1. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 1 Experimental Systematics OUTLINE starting from Janot’s work, will try to initiate a reflexion on systematic errors.starting from Janot’s work, will try to initiate a reflexion on systematic errors.. MICE measures e.g. (  out  in ) exp = 0.904 ± 0.001 (statistical) and compares with (  out  in ) theory. = 0.895 and compares with (  out  in ) theory. = 0.895 and tries to understand the difference. SIMULATION REALITY MEASUREMENT theory systematics: modeling of cooling cell is not as reality experimental systematics: modeling of spectrometers is not as reality

2. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 2 DWARF4.0 What’s in it?  Particle transport in magnetic field and in RF; homogeneous field.  Multiple Scattering in matter;  tracker: 4 sets of three layers of 500 micron scintillating fibers  Energy Loss (average and Landau fluctuations) in matter;  Bremsstrahlung in matter; no showering  Beam contamination with pions, pion decay in flight;  Muon decay in flight (with any polarization), electron transport;  Poor-Man Cooling Simulation (only B z and E Z ) to quantify particle and correlation losses with cooling; particle and correlation losses with cooling;  Gaussian errors on measured quantities (x, y, t).

3. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 3 DWARF4.0: What’s not in ?  Imperfections of magnetic fields; heating at solenoid exits; (A field map and step tracking will be needed here… (A field map and step tracking will be needed here… Might be the source of important bias and systematic uncertainty Might be the source of important bias and systematic uncertainty  Dead channels;  Misalignment of detector elements;  Background of any origin (RF, beam, …) (Could well spoil the measurement. Need redundancy in case…) (Could well spoil the measurement. Need redundancy in case…)  track fit in presence of noise and dead channels (pattern recognition)  electron ID detector (definitely needs a geant4 type simulation for showers) Fortran 77 + PAW

4. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 4 Step III: TWO spectrometers At this step we: -- Turn on and map the second solenoid -- Debug Spectrometer # 2 -- Measure  in  out and the ratio -- Field reversal is important for E ^ B effects THIS IS A VERY IMPORTANT STEP : THESE RESULTS WILL BE PART OF THE FINAL ONES (Systematics on  in  out ) + + and - -

5. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 5 tracking detectors simulated

6. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 6 Emittance Reduction: Results R =  out /  in Generated Measured R GEN,  1. R MEAS,  (1.+  ) 2 Note:  is purely instrumental (mostly due to multiple scatt. in the detectors). It can be in the detectors). It can be predicted and corrected for, predicted and corrected for, if not too large. if not too large. A 0.9% measurement with 1000 single  ’s (corresponding to 25,000 single  ’s produced 25,000 single  ’s produced 70,000 “20 ns bunches” sent 70,000 “20 ns bunches” sent Each entry is the ratio of emittances (out/in) from a sample of 1000 muons. Biases and resolutions are determined from this kind of plots in the following. (No cooling) Bias  1% (No cooling)

7. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 7 Resolution, bias, systematics The emittance is obtained from the second moments of the 6D distribution (width) The width of measured distribution is the result of the convolution of the true width with the measurement resolution the true width with the measurement resolution  x meas ) 2 =  x true ) 2 +  x det ) 2 The detector resolution generates a BIAS on the evaluation of the width of the true distribution. This bias must be corrected for.  x meas =  x true ( 1 + ½  x det ) 2 /  x true ) 2 ) For the bias to be less than 1%, the detector resolution must be (much) better than 1/7 of the width of the distribution to be measured, i.e. the beam size at equilibrium emittance. Say 1/10. The systematic errors result from uncertainties in the bias corrections. Rule of experience says that the biases can be corrected with a typical precision of 10% of their value (must be demonstrated in each case).

8. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 8 Equilibrium emittance: 3000 mm.mrad = 75 mm X 40 mrad 1. Spatial resolution must be better than 10 mm VERY EASY, The resolution with a 500 micron fiber is 500/  12 =144  m 2. Angular resolution must be better than 6 mrad…  2 x’ = (  2 x1 +  2 x1 )/D + (  x’ (m.s.) ) 2 (  2 x1 +  2 x1 )/D < 1mrad for D = 30 cm.  x’ (m.s.) = 13.6/  P  x/X° x = detector thickness X° = rad. Length of material x = 1.5 mm of scintillating fiber (3 layers of 500 microns) X° = 40 cm x = 1.5 mm of scintillating fiber (3 layers of 500 microns) X° = 40 cm =>  x’ (m.s.) = 6 mrad…. =>  x’ (m.s.) = 6 mrad…. JUST MAKE IT! Bias is due to M.S. in the last planes of tracking detectors. Less MS is clearly desirable…. Requirements on detectors

9. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 9 Requirements on detectors (ctd) 3. Time resolution Must be better than 1/7 of the rms width of the particles contained in the RF bucket. 200 MHz => 5 ns period, 2.5 ns ½ period, rms = 700 ps approx. Need 70 ps or better. Fast timing with scintillators gives 50 ps (with work) OK. (This also provides pi/mu separation of incoming particles) 4. t’ = E/Pz resolution. Trickier, needs reconstruction. * -> OK

10. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 10 Tracker performance Resolution on p T : Same for all particles; (4 plates) Same for all particles; (4 plates)  (p T )  0.8 MeV/c.  (p T )  0.8 MeV/c. Resolution on p Z : Strong dependence on p T ; Strong dependence on p T ; Varies from 1 to 50 MeV/c. Varies from 1 to 50 MeV/c. 20% 10,000 muons

11. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 11 Emittance Measurement Transverse variable Resolution (  p T /p Z )  (p T /p Z )  2.5% Longitudinal variable Resolution (  E/p Z )  (E/p Z )  0.25%

12. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 12 In order to keep experimental systematics at the level of statistical errors, MICE must get  syst.  (  out  in ) exp < 10 –3 This will be a sum of possible effects (non exhaustive list…. do you see more?) (non exhaustive list…. do you see more?) -- magnetic field knowledge (will scale emittance prop to  B/B)  need statement on magentic field measurements - - uncertainty on MS in last tracker planes and in space between tracker and cooling cell and in space between tracker and cooling cell  need thought and statement.  need thought and statement. -- fake points or fake tracks due to noise/inefficiencies, field inhomogeneities, etc.. field inhomogeneities, etc..  need simulation !! each of which should be << 10 -3.

13. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 13 Tracking devices T.O.F. III Precise timing Electron ID Eliminate muons that decay Tracking devices: Measurement of momentum angles and position T.O.F. I & II Pion /muon ID and precise timing

14. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 14 Emittance measurement Each spectrometer measures 6 parameters per particle x y t x y t x’ = dx/dz = P x /P z y’ = dy/dz = P y /P z t’ = dt/dz =E/P z x’ = dx/dz = P x /P z y’ = dy/dz = P y /P z t’ = dt/dz =E/P z Determines, for an ensemble (sample) of N particles, the moments: Averages etc… Second moments: variance(x)  x 2 = 2 > etc… covariance(x)  xy = > covariance(x)  xy = > Covariance matrix M = M = Evaluate emittance with: Compare  in with  out Getting at e.g.  x’t’ is essentially impossible is essentially impossible with multiparticle bunch with multiparticle bunch measurements measurements

15. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 15 Statistics Measure a sample with N particles Statistical error on is   x  Where  x  is the width of the measured distribution Stat error on width of distribution is also  x  x  Stat error on emittance is  6D =  6D  6/N Verify by generating M samples of N muons, that the spread of results obeys the above laws. Input and output particles are the same! The emittances measured before and after the cooling channel are strongly correlated. The variation of a muon transverse momentum going through a short channel is smaller than the spread of transverse momenta of the muons. This explains that  in  out ) <<  in  in

16. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 16 Emittance Measurement: Results Cooling channel without cooling No  contamination, no  decay 1111  in  out 4444  in mes  out mes With 1000 samples of 1000 accepted muons each: 0.5% 0.6% with 1000  GeneratedMeasured GeneratedMeasured Ratio meas/gen  in  out

17. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 17 Figure V.4: Cooling channel efficiency, measured as the increase of the number of muons inside an acceptance of 0.1 eV.s and 1.5  cm rad (normalized), corresponding to that of the Neutrino Factory muon accelerator, as a function of the input emittance [31]. 28 MeV cooling experiment (kinetic energy E i =200 MeV) Equilibrium emittance = 4200 mm. mrad(here) Cooling Performance = 16% MICE: what will it measure?

18. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 18 Spectrometer principle d d T.O.F. Measure t With  t  70 ps Three plates of, e.g., three layers of sc. fibres (diameter 0.5 mm) Measure x 1, y 1, x 2, y 2, x 3, y 3 with precision 0.5mm/  12 Solenoid, B = 5 T, R = 15 cm, L > 3d Need to determine, for each muon, x,y,t, and x’,y’,t’ (=p x /p z, p y /p z, E/p z ) at entrance and exit of the cooling channel: Note: To avoid heating exit of the solenoid due to radial fields, the cooling channel has to either start with the same solenoid, or be matched to it as well as Possible. (to keep B uniform on the plates) Extrapolate x,y,t,p x,p y,p z, at entrance of the channel. Make it symmetric at exit. z

19. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 19 Emittance Reduction: Optimization (I) (1000  ’s, No cooling, Perfect  /e Identification) Optimization with respect to the distance between the 1 st and the last plates  6D reduction: Resolution  6D reduction: Bias  4D reduction: Resolution  4D reduction: Bias No clear minimum, but the resolution and bias on the long. emittance reduction become (slightly) worse when the average muon cannot do a full turn between 1 st and last plates… (possibly alleviated with reconstruction tuning ?)

20. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 20 Emittance Reduction: Optimization (II) (1000  ’s, No cooling, Perfect  /e Identification) Optimization with respect to the scintillating fibre diameter 6D resolution 4D resolution 6D bias 4D bias Measured Perfect detectors The smaller the better… Keeping the 6D bias and resolution at the % level requires a diameter of 0.5 mm. Still acceptable with 1 mm, though. (2% bias, 1.2% resolution)

21. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 21 Pion Rejection: Principle z z0z0z0z0 z1z1z1z1 0.1 X 0 (Pb) 4 X 0 (Pb) Measure t 0 Measure t 1 Measure x 0, y 0 Measure x 1, y 1  Compare with Measured in solenoid -34 MeV (  ) -31 MeV (  ) 1.11 for  ’s 1.06 for  ’s 1.08 for  ’s and  ’s   Cut With  t = 70 ps Beam (p = 290 Mev/c) 10 metres

22. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 22 Pion contamination in a solenoid muon beam line (muE1 or muE4) set B1 to 200 MeV/c This is the pion and muon yield as a function of B2 setting  ratio in beam is less than 1% if P(B2)/P(B1) < 0.8 TOF monitors contamination and reduces it to <10 -4. => No effect on emittance or acceptance measurements.

23. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 23 Poor-Man Electron Identification (I)  At the end of the cooling channel, a few electrons from muon decays (up to 0.4% of the particles for a 15 m-long channel) are detected in the diagnostic device. of the particles for a 15 m-long channel) are detected in the diagnostic device.  These electrons have very different momenta and directions from the parent muons, and they spoil the measurement of the RMS emittance (6D and 4D) muons, and they spoil the measurement of the RMS emittance (6D and 4D)  About 80% of them can be rejected with kinematics, without effect on muons Poor fits for electrons (Brems) e  Large p Z difference (p in -p out )  e

24. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 24 status & next steps  A measurement(stat) of 6D/4D cooling can be achieved with reasonable detectors 10 -3 stat error requires a few 10 5 muons 10 -3 stat error requires a few 10 5 muons 1% systematic bias on 6D cooling and and 0.5% bias on transverse cooling 1% systematic bias on 6D cooling and and 0.5% bias on transverse cooling Three time measurements with a 50-100 ps precision Three time measurements with a 50-100 ps precision  Two 1.5 to 2 m long, 5 T solenoids (1m useful length)  Ten (twelve?) 0.5 mm diameter scintillating fibre plates (three layers each)  One Cerenkov detector and/or one electromagnetic calorimeter (10 X 0 Pb)  However, systematic effects to be addressed with further and/more detailed simulation  Effect of magnetic field (longitudinal and radial) imperfections  Effect of backgrounds  Effect of dead channels and misalignment  Multiple scattering dominates resolution, biases and systematics we achieve 1% bias for nominal emittance, we achieve 1% bias for nominal emittance, will this be the case for equilibrium emittance? will this be the case for equilibrium emittance?  Other possibilities should be studied to evaluate their potential/feasibility  Thin silicon detectors instead of scintillating fibres ?  TPC-GEM ?

25. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 25 (Obsolete) Experimental Layout (I) Pb, 0.1X 0 Pb, 4X 0 Measure t, x, y For pion rejection 10 m Measure x, y p x, p y, p z About 5% of the muons arrive here Determine, with many  ’s: Initial RMS 6D-Emittance  i Initial RMS 6D-Emittance  i Final RMS 6D-Emittance  f Final RMS 6D-Emittance  f Emittance Reduction R Emittance Reduction R Channel with or without cooling B = 5 T, R = 15 cm, L = 15 m 88 MHz

26. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 26 10 m 2 m 6 m 2 m Incoming muon beam TOF I & II Diffusers Experimental Solenoid I Experimental Solenoid II Spectrometer trackers I Focusing coils Liquid Hydrogen absorbers 4-cell RF cavities Coupling coil Electron ID Spectrometer trackers II TOF II 2 m

27. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 27 Emittance Measurement: Principle (II) x 1, y 1 x 2, y 2 x 3, y 3 In the transverse view, determine a circle from the three measured points: C R  12  23  Compute the transverse momentum from the circle radius: from the circle radius: p T = 0.3 B R p T = 0.3 B R p x = p T sin  p x = p T sin  p y = -p T cos  p y = -p T cos   Compute the longitudinal momentum from the number of turns from the number of turns p Z = 0.3 B d /  12 p Z = 0.3 B d /  12 = 0.3 B d /  23 = 0.3 B d /  23 = 0.3 B 2d /  13 = 0.3 B 2d /  13 (provides constraints for alignment) (provides constraints for alignment)  Adjust d to make 1/3 of a turn between two plates (d = 40 cm for B = 5 T and two plates (d = 40 cm for B = 5 T and p Z = 260 MeV/c) on average p Z = 260 MeV/c) on average  Determine E from (p 2 + m 2 ) 1/2 d = p z /E  c  t R  12 = p T /E  c  t p z /d = p T / R  12

28. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 28 Emittance Measurement: Improvement (I) z 30 cm 35 cm 40 cm  The previous (minimal) design leads to reconstruction ambiguities for particle which make  a full turn between the two plates (only two points to determine a circle) make  a full turn between the two plates (only two points to determine a circle)  It also leads to reconstruction efficiencies and momentum resolutions dependent on the longitudinal momentum, which bias the emittance measurements. on the longitudinal momentum, which bias the emittance measurements. Solution: Add one plate, make the plates not equidistant (optimal for 5 T) To find p T and p Z, minimize:

29. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 29 Emittance Measurement: Improvement (II)? 5 cm  The previous design is optimal for muons between 150 and 450 MeV/c (or any dynamic range [x,3x]. dynamic range [x,3x].  Decay electrons have a momentum spectrum centred a smaller values and some of them may make many turns between plates. The reconstructed momentum of them may make many turns between plates. The reconstructed momentum is between 150 and 450 MeV anyway. Very low momentum electrons cannot be is between 150 and 450 MeV anyway. Very low momentum electrons cannot be rejected later on… rejected later on…  Possible cure: Add a fifth plate close to the fourth one in the exit diagnostic device. First try in the simulation (yesterday) looks not too good, but the device. First try in the simulation (yesterday) looks not too good, but the reconstruction needs to be tuned to this new configuration. (The rest of the reconstruction needs to be tuned to this new configuration. (The rest of the presentation uses the design with four plates.) presentation uses the design with four plates.) z 30 cm 35 cm 40 cm

30. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 30 Emittance Reduction: Optimization (III) (1000  ’s, No cooling, Perfect  /e Identification) Optimization with respect to the TOF resolution  time resolution is almost irrelevant (up to 500 ps) for the emittance measurement: no effect on the transverse emittance, and measurement: no effect on the transverse emittance, and marginal effect on the 6D emittance (resolution 0.9%  1.1%); marginal effect on the 6D emittance (resolution 0.9%  1.1%);  Quite useful to determine the timing with respect to the RF, so as to select those muons in phase with the acceleration crest as to select those muons in phase with the acceleration crest 1/10 th of a period (i.e., 1.1 ns for 88 MHz and 0.5 ns for 200 MHz). 1/10 th of a period (i.e., 1.1 ns for 88 MHz and 0.5 ns for 200 MHz). Resolution must be  10% of it, i.e., 100 ps for 88 MHz and Resolution must be  10% of it, i.e., 100 ps for 88 MHz and 50 ps for 200 MHz. 50 ps for 200 MHz.  Essential to identify pions at the entrance of the channel: Indeed the presence of pions in the muon sample would spoil the longitudinal. the presence of pions in the muon sample would spoil the longitudinal. emittance measurement (E is not properly determined for pions, emittance measurement (E is not properly determined for pions, and part of these pions decay in the cooling channel). and part of these pions decay in the cooling channel).

31. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 31 Pion Rejection: Optimization (II) (1000  ’s, No cooling, Perfect e Identification) Beam Purity Requirement (confirmed with cooling) Measured Perfect detectors 6D bias 6D resolution 4D bias 4D resolution Need to keep the pion contamination below 0.1% (resp 0.5%) to have a negligible effect on the 6D (resp. 4D) emittance reduction resolution and bias. It corresponds to a beam contamination smaller than 10% (50%) when entering the experiment.

32. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 32 Pion Rejection: Optimization (III) (1000  ’s, Perfect e Identification) Beam Purity Requirement with Cooling (Four 88 MHZ cavities) 1) 6D-Cooling and Resolution 2) Statistical significance with 1000  ’s Pion cut at 1.00 Pion cut at 0.99 NoEffect (in the beam) 6D Cooling Resolution

33. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 33 Pion Rejection: Optimization (IV) (1000  ’s, Perfect e Identification) Beam Purity Requirement with Cooling (Four 88 MHZ cavities) No Effect Pion cut at 1.00 Pion cut at 0.99 (in the beam) 1) Transverse-Cooling and Resolution 2) Statistical significance with 1000  ’s Resolution 4D Cooling

34. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 34 Pion Rejection: Optimization (I) (1000  ’s, No cooling, Perfect e Identification) Optimization with respect to the TOF resolution  Assume an initial beam formed with 50% muons and 50% pions with 50% muons and 50% pions (same momentum spectrum) (same momentum spectrum)  Vary the T.O.F. resolution  Apply the previous pion cut (E/p)/(E  /p) < 1.00 and check (E/p)/(E  /p) < 1.00 and check the remaining pion fraction the remaining pion fraction in a 10,000 muon sample. in a 10,000 muon sample. Remaining pion fraction Because of the beam momentum spread and of the additional spread introduced by the 4X 0 Pb plate, the  /  separation does not improve for a resolution better than 100-150 ps (for a path length of 10 m)

35. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 35 Poor-Man Electron Identification (II) (1000  ’s, with cooling, 0 to 20 RF cavities) 1) 6D-Cooling and Resolution 2) Statistical significance with 1000  ’s Generated Generated Measured, perfect e-Id Measured, perfect e-Id Measured, poor man e-Id Measured, poor man e-Id 6D Cooling Resolution Need better e-Id to get back to the red curve! Cerenkov detector (1/1000) Cerenkov detector (1/1000) El’mgt calorimeter (?) El’mgt calorimeter (?) Remaining electron fraction 3 10 -4 6 10 -4 8 10 -4

36. Alain Blondel, MICE collab. meting @ RAL 8-10 July 2002 Systematics 36 Poor-Man Electron Identification (III) (1000  ’s, with cooling, 0 to 20 RF cavities) 1) Transverse Cooling and Resolution 2) Statistical significance with 1000  ’s Generated Generated Measured, perfect e-Id Measured, perfect e-Id Measured, poor man e-Id Measured, poor man e-Id Remaining electron fraction 3 10 -4 6 10 -4 8 10 -4 4D Cooling Resolution No need for more e Id For the transverse cooling measurement