Investigating Lepton Universality via a Measurement of the Positronic Pion Decay Branching Ratio

Transcription

1 Investigating Lepton Universality via a Measurement of the Positronic Pion Decay Branching Ratio Anthony Palladino Advisor: Dinko Počanić Ph.D. Dissertation Defense Charlottesville, Virginia, USA 6 December 211 Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 1 / 37

2 Outline Introduction Theory of Pion Decay Review of Helicity Suppresion Physics Motivation Lepton Universality PEN Experiment Previous Measurements TRIUMF and PSI PEN Detector Analysis Waveform Fitting Pulse Shaping and the Modified χ 2 Objective Function Maximum Likelihood Analysis Observables, Processes, and Probability Distribution Functions Conclusions Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 2 / 37

3 Introduction Theory of Pion Decay Quark Content: π + = ud Theory of π + Decay Mass: m π + = MeV Lifetime: τ π + = 26.3 ns Decay Mode Branching Fraction π + µ + ν µ (γ) (4) π + µ + ν µ γ (Eγ >1MeV) 2.(25) 1 4 Bressi et al. 98 π + e + ν e (γ) 1.23(4) 1 4 Czapek et al. 93, Britton et al. 92, Bryman et al. 8 π + e + ν e γ (Eγ >1MeV) 7.386(54) 1 7 Bychkov et al. 9 π + π e + ν e 1.36(6) 1 8 Počanić et al. 4 π + e + ν e e + e 3.2(5) 1 9 Egli et al. 89 Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 3 / 37

4 Introduction Theory of Pion Decay Theory of π + Decay Why is π + e + ν e a rare decay? Helicity Suppression Conservation of Angular Momentum: In π rest frame, the π has S =. The outgoing lepton pair (each spin 1/2) must combine to give S = both Right-Handed (Positive Helicity), or both Left-Handed (Negative Helicity) Property that if m = : All S = 1/2 particles are Left-Handed (Negative Helicity) All S = 1/2 antiparticles are Right-Handed (Positive Helicity) The negative helicity ν e (ν µ ) forces the e + (µ + ) into a negative helicity state. But, m e + m µ + (m µ + 2m e +) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 4 / 37

5 Introduction Theory of Pion Decay Theory of π + Decay Helicity: For v = c, fraction violating =. For a given E, v e > v µ e is less likely to have wrong helicity. Helicity Conservation v 2 c.. Helicity Violation v 2 c HelicityViolation (e + ) HelicityViolation (µ + ) π Decay Phase Space: Since the e + is lighter, the π + e + ν e decay has a larger phase space than the π + µ + ν µ decay. gives a factor 3.3 Γ(π + e + ν e) Γ(π + µ + ν µ) 3.3 ( ) 1 4 Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 5 / 37

6 Introduction Theory of Pion Decay Theory of π + Decay π + e + ν e 2-body decay E e + = 69.8 MeV π + µ + ν µ followed by µ + e + ν e ν µ sequential decay Ee max = 52.5 MeV + Arbitrary Normalization Total Positron Energy (MeV) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 6 / 37

7 Introduction Physics Motivation The PEN Experiment Precision Measurement of the π + e + ν e branching ratio. ( ) R πe2 = Γ(π+ e + 2 ( ) 2 ν e(γ)) Γ(π + µ + ν = ge me (1 me 2/m2 µ) 2 µ(γ)) g µ m µ (1 + δr (1 mµ 2 /m2 π) 2 πe2 ) ( ±.5) 1 4 Marciano & Sirlin, [PRL 71, 3629 (1993)] Rπ calc e2 = ( ±.2) 1 4 Finkemeier, [Phys. Lett. B 387, 391 (1996)] ( ±.1) 1 4 Cirigliano & Rosel, [PRL 99, (27)] R exp π e2 = (1.23 ±.4) 1 4 Experiment World Average (Current PDG) Our Goal: R exp R R PDG: exp exp R exp Lepton Universality: W. Loinaz, et. al., Phys. Rev. D 65, 1134 (24) [hep-ph/4336] ( ge g µ = 1.21 ±.16 )π Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 7 / 37

