Data Analysis for the MEG Experiment. Francesco Renga & Cecilia Voena INFN Roma

Transcription

1 Data Analysis for the MEG Experiment Francesco Renga & Cecilia Voena INFN Roma

2 Outline Historical & Theoretical Introduction The m e g signature The detector Analysis Strategy Event Reconstruction & Selection Statistical Analysis 2

3 Data Analysis for the MEG Experiment Francesco Renga & Cecilia Voena INFN Roma

4 History & Theory 4

5 In The Muon Decay The nature of the muon decay products is still debated Hincks & Pontecorvo [Phys. Rev. 73 (1948) 257]: BR(m e g) < 10% muon is not an excited electron arguments in favor of the m e n n hypothesis Lepton Flavor Violation (LFV) searches concurred to the development of particle physics just after the concept of Lepton was proposed and well before the concept of Flavour was introduced 5

6 One or two neutrinos In It is not yet clear if the two neutrinos produced in the muon decay are of the same nature MICHEL DECAY 6

7 One or two neutrinos In It is not yet clear if the two neutrinos produced in the muon decay are of the same nature 7

8 One or two neutrinos? In It is not yet clear if the two neutrinos produced in the muon decay are of the same nature Lokanathan & Steinberger [Phys. Rev. A 98 (1955) 240] BR(m e g) < 2 x 10-5; strong argument in favor of the ne + nm hypothesis. The lepton flavor saga begins 8

9 LFV today LFV is a standard probe for New Physics (NP) beyond the Standard Model (SM): unobservable rates in the SM SM BR < Observing LFV would be an unambiguous evidence of NP 9

10 LFV today LFV is a standard probe for New Physics (NP) beyond the Standard Model (SM): unobservable rates in the SM naturally enhanced by NP (SUSY, Extra Dimensions, unparticles, etc.) SM BR < Observing LFV would be an unambiguous evidence of NP SUSY BR ~ LFV through renormalization group running even if the theory is LF conserving at the high energy scale 10

11 Experimental Approach 11

12 How to search for m e g The best way to search for m e g is to use a muon beam stopped in a thin target: g high rate ( m/s) low material before the detectors closed kinematics: m e Monochromatic (52.8 MeV), back-to-back e+ g produced at the same time in the same point 12

13 Signal & Background g m e Monochromatic (52.8 MeV), back-to-back e+ g produced at the same time in the same point RADIATIVE MUON DECAY (RMD) ACCIDENTAL BACKGROUND n DOMINANT m n g e g m n e n N.B. the accidental background g can come from: RMD of another muon (dominant up to high Eg) Annihilation in flight of another positron (dominant at very high Eg) Cosmic ray or environmental neutron reconstructed as a g (rare) 13

14 Signal & Background m g e Monochromatic (52.8 MeV), back-to-back e+ g produced at the same time in the same point RADIATIVE MUON DECAY (RMD) ACCIDENTAL BACKGROUND n DOMINANT m n Sens. g S/sqrt(S + B) e g m n e B~0 Sens. S G n B >>and S Signal/Background discrimination from photon positron Sens.relative S/sqrt(B) = const. energies, relative angles and time 14

15 The MEG Experiment A search for m e g with the most intense DC muon beam of the world (3 x 107 PSI, Switzerland); Running in % acceptance LXe calorimeter for photon detection 16 drift chambers for positron tracking 30 scintillating bars for positron timing and trigger (Timing Counter, TC) 15

16 The pe5 beam line at PSI Most intense DC muon beam in the world: up to 108 m/s; only 3 x 107 m/s for the MEG running (optimized statistics vs. background) Proton beam current : ~ 2.2 ma Muon production Muon Momentum : from p decaying in the proton target surface : 28 MeV/c ± 3% 16

17 LXe Calorimeter (XEC) 800 liter LXe detector read by 846 PMTs Not just a calorimeter! se ~ 52.8 MeV sxy ~ 5 6 mm st ~ 60 ps 17

18 Drift Chambers (DC) 16 drift chambers sr ~ 300 mm, sz ~ 1 mm Gradient magnetic field Tracking performances svtx sp ~ 300 kev ~ 1.2 (x), 2.4 (y) sy,f ~ 9 mrad 18

19 Timing Counter (TC) 2 x 15 scintillating bars for trigger and positron timing (st ~ 60 ps) z 2 x 256 fibers to measure the z coordinate e+ 19

