Recent Results from MICE on Multiple Coulomb Scattering and Energy Loss Scott Wilbur on behalf of the MICE collaboration University of Sheffield Scott Wilbur MICE Scattering and Energy Loss 1
Ionization Cooling • Emittance change depends on energy loss and multiple Coulomb scattering • Energy loss reduces momentum • Scattering increases entropy of the beam • RF re-acceleration restores p L β ⊥ (13 . 6 MeV) 2 dǫ n ǫ n � dE � 1 dz ≈ − + β 2 β 3 rel E µ dz 2 E µ m µ X 0 c 2 rel • We want to understand both energy loss and scattering terms Scott Wilbur MICE Scattering and Energy Loss 2
The MICE Detector Variable thickness Time-of-flight 7th February 2015 high- Z diffuser hodoscope 1 Absorber/focus-coil (ToF 0) module Upstream Downstream spectrometer module spectrometer module Electron MICE Muon Muon Ranger Beam (EMR) (MMB) Liquid-hydrogen ToF 1 Cherenkov absorber Pre-shower counters (KL) (CKOV) Scintillating-fibre MICE ToF 2 trackers • TOF counters measure location and time of particle hits • Trackers measure trajectories and momenta – Scattering and energy loss analyses have been done with no tracker field – Further studies are using data with tracker fields to refine measurements • Absorber is Lithium Hydride or liquid Hydrogen Scott Wilbur MICE Scattering and Energy Loss 3
Overview of Multiple Coulomb Scattering • The PDG recommends the formula � � � ∆ z �� θ 0 ≈ 13 . 6MeV ∆ z 1 + 0 . 038 ln p µ β rel c X 0 X 0 • GEANT4 uses full Legendre polynomial expansion • Other models also considered: Moliere, Cobb-Carlisle • MUSCAT showed poor agreement between theory and low-Z material data • MICE has taken scattering data on a LiH target: – 81% 6 Li, 4% 7 Li, 14% 1 H (traces of C, O, Ca) • Results are compared to multiple theories and models Scott Wilbur MICE Scattering and Energy Loss 4
Scattering Data Field-off data sets from ISIS run periods 2015/03 and 2015/04 • Measure scattering with empty channel • Prediction: convolve with physics model of scattering • Measure scattering with absorber • Deconvolve measured distribution • χ 2 comparison between data and prediction • Calculate width of scattering distribution: Θ( p ) Scott Wilbur MICE Scattering and Energy Loss 5
Selection • Require one upstream track and at most one downstream track (if no DS track, set scattering angle to overflow value) • TOF cut to select muons at a target momentum • Require US track to extrapolate to within DS tracker even if it scatters 12 mrad outward Scott Wilbur MICE Scattering and Energy Loss 6
Scattering Data Define projection angles: � p DS · (ˆ y × p US ) � θ y = atan | ˆ y × p US || p DS | � p DS · ( p US × (ˆ y × p US )) � θ x = atan | p US × (ˆ y × p US ) || p DS | so that θ 2 x + θ 2 y ≈ θ 2 scatt and: cos( θ scatt ) = p US · p DS | p US || p DS | Scott Wilbur MICE Scattering and Energy Loss 7
Tracker Acceptance • Match upstream and downstream track • TOF selection • Calculate scattering angles θ x and θ y • Define downstream acceptance: reconstructed tracks in MC truth θ bin tracks in MC truth θ bin 0.9 0.9 0.8 0.8 0.7 0.7 Tracker Acceptance Tracker Acceptance 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 MICE preliminary [simulation] MICE preliminary [simulation] 0.2 ISIS Cycle 2015/04 ISIS Cycle 2015/04 0.1 0.06 0.04 0.02 0 0.02 0.04 0.06 0.06 0.04 0.02 0 0.02 0.04 0.06 _x (mrad) _y (mrad) Scott Wilbur MICE Scattering and Energy Loss 8
Deconvolution • Deconvolve observed scattering distribution to remove effects of detector resolution, etc • Use an iterative algorithm that uses the conditional probability of a true scattering angle given an observed scattering angle P ( E j | C i ) P 0 ( C i ) P ( C i | E j ) = Σ n c l =1 P ( E j | C l ) P 0 ( C l ) • We measure E j = ∆ θ tracker , the measured deflection angle in the first tracker plane y • We want to know C i = ∆ θ abs , the deflection angle in the absorber y Scott Wilbur MICE Scattering and Energy Loss 9
Scattering Results Probability per mrad Probability per mrad 172 MeV/c 172 MeV/c 200 MeV/c 200 MeV/c 240 MeV/c 240 MeV/c 2 10 − 2 10 − MICE Preliminary MICE Preliminary MICE Preliminary MICE Preliminary 3 10 − ISIS cycle 2015/04 ISIS cycle 2015/04 LiH, Muon Beams, MAUS v2.9.1 LiH, Muon Beams, MAUS v2.9.1 LiH, Muon Beams, MAUS v2.9.1 LiH, Muon Beams, MAUS v2.9.1 0.06 0.04 0.02 0 0.02 0.04 0.06 0.06 0.04 0.02 0 0.02 0.04 0.06 − − − − − − (radians) (radians) ∆ θ ∆ θ X Y • θ x and θ y measured at each momentum point using deconvolution • Final value is Θ = width of gaussian fit from +40 to − 40 mrad Scott Wilbur MICE Scattering and Energy Loss 10
