribution **must** be symmetric. You are doing something wrong as it is very not symmetric.

Response to comment #2:

As above, the statistical significance is insufficient to understand anything.

Can you please use a binning that is in radians and equivalent to the muscat binning, as we are trying to do a like-for-like comparison. The binning they use is in Table 2.

#### Updated by Nugent, John about 7 years ago

**File**P_theta_0_plot.pdf P_theta_0_plot.pdf added**File**PID_theta_0_plot.pdf PID_theta_0_plot.pdf added**File**intsect_plot_theta_0_plot.pdf intsect_plot_theta_0_plot.pdf added

I have re-done all of the plots with the MuScat binning for a clearer comparison. The re-processing of the MC with the latest geometry is now finished so all of the plots now have an order of magnitude more statistics. I have implemented the expression from the PDG for each of the scenarios with the plots attached.

As an aside, your x' distribution must be symmetric. You are doing something wrong as it is very not symmetric.

As I said the alignment study is not complete it may be the case that the trackers have a theta_x or theta_y rotation with respect to each other. In this scenario we would expect an asymmetric distribution. Additionally unpacking the tracker resolution will include a statement on how efficiently tracks are reconstructed at various angles scanning along the tracker spacepoints. If the recon is doing better at some angles compared to others then the distribution may again be asymmetric. This may be particularly noticeable in bins with a low population.

Cheers,

John

#### Updated by Nugent, John about 7 years ago

**File**scat_P_mc_plot.pdf scat_P_mc_plot.pdf added**File**scat_P_mc_MuScat.pdf scat_P_mc_MuScat.pdf added

I doubled checked with Ryan the geometry used in the MC runs does indeed include misalignments that we have measured to the best of our knowledge. This is one possible explanation for the asymmetry in the scattering plots. I have also switched to the MC values when measuring the scattering. If the issue was due to reconstruction problems then this would have resolved it. While the asymmetry is slightly reduced it nevertheless remains. As before further unpacking of the alignment and tracker resolution may resolve the rest.

I have attached a plot showing the scattering distribution for two different samples. The first are particles with 219<P<239 MeV/c and the second are particles with 239<P<259 MeV/c. I have included plots with the y-axis as events and probability per radian. The latter should hopefully allow for easier comparison with MuScat.

Thank for the heads up earlier about the DS. I have looked at pion runs from June without the DS for numbers. Looking at run 7185 in nearly 2hrs they collected 30k TOF2 triggers. If I believe that half of these triggers are muons then this is roughly in line with the numbers that I expected from the previous setting.

I hope that the updated plots answers the main question from Friday - how the number of muons in the outer most bin varies with P. If you need further numbers of figures could you let me know before Wednesday Chris?

Cheers,

John

#### Updated by Rogers, Chris about 7 years ago

- The systematic errors you calculate are some horrible convolution of the beam distribution in pz and the scattering angle dependence on pz.
- It looks like you did not normalise your histograms properly scat_P_mc_MuScat.pdf green dashed looks like it has around a factor 50 % excess of events compared to red - maybe you will tell me that I am wrong?
- I don't really know what to make of the asymmetry.

I think you need to step back to something simpler using a trivial geometry i.e. no trackers, no windows, no aperture, just liquid Hydrogen, and then add layers of complexity. So...

Can you please make the following plots:

- Calculate the acceptable pz width for your analysis
- Assume the Gaussian Moliere MCS distribution. Fire an ensemble of 1e6 muons through 350 mm liquid Hydrogen with pz 200 MeV/c. Make into a histogram showing on the y axis "probability per radian" and on the x axis "angle, radians". Count the number of particles in each bin.
- Repeat, scanning pz from 140 to 240 MeV/c in 5 MeV/c steps.
- Plot "probability per radian" against pz for scattering angle in the ranges (0.000 - 00269), (0.0347-0.0463), (0.0938-0.1151).
- Extract the momentum bite for your analysis that gives fractional error of 10% of the statistical errors quoted in the MuScat paper, i.e. 1.7/40.6/10., 0.028/0.117/10., 0.003/0.008/10 respectively for each bin (quoting numbers from 1.90 data line of the MuScat note).

- Assuming axial tracks, plot the pz distribution that one expects from a typical pion run (e.g. run 7185). This tells you the approximate rate of "good muons" that you expect from the pion run. How long do we have to run to get > 50,000 "good muons"?

- Repeat using the Geant4 MCS distribution, assuming a 350 mm cylindrical liquid Hydrogen absorber and no trackers or windows. I can help.

- Repeat varying thickness of the absorber. Then,
- Find out the radial thickness profile of the absorber. I can help.
- Deduce at what radius does the thickness of the absorber make a significant change to the MCS distribution. This becomes a radial acceptance cut on the absorber.
- Assuming a point source at TKU, what is the solid angle acceptance of the absorber assuming radial acceptance cut?
- Assuming a point source at TKU, what is the solid angle acceptance of TKD?
- Ratio of these solid angles is probably a good guesstimate of the number of muons that will be lost. Or you can do the full analysis using a pion reference run beam.

You will need to do this sort of analysis in the end anyway.