The π 0 Lifetime: Experimental Probe of. Dustin E. McNulty MIT/UMass for the PrimEx Collaboration April 16, 2008

Transcription

1 The π Lifetime: Experimental Probe of the QCD Axial Anomaly Dustin E. McNulty MIT/UMass for the April 16, 28

2 The π Lifetime: Experimental Probe of the QCD Axial Anomaly Outline Physics Motivation Experimental Overview Calibration Reactions Pair Production Compton Scattering π Analysis Details Preliminary Γ π γγ Result Summary and Outlook Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 1

3 . Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 2

4 Physics Motivation: Anomalies in QCD Anomaly: When a symmetry of the classical theory is not present in the quantized version. In QCD, the anomaly is not anomalous, it is an essential part of the theory. For which processes does the anomaly occur? Define a multiplicative quantum number natural parity (NP) = 1 for S, V,... particles. NP = -1 for PS, PV,... An anomalous reaction changes the NP: γπ(np = -1) γπ(np = -1) not anomalous π (NP = -1) γγ(np = 1) anomalous γπ(np = -1) ππ(np = 1) anomalous All anomalous reactions are governed by the Wess-Zumino Lagrangian in ChPT In the Chiral limit, the absolute rate of these rections are predicted by QCD Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 3

5 Physics Motivation π decay rate is a fundamental prediction of QCD. Chiral Anomaly Presence of closed loop triangle diagram results in nonconserved axial vector current, even in the limit of vanishing quark masses. In the leading order (chiral limit), the anomaly leads to the decay width: Γ π γγ = α2 m 3 π 64π 3 F 2 π = ±.44 ev (1) where F π = ±.25 MeV is the pion decay constant. Current Particle Data Book value is 7.84 ±.56 ev Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 4

6 Physics Motivation LO prediction exact in Chiral limit For m q, there are corrections: Due to isospin sym-breaking (m u m d ), π, η and η mixing induced. Further corrections induced by terms in the Chiral Lagrangian. NLO prediction for the decay width is 8.1 ev ± 1% Calc. using Chiral Perturbation Theory and 1/N c expansion. J.L.Goity et al, Phys. Rev. D66, 7614 (22); B.Moussallam, Phys. Rev. D51, 4939 (1995) This is 4% higher than current experimental value! A precision measurement of the π decay width is needed. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 5

7 CERN (Direct Method) Decay Length Measurement τ π s too small to measure Solution Measure decay length of highly energetic π s: L = vτ π E/m (2) for E = 1GeV, L 1µm (very challenging experiment) Performed in 1984: Used 45GeV protons Result: Γ (π γγ) = 7.34eV±3.1% Dominant syst. error: Uncertainty in E π (±1.5%) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 6

8 The Primakoff Effect π photoproduction from Coulomb field of nucleus. Equivalent production (γγ π ) and decay (π γγ) mechanism implies Primakoff cross section proportional to π lifetime. Primakoff π produced at very forward angles. dσ P dω = Γ 8α em Z 2 β 3 E 4 (π γγ) m 3 Q 4 F em (Q) 2 sin 2 θ π (3) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 7

9 Full Cross Section Components dσ π dω = dσ P dω + dσ C dω + dσ I dω + 2 Primakoff Nucl.Coherent Incoherent Interference dσp dω dσ C cos(φ) (4) dω Primakoff: Proportional to Z 2, peaked at θ π = m 2 π /2E 2 γ Nuclear Coherent: dσ C dω = C A2 F N (Q) 2 sin 2 θ π (5) Nuclear Incoherent: dσ I dω = ξa(1 G(Q)) dσ H dω Interference: (6) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 8

10 Experiment Overview Conducted at Jefferson Lab, Fall 24 Used 5.75 GeV continuous e beam and Hall B γ-tagging facility Tagged photons incident on 5%X targets: 12 C and 28 Pb New PrimEx/Hall B calorimeter (HyCal), upstream of CLAS, designed to detect π decay γ s Measured 3 physical processes (absolute cross sections): Primary - π production, Secondary - Compton and e + e pair production Improvements over previous experiments: Precision tagged γ flux and incident γ energy info, enhanced π angular and mass resolution, and identification and subtraction of background event contamination Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 9