8 Introduction Physics Motivation Lepton Universality From Loinaz et al.,prd 7 (24) 1134 where l l = ε l ε l g l g = 1 + ε l ε l l 2 π + { u d W + g l l + ν l Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 8 / 37

9 Introduction Physics Motivation Deviations from SM Prediction A Branching Ratio that is different from the SM prediction could be caused by: lepton non-universality, charged Higgs particles in theories with more Higgs than SM, pseudoscalar leptoquarks in theories with dynamical symmetry breaking, vector leptoquarks in GUTs, SUSY partner particles appearing in loop diagrams, non-zero neutrino masses, Majorons. Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 9 / 37

10 Introduction Physics Motivation Mass Limits on Leptoquark and Supersymmetric Particles A measurable deviation in R πe2 from the SM prediction is clear evidence of physics beyond the SM, sensitive to mass scales of many TeV. Particle Current Bounds Projected Mass Sensitivity Charged Higgs Boson m H > 2 TeV > 6.9 TeV Pseudoscalar Leptoquark m p > 1.3 TeV > 3.8 TeV Vector Leptoquark M G > 22 TeV > 63 TeV Following the calculations in Shanker, NP B24 (82) 375 Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 1 / 37

11 PEN Experiment Previous Measurements History of the Measurement Czapek (1993) Britton (1992) Bryman (1986) DiCapua (1964) Anderson (196) Branching Ratio Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

12 PEN Experiment PEN Detector Paul Scherrer Institute Villigen, Aargau, Switzerland Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

13 PEN Experiment PEN Detector The PEN Apparatus stopped π + beam active target counter 24-det. pure CsI calo. central tracking digitized PMT signals stable temp./humidity BC PEN Detector 28 π + beam vac. pure CsI wad AT PMT PH MWPC1 MWPC2 wad (x4) 1 cm Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

14 PEN Experiment PEN Detector PEN Detector Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

15 PEN Experiment PEN Detector Beam Counter, Focusing Magnets, and Detectors Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

16 PEN Experiment PEN Detector The PEN Apparatus: 28 stopped π + beam active target counter 24-det. pure CsI calo. central tracking digitized PMT signals stable temp./humidity BC PEN Detector 28 π + beam vac. pure CsI wad AT PMT PH MWPC1 MWPC2 wad (x4) 1 cm Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

17 PEN Experiment PEN Detector The PEN Apparatus: 28 wad AT Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

18 PEN Experiment PEN Detector The PEN Apparatus: 28 Novel, low cost, four-piece, Wedged Degrader. (UZh: P. Robmann) Pros: x,y position sensitivity of beam π + Cons due to thicker degrader (13mm as opposed to 5mm): higher beam momentum required more nuclear reactions in target. more material increases multiple scattering π position resolution suffers. Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

19 PEN Experiment PEN Detector The PEN Apparatus: 28 Target Counter Photomultiplier Module Hamamatsu H Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

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21 PEN Experiment PEN Detector Acqiris Digitizer Acqiris High Speed 1-bit PXI/CompactPCI Digitizer, Model DC282 4 Channels, each with 2 GS/s Digitized PMT waveforms from three beamline detectors: Upstream Beam Counter Active Degrader Active Target Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 2 / 37

22 PEN Experiment PEN Detector Fwd Beam Counter B Waveform Degrader Top & Bottom DEGLR Waveform Degrader Left & Right DEGTB Waveform Target TGT Waveform Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

23 Analysis Waveform Fitting Target Waveform Analysis Calibrate target energy to monoenergetic muon. Provide cuts, useful for distinguishing the various processes. Digitizer Amplitude TGT Waveform Digitizer Amplitude TGT Waveform Channel Number (ns*2) π + µ + e + Event Channel Number (ns*2) π + e + Event. Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