20 Trigger and DAQ FPGA based trigger system Beam Intensity x acceptance Hz + XEC Energy E > 45 MeV Hz + e g Timing Teg < 10ns Hz + e g Angle...10 Hz Buffering for dead time suppression since 2011 normalization factor +20% Full digitization of all readout channels for offline analysis: custom digitization chip (DRS) ~ 9 MB/event 20

21 Analysis Strategy 21

22 Analysis Strategy (I) We reconstruct tracks in the spectrometer and energy deposits in the calorimeter in our setup: (positive) tracks can only be positrons deposits in the calorimeter can only be photons (few exceptions: cosmic rays, neutrons; see later) background (almost) exclusively comes from pairs of a real positron and a real photon vertex cannot be fully reconstructed (no direct info on photon direction) no need of particle identification (PID), no possible selection besides kinematics and time 22

23 Analysis Strategy (II) A Likelihood Analysis is applied using all the available discriminating variables: Positron Energy (signal: 52.8 MeV peak background: m decay spectrum) Photon Energy (signal: 52.8 MeV peak background: continuous spectrum) Relative e-g angles (signal: back-to-back peak background: ~ flat) Relative e-g time (signal: peak at 0 background: flat) 23

24 Analysis Strategy (III) TYPICAL GENERAL-PURPOSE EXPERIMENT MEG Choice of trigger Reconstruction of abstract objects (tracks, neutrals, ) Particle and signature specific reconstruction PID Selection for background rejection Selection for good reconstruction quality Statistical Analysis Statistical Analysis 24

25 Exceptions to this scheme A background-rejecting selection can be applied to detector-related and non-m-related backgrounds: cosmic rays and environmental neutrons in the calorimeter can be rejected based on the XEC shower shape events with two photons in the XEC are rejected based on the XEC shower and waveform shape some events with the photon coming from the annihilation of a positron in the DC can be rejected with a dedicated reconstruction (under development) 25

26 Event Reconstruction 26

27 DC Reconstruction 3 steps: Hit reconstruction Track finding Track Fit A (V) measured time threshold = pedestal + 3s T (ms) 27

28 DC Reconstruction 3 steps: Hit reconstruction Track finding Track Fit TRACK SEED 3 hits in adjacent chambers large R xy position assumed on wire TRACK CANDIDATE prolongation of the seed estimate of track time determination of precise xy position 28

29 DC Reconstruction 3 steps: Hit reconstruction Track finding Track Fit Also provides an estimate of the error on track parameters at the target!!! KALMAN FILTER take a first estimate of the track from the track candidate start from the end of the track and update the estimate iteratively, going back through all hits, taking into accounts measurements and material effects propagate to the target 29

30 TC Reconstruction e+ PMT0 PMT1 z L Ingredients: L/veff: propagation of light in the bar b: time offset (PMTs and other delays) c/ A: time walk correction Bar dependent 30

31 XEC Reconstruction ENERGY Use the sum of the charge collected by the PMTs #phe Charges Gain #ph Q.E. Energy Calib. Ingredients: Sum of charges collected by PMTs (Qsum); PMT response (Gain & Q.E.); Calibration of Energy vs. #photons; Corrections for PMT/shower relative position (absorption, solid angle seen by PMT, energy leakage). 31

32 XEC Reconstruction POSITION Charge seen by a PMT depend on distance from the shower, attenuation, solid angle under which the shower is seen, etc. calibration constant Energy function modeled from MC Solid angle A x2 can be built and minimized 32

33 XEC Reconstruction TIME Titw : time measured by the PMT rint: path before conversion; one measurement for each PMT Rint Pi : distance between conversion and PMT; TPMT: intrinsic PMT delay; Tdly: delay from PMT to digitizer. All T0 measurements combined in a x2 33

34 XEC Pileup Rejection x2 of the time fit Light distribution (lighter color more light) 34

35 Combined Measurements: Teg Teg = Te Tg To measure Te, the track is propagated to the TC and matched with a TC hit, based on space and time proximity: provides the best estimate of track time for track reconstruction (matching performed within the Kalman Filter) TC time propagated back to the target to get the best estimate of the positron emission time Te (track-length subtraction) 35

36 Combined Measurements: Relative Angles XEC does not provide g direction: g is assumed to come from the intersection of the track with the target (decay point) g direction from decay poiny to g conversion point pg rg pe retarget 36

37 Statistical Approach How to find a frequentistic confidence interval for BR(m e g) 37

38 Reminder: Confidence Intervals To find a frequentistic interval for a parameter p with confidence level CL, the so-called confidence belts can be used Measurement CONFIDENCE BELT The belt is defined by: S P(Meas belt p) = CL p 38