11 Experiment Overview Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 1

12 Hall B Photon Tagger Single dipole magnet combined with a hodoscope containing two planar arrays of plastic scintillators to detect energy-degraded electrons from a thin bremsstrahlung radiator. Tagger has.1% energy resolution and is capable of 5 MHz rates. e-beam Photon-beam PrimEx energy Range Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 11

13 Photon Flux Control PrimEx achievement: Total uncertainty in photon flux = 1.1%. Number of tagged photons on target (N γ ) calibrated periodically using a Total Absorption Counter (TAC). Any drifts in the tagging ratio, occuring between calibration points, are monitored online with the e + e pair spectrometer. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 12

14 PrimEx Hybrid Calorimeter HyCal. Optimal performance/cost design 1.2 m 1.2 m, 1728 channels 576 Lead-glass (outer layers) 1152 Lead-Tungstenate crystal (inner layers) Lead-glass PbWO 4 Energy Res. ( E/E) 3 5 % 1 2 % Position Res. ( x,y) 5 mm 1.5 mm Angular Res. ( θ π ) 675 µrad 3 µrad Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 13

15 PrimEx Hybrid Calorimeter HyCal. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 14

16 HyCal Calibration Full x,y motion allowed each ch. to be scanned through tagged γ beam. Performed at both the beginning and end of the experiment. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 15

17 Calibration Reactions: e + e Pair Production. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 16

18 Calculation of Pair Production Cross Section at PrimEx Kinematics Bethe-Heitler mechanism of pair production on the nucleus with screening effects due to atomic elactrons and Coulomb distortion Pair production off atomic electrons, considering excitation of all atomic states and correlation effects due to the presence of other electrons and the nucleus Radiative corrections (of order α/π) (i) virtual photon loops and (ii) real photon process like γ + A e + + e + A + γ Nuclear incoherent contribution, γ + p e + + e + p Nuclear coherent contribution (VCS), γ + A γ + A e + + e + A Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 17

19 Pair Production Preliminary Result Agreement with theory at 1.% level Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 18

20 Calibration Reactions: Compton Scattering Lead-Glass HyCal Measured Eo incident photon scattered atomic electron scattered photon θ γ beamline e:(x,y,e) Measured A well known process, useful in several ways: Detector/beam alignment HyCal gain monitoring PbWO 4 γ:(x,y,e ) Measured Lead-Glass Overall check of PrimEx setup to measure absolute cross sections Dedicated Double-Arm Compton Runs: Performed on a weekly basis, B PS =, I beam 5 1 na Both e and scattered photon detected in HyCal Compton Cross Section Measured: 12 C and.5%x 4 Be Single-Arm Compton Data: Dominant Source of Events in π production dataruns B PS 2 T, I beam 1 na, only scattered photon detected Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 19

21 Beam Alignment Monitoring using Single-Arm Compton. (Y Compt - Y) mean (X Compt - X) mean Only scattered γ measured X reported HyCal coord X Compt calc. (x,y) from Hycal E and Compton kin. If beam alignment perfect: (X Compt -X) = Technique tracks alignment at.1 mm level Jump in X correlated with beamline BPM Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 2

22 Compton Cross Section Preliminary Result Average statistical error:.6% Total error: 1.3% (dominated by photon flux: 1.%) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 21

23 Analysis Details: π Event Selection We measure: initial photon energy: E γ energies of decayed photons: E γ 1, E γ 2 X,Y positions of decayed photons Kinematical constrains: Conservation of energy Conservation of momentum m γγ invariant mass Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 22

