1. 18 th March 2008Measuring momentum using the TOFsSlide 1 Measuring momentum using TOF0 and TOF1 Progress report Mark Rayner (Oxford/RAL) Analysis Meeting, 18 th March 2008

2. 18 th March 2008Measuring momentum using the TOFsSlide 2 P resolution just after TOF1  Expected p resolution performance:  Each TOF has a timing resolution of 50ps  Time of flight has a resolution ~70ps  Assume (for now) this is the dominant error  Resolution of 2–3 MeV/c for 200 MeV/c muons ~m  MeV/c recon recon using truth

3. 18 th March 2008Measuring momentum using the TOFsSlide 3 Using TOF 0 and TOF 1 with Tracker 1  Some unpolished thoughts – work in progress  TOF momentum measurements  TOFs helping the tracker  Is there any parameter space where pz may be measured more precisely using the TOFs?  Tracker helping the TOFs  Does the tracker pt measurement allow us a correction to the TOF pz measurement?  Caveat  Is this compatible with TOF PID?

4. 18 th March 2008Measuring momentum using the TOFsSlide 4 p z resolution at low p t  Difficult to measure p z at low p t (transverse momentum) in the tracker (see plot…)  Make the same plot for the TOF  Understanding the plot  “Pz Resolution” is presumably the RMS (p z recon – p z truth )  For large n an unbiased estimator of the population standard deviation  Does not reflect sample size in bin  TOF plot complications  Extrapolating p z through fringe field  Not tackled here!  Using Tracker reconstruction  Not tackled here!  Note – this is an unsophisticated first pass at the problem  promising results nevertheless MICE note 90 recon using truth NEEDS REFINEMENT!!

5. 18 th March 2008Measuring momentum using the TOFsSlide 5  Pz extrapolation requires some thought  Solenoidal field reduces pz TOF1  Tracker1 Fringe fields TOF1  Tracker 1 TOF1 & cage Tracker Solenoid 1 Tracker 1 Photon Muon Electron Focus coil RF H2 absorber

6. 18 th March 2008Measuring momentum using the TOFsSlide 6 Busch’s theorem Transverse momentum [MeV/c] Just after TOF1 Tracker Ref Plane 0  p r [MeV/c

7. 18 th March 2008Measuring momentum using the TOFsSlide 7 Radius unimportant for the TOFs  pz ?  Busch required paraxial approx.  SciFi works better with large radii radius [mm]

8. 18 th March 2008Measuring momentum using the TOFsSlide 8 Extra slides

9. 18 th March 2008Measuring momentum using the TOFsSlide 9 Simple momentum reconstruction  For each individual muon:  Estimate p in the air between TOF0 and TOF1  Time of flight  Straight line distance TOF0 hit to TOF1 hit  Estimate p before TOF0  Momentum losses from PDG dE/dx for minimum ionizing particles  Estimate p after TOF1

10. 18 th March 2008Measuring momentum using the TOFsSlide 10 Possible factors affecting p resolution  Properties of the TOF0  TOF1 beam line  Width of the Landau distribution of energy loss  Scattering  Focusing in quadrupole magnets  Scraping  Properties of the TOF stations  Timing resolution  Spatial resolution  Dealing with ‘corner clippers’

11. 18 th March 2008Measuring momentum using the TOFsSlide 11 What is ?  Histograms  Shaded (“Truth”)  Monte Carlo truth s and t used to construct P air  Line (“Recon”)  reconstructed, simulated ADC and TDC counts used  Statistics boxes  Mean  energy loss to beginning/end of TOF0–1 channel  RMS  RMS deviation of Pair from true P/Pz before/after TOF0–1 channel

12. 18 th March 2008Measuring momentum using the TOFsSlide 12 PDG estimates betadtgammaE - dE = EnewpnewdpX0 98% d  nsMeVMeV c-1 g cm-2cmdegrees 0.9218.082.58261.04238.9911.0143.9042.621.06 0.9229.132.49258.25235.943.0427.25136.250.77 0.912663.412.46256.65234.191.7536.6230390.040.48 0.9118.272.44246.53223.0611.1443.9042.621.15 detectormaterialdetailsthicknessdensitydE/dx (min I)dEmasspE cmg cm-3MeV g-1 cm2MeVMeV c-2MeV c-1MeV TOF0scintillatorpolyvinyltoluene5.001.031.9710.12105.00250.00271.15 Cherenkovaerogelsilica aerogel8.000.201.742.78105.00238.99261.04 Airairdry, 1 atm730.000.001.821.60105.00235.94258.25 TOF1scintillatorpolyvinyltoluene5.001.031.9710.12105.00234.19256.65