39 Reminder: Confidence Intervals To find a frequentistic interval for a parameter p with confidence level CL, the so-called confidence belts can be used Measurement CONFIDENCE BELT The belt is defined by: S P(Meas belt p) = CL p 39

40 Reminder: Confidence Intervals The definition of the confidence belt is not unique: Measurement need to rank the possible measurements 40

41 Reminder: Confidence Intervals The definition of the confidence belt is not unique: Measurement need to rank the possible measurements 41

42 Reminder: Feldman-Cousins The Feldman-Cousins Approach ranks the possible measurements according to: P(Meas p) = L(p) = Likelihood R(p) = Likelihood ratio where only physically allowed values of the parameters p are considered (e.g. p > 0 if p is a number of events or a branching ratio) In practice, simulated experiments (Toy Monte Carlo) are used to determine the distribution of R and build the confidence belt 42

43 Statistical Analysis in MEG (I) Extended likelihood with 5 discriminating variables: Ee, Eg, yeg, feg, Teg...and 3 parameters (signal, accidental and RMD yields) 43

44 Statistical Analysis in MEG (I) Extended likelihood with 5 discriminating variables: Ee, Eg, yeg, feg, Teg...and 3 parameters (signal, accidental and RMD yields) PDF 44

45 Statistical Analysis in MEG (II) A Feldman-Cousins-like Approach based on the Profile-Likelihood-Ratio: A Bayesian approach was also developed as an alternative 45

46 Construction of PDFs How to write P(Ee,Eg,feg,yeg, Teg) for signal, accidental background and RMD 46

47 Factorization of the PDFs In the absence of correlations among observables P(A,B) = P(A)P(B) If correlations exist, they NEED to be taken into account we can still factorize the PDF following the Multiplication Rule P(A,B) = P(A B)P(B) 47

48 PDF Projections P(A) = P(A,B,C...)dBdC Signal Accidental RMD Signal (BR 3x10-11) 48

49 Blinding Strategy The probability distribution functions (PDFs) for signal and background events (Psig, Pacc, PRMD) have to be determined. Blind analysis: Events falling in the signal region in the Eg vs. Teg plane are initially removed PDFs are built using signal-free samples (sidebands) The statistical approach is applied to the signal region only once it is fully defined 49

50 Accidental Background PDFs 50

51 Accidental PDFs In the Teg sidebands (left, right), only accidental events are present: the accidental background PDFs coincide with the distributions on the discriminating variables in the Teg sidebands Eg Ee 51

52 Accidental PDFs In the Teg sidebands (left, right), only accidental events are present: the accidental background PDFs coincide with the distributions on the discriminating variables in the Teg sidebands The accidental background PDFs are completely extracted from data (no model, no simulation): very solid determination of the largely dominant background 52

53 Signal & RMD PDFs 53

54 Signal & RMD PDFs Signal is characterized by fixed values of the observables: Ee = Eg ~ 52.8 MeV; feg = yeg = Teg = 0 PDF = resolution function = P(A - A true) RMD is characterized by Teg = 0 and a 4D kinematic spectrum Ptheo(Ee,Eg,feg,yeg) Teg PDF = resolution function P(Ee,Eg,feg,yeg) = Ptheo(Ee,Eg,feg,yeg) reso The construction of Signal & RMD PDFs corresponds to the determination of the resolution functions P(A - A true) 54

55 Role of Calibrations We need to determine the resolution functions to build the signal and RMD PDFs We want to avoid extended use of simulations The MEG design does not provide a lot of control samples (almost all events are Michel muon decays): we are able to extract only the positron and Teg signal and RMD PDFs from normal MEG data in order to determine the photon signal and RMD PDFs, specific calibration data have to be collected and combined 55

56 Relative Time PDF Events in the Eg sidebands include RMD events, where positron and photon are emitted at the same time: very good sample to estimate the Teg PDF for both signal and RMD s(teg) ~ 122 ps 56

57 Positron Momentum PDF The spectrum of the normal muon decay is well known theoretically The observed spectrum in MEG data is a combination of theoretical spectrum, energy acceptance and resolution: we can determine the positron energy resolution function (= signal PDF) with a fit to the observed spectrum 57

58 Positron Angle and Decay Point PDFs A few % of the Michel positrons make 2 or more turns within the spectrometer If we treat two turns as independent tracks, the difference of the track parameters in an intermediate point gives the resolution function (= signal PDFs) Need of MC based corrections to take into account that the sample is biased w.r.t. the whole track sample 58