24 Analysis Details: π Event Selection. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 23

25 ' $ Analysis Details: π Yield Extraction mass_all_th_e3 mγ γ, 12C, crystal only Events/1.MeV for.6 < θπ.8 1 All Ibeam, Radiator B 122 χ 2 / ndf / ± 24.8 const1+2 tdiff:[-7.4,.6] ns (BC) 8 Entries mean ±.6 sigma ±.516 const ± elastic cut:[.96,1.86] 6 mean ±.6 sigma ±.85 p e-5 ± 6.82e-9 p ±. p ±. p ±. 4 # of πs = ± mγγ (MeV) χ 2 / ndf Correct for inelastic bkgd by evaluating π elasticity distribution explicitly for each θπ ; evaluate inelastic bkgd under the elastic peak using fit and subtract from yield. & Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC π Yield/.1 For each θπ bin, apply elastic cut and form mγγ distributions; perform fit and extract peak counts = uncorrected yield. 1 1 All Ibeam, Radiator B θ π : [1.2,1.3] deg tdiff:[-7.4,.6] ns (BC) / ± 69.1 const C, crystal only mean ±.19 sigma1.25 ±.1 const ± mean ±.5 sigma ± e+4 ± 49 p3.6 p e+4 ± 9 p e+4 ± 19 p -1.15e+4 ± 67 Peak cts = 3982 ± Bkgdine:[.96,1.86] = 583=>12.8% EclusterPair /E tagger Elasticity = EclusterPair /E tagger 24 %

26 Analysis Details: Yield Result for 12 C and 28 Pb ) o Yield (per.2 π π Photoproduction Yield ( C, crystal only) Preliminary elastic range:[.96,1.86] Elastic π yield + bkgd Inelastic π bkgd Total π s = 9733 o π s:[,.3 ]= 289 ) o Yield (per.2 π π Photoproduction Yield ( Pb, crystal only) Preliminary elastic range:[.96,1.86] Elastic π yield + bkgd Inelastic π bkgd Total π s = 661 o π s:[,.3 ]= π Production Angle, θ (degrees) π Production Angle, θ (degrees) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 25

27 Yield Results for 12 C and 28 Pb /2.334e+12 incident γ s o Yield/.2 π π Photoproduction Yield ( C, crystal only) elastic range:[.96,1.86] Preliminary Elastic π yield Total π s = 644 π s:[,.3 ]= 5187 o /1.311e+12 incident γ s o Yield/.2 π π Photoproduction Yield ( Pb, crystal only) elastic range:[.96,1.86] Preliminary Elastic π yield Total π s = 8443 o π s:[,.3 ]= π Production Angle, θ (degrees) π Production Angle, θ (degrees) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 26

28 Analysis Details: Γ π γγ Determination Convert Yield to Cross Section. dσ exp dθ π = N yield π (θ π ) N γ N t ε π (θ π ) θ π (7) where N γ # of γ s on target (uncertainty 1.%). where N t target atoms/cm 2 (thickness mapped to.5%). where ε π experimental acceptance (uncertainty.6%). Fit experimental data with parameterization: dσ exp dθ π dσ P = b p dω + b dσ N c dω + b dσ I i dω + 2cosφ b p b c dσ P dω dσ C dω (8) where the parameter b p = Γ γγ Vary the four parameters (b p, b c, b i, and φ) and minimize χ 2. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 27

29 Photon Flux Total Incident photon flux Total γ-flux vs. Energy ( C, radiator B) Total Incident photon flux Total γ-flux vs. Energy ( Pb, radiator B) Tagged Photon Energy (GeV) Flux for 12 C: γ s Tagged Photon Energy (GeV) Flux for 28 Pb: γ s Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 28

30 . Hycal Geometric acceptance of both π decay γ s ) o Acceptance (per.2 π 2γ HyCal π Geometric Acceptance (All Fiducials) All Channels Crystal Only Glass Only Mixed (Glass-Crystal) allnogonly True Crystal Only π Production Angle, θ (degrees) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 29

31 Experimental Efficiencies: 12 C Losses (%) Description 12 C 28 Pb Photon Absorption in Target 5.41 ± ±.1 Best (tdiff) Candidate selection 2.5 ± ±.3 Elasticity Cut: [.96, 1.86] 1.7 ± ±.3 Veto Cut: all flags (, 1, 2, 3) 1.97 ± ±.12 Branching Ratio π γγ 1.2 ± ±.3 Total 12.8 ± ±.4 Table 1: Summary of non-geometric losses. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 3

