4.12 Pion identification
4.12.2 Separate velocity measurement
An alternative route to identifying pions from the range is to use the velocity information provided by the time-of-flight. Equation4.46can be rewritten
2] m [MeV/c
0 20 40 60 80 100 120 140 160 180 200
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
mixture µ π
sample µ
Entries 112374 Mean 106.352 ± 0.088 RMS 21.980 ± 0.062 MICE
ISIS Cycle 2013/03 Run 5384-5598 MAUS v3.0.0
Figure 4.57:Stacked distributions of particle masses as reconstructed from the range and charge information. The mean and RMS are quoted for the muon sample.
in terms of the velocity as
R ' mc2 K∗
(γ−1)2
γ . (4.71)
withγ= 1−β2−1
, the Lorentz gamma. The time-of-flight,t, translates to the Lorentz parameter through
γ= 1−(s/ct)2−1/2
, (4.72)
withsthe path-length. Plugging the last expression into equation4.71yields a formula for the mass:
mc2=K∗R
p1−(s/ct)2 hp
1−(s/ct)2−1i2. The theoretical measurement error now reads
σm=mσR
R ⊕(1 +γ)2σt t
. (4.73)
The uncertainty grows quickly with the particle energy but, at the momenta of interest in MICE, the error coming from the time-of-flight measurement is small. For a 200 MeV/cmuon of massm= 105.66 MeV/c2, one getsγ'1.89, t'30 ns,σt'0.150 ns,R'400 mm andσR'5 mm. This corresponds to an uncertainty on the mass of 5 MeV/c2, which is sufficient to resolve the
∼34 MeV/c2split between the muon and pion masses.
The velocity of the particle is measured prior to its crossing of TOF2 and the KL. The energy loss is not only function of the velocity, but also
of the particle mass. The change in γ-factor is represented in figure 4.58 as a function ofβγ=p/mcof the particle upstream of TOF2 and the KL for muons and pions. In the absence of prior knowledge about the particle species, the energy loss is computed for a muon.
1 1.5 2 2.5 3
0.2 0.3 0.4 0.5
βγ
∆γ
Muon Pion
Figure 4.58: Change inγ-factor experienced by muons and pions going through TOF2 and the KL, as a function of their downstreamβγ=p/mc.
The particle mass is estimated for each particle in the muon sample and in the remainder of the particle sample, including the beam pions and the background pion decay products. Figure4.59shows the mass distribution in both samples. The muon sample has been selected using the time-of-flight three-peak pattern. The muon mass is very well reconstructed but the pions produce a smeared mass distribution due to their nuclear interactions that reduce their measured range.
While the range is biased by nuclear interactions, the calorimetric infor-mation, in the form of the total charge, should remain unbiased, provided that the detector is not transparent to the products of the interaction. The mass hypothesis is reconstructed through:
m= T
(γ−1)c2 = Q
C∗(γ−1)c2. (4.74) The theoretical measurement error now reads
σm= ∂m
∂RσR⊕∂m
∂t σt=m σQ
Q ⊕γ(γ+ 1) γ−1
σt t
. (4.75)
For a 200 MeV/c muon of mass m = 105.66 MeV/c2, one gets γ ' 1.89, t'30 ns,σt'0.150 ns,Q'5500 mm andσR'350 mm. This corresponds to an uncertainty on the mass of 7.5 MeV/c2.
2] m [MeV/c
0 20 40 60 80 100 120 140 160 180 200
0 2000 4000 6000 8000 10000 12000 14000 16000
mixture µ π
sample µ
Entries 127170 Mean 105.064 ± 0.048 RMS 11.940 ± 0.034 MICE
ISIS Cycle 2013/03 Run 5384-5598 MAUS v3.0.0
Figure 4.59:Distribution of particle masses as reconstructed from the range and the time-of-flight information. The mean and RMS are quoted for the muon sample.
2] m [MeV/c
0 20 40 60 80 100 120 140 160 180 200
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
mixture µ π
sample µ
Entries 129558 Mean 105.593 ± 0.045 RMS 11.256 ± 0.032 MICE
ISIS Cycle 2013/03 Run 5384-5598 MAUS v3.0.0
Figure 4.60:Distribution of particle masses as reconstructed from the charge and the time-of-flight information. The mean and RMS are quoted for the muon sample.