Θ as a Function of Momentum • Scan across momentum range and measure Θ x and Θ y in each bin � z z • Compare to PDG formula with fit for a = X 0 (1 + 0 . 038 ln X 0 ) 28 28 (milliradians) (milliradians) Data Data 26 26 24 24 13.6 a 13.6 a Fit to (a=195.39 ± 2.39) Fit to (a=191.19 ± 2.34) p ̀ p ̀ 22 22 X Y ̀ ̀ Fit plus/minus error Fit plus/minus error 20 20 18 18 16 16 14 14 MICE Preliminary MICE Preliminary 12 12 ISIS Cycle 2015/04 ISIS Cycle 2015/04 160 180 200 220 240 160 180 200 220 240 Momentum (MeV/c) Momentum (MeV/c) • Preliminary analysis shows that scattering is higher than predicted by GEANT and lower than predicted by the PDG model Scott Wilbur MICE Scattering and Energy Loss 11
Overview of Energy Loss • The Bethe-Bloch formula gives � e 2 � 2 m e c 2 β 2 � 2 � m e c 2 · nz 2 � dE � 4 π � � − β 2 − = β 2 · ln I · (1 − β 2 ) dx 4 πǫ 0 • GEANT includes Bethe-Bloch and corrections, but MICE is firmly in Bethe-Bloch energy range Scott Wilbur MICE Scattering and Energy Loss 12
Energy Loss Measurement Using TOF Variable thickness Time-of-flight 7th February 2015 high- Z diffuser hodoscope 1 Absorber/focus-coil (ToF 0) module Upstream Downstream spectrometer module spectrometer module Electron MICE Muon Muon Ranger Beam (EMR) (MMB) Liquid-hydrogen ToF 1 Cherenkov absorber Pre-shower counters (KL) (CKOV) Scintillating-fibre MICE trackers ToF 2 • Assume energy loss in TOF and tracker is known • t TOF1 − t TOF0 gives initial velocity • Assume energy loss in TOF1 and US tracker to find v ua = velocity before absorber • Guess v ad = velocity after absorber, assume energy loss in DS tracker • With known velocity at every point between TOF1 and TOF2, calculate t TOF2 • Refine guess of v ad until t TOF2 time matches observed value Scott Wilbur MICE Scattering and Energy Loss 13
Energy Loss Results using TOF MPV Energy Loss MC Truth 9 . 18 ± 0 . 01 MeV MC Reco 9 . 12 ± 0 . 04 MeV Data Reco 9 . 23 ± 0 . 13 MeV • MC studies show good reconstruction of peak energy loss, but not shape • Good agreement between MC and data Scott Wilbur MICE Scattering and Energy Loss 14
Field-On Energy Loss Measurement • Data taken from ISIS run period 2017/02 and 2017/03 • Require one upstream track and one downstream track • Require tracks to have p t /p > 0 . 1 • Use two-dimensional TOF/tracker cut to select muons Scott Wilbur MICE Scattering and Energy Loss 15
Combining TOF and Tracker Measurements • Combine TOF01 and US Tracker to get US momentum • Use DS Tracker to measure DS momentum • Slightly improved US measurement, significantly improved DS measurement • Measure energy loss distribution with and without absorber Scott Wilbur MICE Scattering and Energy Loss 16
✁ ✁ ✁ ✁ Convolution Fit Empty Absorber (140 MeV/c) Empty Absorber (140 MeV/c) 1000 9000 8000 800 7000 6000 of Events 600 5000 4000 400 # 3000 200 2000 1000 0 0 20 15 10 5 0 5 10 15 20 0 5 10 15 20 25 30 35 40 45 50 Momentum Change Momentum Loss • Measure energy loss with no absorber, fit distribution to a gaussian G 0 (∆ p ) • Measure energy loss with absorber • Fit distribution to L true × G 0 (∆ p ) L true is a Landau distribution of the true energy loss Scott Wilbur MICE Scattering and Energy Loss 17
Field-On Energy Loss Results 18 Data Bethe-Bloch MC 17 16 Momentum Change [MeV/c] 15 14 13 12 11 10 130 140 150 160 170 180 190 200 210 220 230 240 Muon Momentum [MeV/c] • Preliminary results: MC (energy loss modeled by GEANT) agrees with data • Also seems to agree well with Bethe-Bloch prediction • Systematic uncertainties are preliminary Scott Wilbur MICE Scattering and Energy Loss 18
Conclusions • MICE has measured Coulomb scattering and energy loss of muons in LiH with 140 MeV /c < p < 240 MeV /c • Data has been compared to simulation packages such as GEANT and other relevant models • Multiple publications in the works (MCS paper forthcoming, energy loss in Rhys Gardener’s thesis at Brunel) • Work is ongoing to refine measurements with field-on data and expand measure- ments to liquid Hydrogen Scott Wilbur MICE Scattering and Energy Loss 19
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