24 Analysis Waveform Fitting Pulse Shaping Developed an iterative program to create a digital adaptive filter. Input: Averaged system response waveform array, w i Desired waveform array, w i Output: Shaping array ( Filter ), s i Pulse Shaping: w i = k max Normalized Amplitude Waveform Bin (.5ns) k=k min s k w j where k i j Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

25 Analysis Waveform Fitting Pulse Shaping Filter Amplitude Amplitude (Arbitrary Units) π + Target Waveform Filtered Target Waveform + µ + e n (.5 ns) n (.5 ns) Filtering (Shaping) isolates the monoenergetic muon for energy calibration. A. Palladino, A. van der Schaaf, D. Počanić, Reconstructing Detector Waveforms with Overlapping Pulses, to be submitted 211. Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

26 Analysis Waveform Fitting Target Waveform Fit Parameters Pulse Position in time Amplitude π + Known (from Degrader) Known (from TOF and E B + E deg ) σ 65 ps σ 716 kev (5.5%) µ + Unknown Known (monoenergetic) σ 2 kev (4.8%) e + Known (from Plastic Hod.) Known (from tracking) σ 492 ps σ 878 kev (29.2%) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

27 Analysis Waveform Fitting π + µ + e + Event Fit Amplitude (Arbitrary Units) π + µ e + Raw Target Waveform Filtered Target Waveform n (.5 ns) Amplitude (Arbitrary Units) π + µ + e + Filtered Target Waveform Subtracted Target Waveform n (.5 ns) π + e + Event Fit Amplitude (Arbitrary Units) π + µ + e + Filtered Target Waveform 3-peak Fit Result 3-peak Fit Prediction 2-peak Fit Result 2-peak Fit Prediction n (.5 ns) Amplitude (Arbitrary Units) π + e + Raw Target Waveform Filtered Target Waveform n (.5 ns) Amplitude (Arbitrary Units) π + e + Filtered Target Waveform Subtracted Target Waveform n (.5 ns) Amplitude (Arbitrary Units) π + µ + e + Filtered Target Waveform 3-peak Fit Result 3-peak Fit Prediction 2-peak Fit Result 2-peak Fit Prediction n (.5 ns) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

28 Analysis Waveform Fitting i=1 σ w Waveform Fitting Modified χ 2 Function: n ( ) w χ 2 = 1 Fit 2 ( i w i E Fit π n d.o.f. + λ + 1 E Pred π + σ Eπ + ) 2 + λ 2 ( E Fit e + E Pred e + σ Ee + ) 2 2 Shaped Target Waveform w[ t ] Peak Fit Prediction 2 Peak Fit 3 Peak Fit Prediction 3 Peak Fit t (.5 ns / bin) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

29 Analysis Waveform Fitting i=1 σ w Waveform Fitting Modified χ 2 Function: n ( ) w χ 2 = 1 Fit 2 ( i w i E Fit π n d.o.f. + λ + 1 E Pred π + σ Eπ + ) 2 + λ 2 ( E Fit e + E Pred e + σ Ee + ) 2 w[ t ] Shaped Target Waveform 2 Peak Fit Prediction 2 Peak Fit 3 Peak Fit Prediction 3 Peak Fit t (.5 ns / bin) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

30 Analysis Waveform Fitting Waveform Fitting Results 2 peak χ π + µ + e χ 2 3 peak π + e Events per Cell 2 peak - χ 2 3 peak = χ 2 2 χ E e + (MeV) Events per Cell peak - χ 2 3 peak = χ 2 2 χ t e + - t π + Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / Events per Cell

31 Analysis Maximum Likelihood Analysis PEN Data Analysis Strategy: Determine the most likely value of the π + e + ν e branching ratio using a Maximum Likelihood Analysis. Benefits: Provides a unique, unbiased, minimum variance estimate (for a large enough sample). Practical, tractable approach via product PDFs Use as much data as possible to determine R πe2 ; loose cuts. Complication: Critical dependence on PDF Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec 11 3 / 37