32 Cross Sections dσ/dθ (µb/rad) π Photoproduction Cross Section ( C) Preliminary dσ/dθ (µb/rad) π Photoproduction Cross Section ( Pb) Preliminary π Production Angle, θ Wed Feb 27 6:9:52 28 π Production Angle, θ (degrees) π Production Angle, θ Wed Feb 27 5:31:31 28 π Production Angle, θ (degrees) Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 31

33 Yield Fit, Γ γγ Extraction: Procedure Parameterize yield using sum of 4 theoretical shapes smeared according to experimental resolutions. Calculate theory input shapes (cross sections) energy-weighted according to experimental flux. Create π event generator based on above cross sections and run through Primsim Monte Carlo. Digitize simulated data and reconstruct events using same algorithms as for real data. Produce simulated yield distributions with built-in experimental resolutions. Freely vary amplitudes of 4 shapes and minimize χ 2. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 32

34 MC Shape Generation: Exmpl. Thrown & Det. Spectra 3 1 Simulated θ π Distribution (gen63, Wonly) 3 1 Simulated θ π Distribution (gen21, Wonly) 5 mc_theta_wonly Entries mc_theta_wonly Entries Mean Mean.4474 RMS RMS Thu Mar 2 1:21: Fri Mar 21 1:1: C: θ π Thrown θ π Detected 28 Pb: θ π Thrown θ π Detected Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 33

35 MC Shape Generation: Exmpl Fit Input Shapes (smeared) 3 1 Simulated θ π Distribution (gen63, Wonly) 3 1 Simulated θ π Distribution (gen21, Wonly) 5 4 pi_theta_wonly Entries Mean 1.3 RMS pi_theta_wonly Entries Mean.4625 RMS Thu Mar 2 9:38: Fri Mar 21 1:1:59 28 Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 34

36 12 C and 28 Pb Target Yield Fits 12 Preliminary π Photoproduction yield ( C, crystal only) 28 Preliminary π Photoproduction yield ( Pb, crystal only) o Yield/.2 π Measured π Yield Calculated Yield Fit Primakoff Nuclear Coherent Interference Incoherent o Yield/.2 π Measured π Yield Calculated Yield Fit Primakoff Nuclear Coherent Interference Incoherent π Production Angle, θ (degrees) Tue Apr 8 9:38: π Production Angle, θ (degrees) Fri Apr 4 11:31:3 28 Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 35

37 Preliminary Systematic Error Table Description Γ γγ dev (%) m γγ fits + inelast bkgd corr. ±1.1 Inelastic bkgd shape uncert. ±.75 Photon flux ±.98 Experimental efficiencies ±.5 Fiducial Acceptance ±.3 Event Selection ±.9 π bkgd from ω and ρ decay ±1. Target thickness ±.1 branch ratio ±.3 Tagged Photon Energy ±.1 Total Systematic Error ±2.3% Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 36

38 Preliminary Theoretical Input (Model) Error Table Γ γγ dev (%) Description 12 C 28 Pb Incoherent XS shape uncert. ±1.35 ±.11 Nuclear coh. XS energy dep. ±.16 ±.6 F NC intermediate state ±.2 ±.73 π-n cross section uncertainty Total Model Error ±1.38 ±.74 Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 37

39 Γ π γγ Preliminary Result. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 38

40 Summary and Outlook High Quality precision π photoproduction data on 12 C and 28 Pb targets using 4.9 E tagged γ 5.5 GeV has been collected and analyzed by the. Preliminary cross section results from studied calibration reactions e + e production and Compton scattering are both in excellent agreement with theory (at the 2 3% level). All three independent π analysis groups have achieved very consistent results. The preliminary π partial width result: Γ π γγ = 7.93eV ± 1.8%(stat) ± 2.3%(syst) ± 1.1%(model). The mean lifetime: (8.2 ±.24) 1 17 s Preliminary Γ π γγ results from both targets in excellent agreement. Continued work on reducing systematic error and finalizing results. Dustin McNulty, Apr 16, 28, GWU Nuclear Physics Seminar, Washington DC 39