59 Photon Energy PDF Photon Energy PDF (Energy scale, shape) is determined performing dedicated runs with a pbeam and a liquid Hydrogen target p- + p p0 + n p0 g g One photon reconstructed with an ancillary NaI calorimeter, other photon in the XEC Selecting almost back-to-back photons provides an almost monochromatic peak at ~ 55 MeV s(eg) ~ 1.9% 59

60 Photon Position PDFs The PDFs for the photon conversion point positions are estimated from calibration data taken with collimators in front of the XEC Analytically combination with the positron angle and decay point PDFs to get the relative angle PDFs. pg rg pe retarget s(uvw) ~ 6-7 mm 60

61 Some Additional Features 61

62 Correlations (I) GENERAL TREATMENT PDFs with correlations are built exploiting the Multiplication Rule P(A, B) = P(A B) P (B) In MEG, correlations are present between the experimental errors on some observables: Not a correlation between the true values of A and B, but between DA = Ameas Atrue and DB = Bmeas Btrue 62

63 Correlations (II) EXAMPLE The double turn method shows a clear correlation between the errors on Ee and Ye The effect is well understood in terms of geometrical effects, arising from the fact that the decay point is defined as the intersection of the track with the target plane 63

64 Event-by-event errors (I) GENERAL TREATMENT In order to improve the sensitivity of the analysis, we CAN build the PDFs using an event-by-event estimate of the resolution function Psig(Ai) = Gauss(Ai; ma, sa) Gauss(Ai;mA,sA,i) 64

65 Event-by-event errors (I) GENERAL TREATMENT In order to improve the sensitivity of the analysis, we CAN build the PDFs using an event-by-event estimate of the resolution function 65

66 Event-by-event errors (II) EXAMPLE The Kalman Filter strategy provides an estimate of the covariance matrix of the track parameters can be used to build gaussian per-event PDFs CAVEAT: need to prove that the error estimate is correct!!!! pulla = (Ai-Atrue)/sA,i has to be normally distributed if not, e.g. P(pullA) = Gauss(pullA;mA,sA), then: P(A sa) = P(pullA)d(pullA)/dA Gauss(Ai;mA,sA,i) Gauss(Ai;mA-mAsA,sAsA) 66

67 Additional Constraints From the sidebands, we can also get an estimate of the expected background yields in the signal region used as a constraint in the likelihood analysis Almost equivalent to fitting a larger Teg range, but much less computationally expensive estimated expected error on the yields estimate Teg fit range 67

68 Putting all together... SIGNAL PDF (angles & positron energy) p and r parameters describe correlations C parameters make the translation from decay point resolutions to photon direction resolutions s parameters are the widths of the pulls (~ 1) 68

69 Sensitivity Estimate The sensitivity can be estimated using toy MC pseudo-experiments: Stat. approach applied to samples generated randomly according to PDFs and expected yields median Nsig UL ~ 6 ev. 69

70 Control Samples To test the complete scheme, the analysis is applied to a few control samples (sidebands) where no signal is expected 70

71 PDFs ~ 36 x 1013 m stopped at the target Nsig = Nbkg = 2413 ± 37 NRD = 167 ± 24 71

72 Upper Limit on Nsig 72

73 Normalization How to go from a number of events to a branching ratio? During the MEG data taking, a TC-only trigger is also employed (prescaled by 10 7): counting of Michel events counting of stopped m BR = Nsig/Nm only a few correction factors needed most of the uncertainties cancel in the ratio Nsig/Nm 73

74 Systematics GENERAL TREATMENT Background PDFs taken directly from data: systematics are negligible Systematics on signal PDFs can be relevant (control samples are generally biased, and correction have to be used) in the generation of toy MC for the FeldmanCousins-like method, PDF parameters are not constant, but randomly generated according to a gaussian distribution representing the associated error 74

75 Final Result BR(m e g) < 5.7 x incl. systematics 75

76 References MEG Physics Paper ( data): Phys.Rev.Lett. 107 (2011) MEG Physics Paper ( data): Phys.Rev.Lett. 110 (2013) MEG Detector Paper: Eur.Phys.J. C73 (2013) 4, 2365 A lot of material on statistical methods is available: PDG Statistics Review Phys.Rev.D57: ,1998 (Feldman-Cousins) arxiv:physics/ (G. Punzi on profile likelihoods) PHYSTAT2003 proceedings (G. Punzi on per-event errors) 76