32 Analysis Maximum Likelihood Analysis Maximum Likelihood Analysis One likelihood function encompassing many observables and processes. L ( ) N [ M ( xe ; f m = f m P xe ) ] m e=1 m=1 where N is the number of events, and ( x e ) are the observables (f m ) fraction of process m Time between π + and e + f πe2, π + e + Total Positron Energy f πµ2, π + µ + e + Probability [ of Pile-up l ] f Acc, Accidentals / Pile-up P pile-up = ln e dt k /τ µ f DIF, Pion Decays-in-flight k=1 Pion Decay Vertex etc. f Had, Proton f?, etc. Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

33 Analysis Maximum Likelihood Analysis Model: Probability Distribution Functions, P m ( E ) L Total ; f, f πe2 π, f µ2 Acc, f DIF, f Had Energy Histograms stacked on top of each other π µ2 π e2 Accidental Coincidence π Decay-in-flight Hadronic (proton) χ 2 /N dof = E Total (MeV) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

34 Analysis Maximum Likelihood Analysis Model: Probability Distribution Functions, P m ( t ) L ; fπe2, f π, f µ2 Acc, f DIF, f Had π µ2 π e2 Accidental Coincidence π Decay-in-flight Hadronic (proton) χ 2 /N dof = 1.3 Events per bin t e - t π (ns) t e t π (ns) Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

35 L Analysis Maximum Likelihood Analysis Practicality: Negative Log Likelihood l = lnl L = e l N p2e vs. N michel -ln(l) Number of π eν events Number of Michel events Number of π eν events Number of Michel events π eν events Number of Number of Michel events C++ code written specifically for this analysis. Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

36 Analysis Maximum Likelihood Analysis Maximum Likelihood Analysis Framework complete Flexible: can add/remove processes and observables Error analysis correct (weighted events) Errors comparable to χ 2 fit R R R R =.16% (statistical) R 2% (systematic) R <.2% Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

37 Conclusions Conclusion Year 26 (Beam Development Phase): Detector Refurbishment (Same detector from PiBeta Experiment). Year 27 (Experiment Development Phase): More refurbishments / Many new components and upgrades. Year 28 (1 st Production Phase): Use of wedged degrader for π tracking. Recorded π + e + ν e decays Years 29 and 21 (2 nd and 3 rd Production Phases): Use of mini-tpc for improved π tracking. Recorded more π + e + ν e decays Year 211 (Data Analysis Phase): Finalized target waveform analysis Developed Maximum Likelihood analysis framework Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37

38 Conclusions PEN Experiment Collaboration Members: L.P. Alonzi, a V. A. Baranov, c W. Bertl, b M. Bychkov, a Yu.M. Bystritsky, c E. Frlež, a V. Kalinnikov, c N.V. Khomutov, c A.S. Korenchenko, c S.M. Korenchenko, c M. Korolija, f T. Kozlowski, d N.P. Kravchuk, c N.A. Kuchinsky, c M.C. Lehman, a D. Mekterović, f D. Mzhavia, c,e A. Palladino, a D. Počanić, a P. Robmann, g O.A. Rondon-Aramayo, a A.M. Rozhdestvensky, c T. Sakhelashvili, b V.V. Sidorkin, c U. Straumann, g I. Supek, f Z. Tsamalaidze, e A. van der Schaaf, g E.P. Velicheva, c V.V. Volnykh, c a Dept of Physics, Univ of Virginia, Charlottesville, VA , USA b Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland c Joint Institute for Nuclear Research, RU Dubna, Russia d Institute for Nuclear Studies, PL-5-4 Swierk, Poland e IHEP, Tbilisi, State University, GUS-3886 Tbilisi, Georgia f Rudjer Bošković Institute, HR-1 Zagreb, Croatia g Physik Institut der Universität Zürich, CH-857 Zürich, Switzerland blue = Ph.D. Candidate = Spokesperson PEN Web page: Anthony Palladino (UVa) Investigating Lepton Universality with PEN 6 Dec / 37