The two techniques achieve comparable resolutions on the muon mass, of order 10 MeV/c2. Neither of them could be used to efficiently separate muons from pions as the muon mass peak is significantly contaminated by short-range pions. The charge is less affected by nuclear interactions but not all the electromagnetic shower energy is observed. The resolution is damped by energy loss straggling in TOF2 and the KL, which introduces an additional uncertainty on the velocity of particles impinging the EMR.
The pion peak is slightly shifted to higher masses due to the energy loss discrepancy show in figure4.58.
CHAPTER 5
Beam-based detector alignment
MICE is a single-particle experiment. The phase space evolution is studied by measuring the set of (x, y, px, py, pz) of each muon before and after going through the absorber. A sufficient number of tracks are accumulated during data taking and a sample is assembled during the analysis process to measure the phase space volume reduction. The single-particle nature of the experiment requires reliable global track matching throughout, i.e.
the ability to associate a track measured in the upstream tracker with one in the downstream tracker but also with the PID detectors. The detectors must reconstruct space points in a globally consistent fashion to guarantee reliable and efficient track matching. The beam-based alignment algorithm described in this section is designed to achieve global consistency.
5.1 Surveys
The baseline for the beam-based alignment is the surveys of the detectors in the hall using laser telemetry. Surveys were performed regularly throughout the MICE Step IV commissioning phase and data taking period. The TOF1 time-of-flight hodoscope was moved periodically to access the upstream end of the superconducting solenoids and resurveyed systematically. The downstream PID detectors module, composed of TOF2, the KL and the EMR, was also repositioned on occasion. The focus coil module was moved in and out of the beam line to change absorbers. Each of these events was followed by a complete resurvey.
The PID detectors are each equipped with at least four survey monuments and are surveyed directly. The two scintillating fibre trackers, nested in the superconducting solenoids, cannot be accessed that way. The upstream and downstream flanges of each solenoid are surveyed and the end plate of the trackers are located with respect to the flanges. The estimated position of the trackers within the bores are inferred from these measurements. A laser theodolite is used to locate the monuments with respect to the datum point situated under the second dipole magnet, D2. The surveyed locations are used to reconstruct the global position, (xM, yM, zM), and Tait-Bryan angles, (α, β, γ), of each detector module. The values obtained for the 2017/01 ISIS user cycle are summarised in table5.1. The left panel of figure 5.1shows a picture of TOF2 and the location of its survey monuments.
xM[mm] yM[mm] zM[mm] α[mrad] β[mrad] γ[mrad]
TOF0 1.919 1.565 5287.247 6.030 5.252 3.718 TOF1 -3.738 -0.913 12929.563 -5.083 0.033 2.768 TKU 0.761 2.732 14515.055 2.669 -0.041 0.000 TKD -1.027 8.943 19398.921 -6.435 1.283 0.000 TOF2 13.518 -10.981 21139.375 10.735 6.699 -1.406
KL 16.616 -12.855 21221.649 8.717 7.994 -9.841 EMR 35.647 7.827 21937.889 -2.527 6.857 -0.118 Table 5.1:Survey of the detectors in the MICE hall with respect to the datum point at D2 during the 2017/01 ISIS user cycle. The bold figures are the ones sensitive to the beam-based detector alignment.
Figure 5.1:(Left) Picture of the TOF2 time-of-flight hodoscope and its four survey monuments labelled TOF2.1–2.4. (Right) Disposition of the downstream tracker stations along with the CMM measurements of their position with respect to the reference axis [174].
Before being placed inside the magnets, each tracker was surveyed in-dependently using a coordinate-measuring machine (CMM). This ensures that the position of the five stations is well-known within each tracker with
respect to the end plate. The right panel of figure5.1shows the disposition of the stations in the downstream scintillating fibre tracker and their position as measured by the CMM. The reference position is the axis that joins the centre of station 1 to the centre of station 5. The positions of stations 1 to 3 are measured with respect to that axis. The beam will also be used to check the tracker station alignment.
Special care is taken during the installation of the trackers in the magnet bores. The installation platform is adjustable to enable the tracker to be aligned with the bore of the solenoid. The tracker sits on four feet, two at each end. The feet are adjusted to align the tracker with the warm bore of the solenoid. Once this has been done, the location bracket is fitted. The location bracket locks the tracker in itszand azimuthal positions.