1. Takashi Matsushita t.matsushita@imperial.ac.uk Imperial College T. Matsushita 1 Tracker performance Vacuum/helium/air

2. T. Matsushita 2 Purpose Requested to check the tracker performance with tracker volume filled by air at the tracker review meeting on 21 Apr 2006 This study is to answer the request

3. T. Matsushita 3 Material Three different materials compared; Vacuum/Helium/Air Density Vacuum: 1.e-25 g/cm^3; defined as universe_mean_density in CLHEP/Units/PhysicalConstants.h ref; 5e-11 Torr => 8e-17 g/cm^3 He: 0.166 mg/cm^3 @ 293.15K, 1 atm; Air: 1.205 mg/cm^3 @ 293.15K, 1 atm; N:0.7, O:0.3 Radiation length @ 293.15K, 1 atm.x/X0 (x=1m) Helium gas; 5671m1.76e-4 Air; 304m3.29e-3 ref; http://pdg.lbl.gov/AtomicNuclearPropertieshttp://pdg.lbl.gov/AtomicNuclearProperties

4. T. Matsushita 4 Multiple Coulomb scattering  0 =13.6MeV/  cp z(x/X 0 ) 1/2 [1+0.038 log(x/ X 0 )] accurate to 11% or better for 10 -3 < x/ X 0 < 100;PDG y plane (rms) = 1/sqrt(3) x  0  plane (rms) =  0 For 200MeV/c muon  plane (rms)y plane (rms)x/ X 0 He gas;4.7e-41.3e-40.88e-4 (x=0.5m) Air;2.4e-36.8e-41.65e-3 (x=0.5m) A station;4.1e-34.5e-64.5e-3 (x=1.9mm)

5. T. Matsushita 5 Setup Simulation setup Input beam; matched 2.5 pi mm rad. data 10k events G4MICE; Malcolm-demo-T20050208 Performance checked with upstream tracker Baseline spacing; 45-35-20-10 cm for stations 12, 23, 34, 45

6. T. Matsushita 6 Event selection Select number of points used for track fit = 5 Reject if reconstructed value(s) <= -9999. Selection efficiency is about 90%

7. T. Matsushita 7 Residual - Pt RMS of residual distributions All range vac: 5.6 hel: 8.5 air: 5.9 |Pt|<200 vac: 1.9 hel: 1.9 air: 1.8 Not much difference vacuum helium air

8. T. Matsushita 8 Residual - Pz RMS of residual distributions All range vac: 9.5 hel: 8.0 air: 9.1 |Pz|<100 vac: 7.2 hel: 6.7 air: 7.9 Not much difference vacuum helium air

9. T. Matsushita 9 RMS parameterisation From error propagation formulae, parameterise RMS of residual in terms of Pt and Pz  (Pz) =  / Pt(true)  (Pz) =  * Pz(true)^2  (Pt) = 

10. T. Matsushita 10 RMS(Pt) vs Pt(true), Pz(true) RMS(Pt) in terms of Pt/Pz is parameterised by  (constant) RMS(Pt) =  (Pt) RMS(pt) =  (Pz)  (Pt) vac: 1.8 hel: 1.8 air: 1.8  (Pz) vac: 1.8 hel: 1.8 air: 1.8 Not much difference, although parameterisation is not perfect vacuum helium air

11. T. Matsushita 11 RMS(Pz) vs Pt(true), Pz(true) RMS(Pz) in terms of Pt/Pz is parametrised by  RMS(Pz) =  /Pt(true) RMS(pz) =  *Pz(true)^2  vac: 103.1 hel: 99.1 air: 110.8  vac: 0.18E-3 hel: 0.16E-3 air: 0.19E-3 Not much difference, although parametrisation is not perfect vacuum helium air

12. T. Matsushita 12 Summary Analysis with G4MICE show little difference on tracker performance with tracker volume filled by vacuum/helium/air for the default spacing; 45-30-20- 10 cm Probably we need to redo the analysis after fixing the spacing. With the current spacing, 4 mrad deflection caused by a station has 2.25mm lateral displacement between station 1 and 2! (for 200MeV/c muon) Question still remains; do we want to use air instead of helium? By the way, I would like to try the G4MICE version used for MICE-NOTE90 analysis, which is known to be newer than the one I am currently using