Polarized muon decay asymmetry measurement: status and challenges

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1 Polarized muon decay asymmetry measurement: status and challenges Glen Marshall, for the TWIST Collaboration Muon Physics in the LHC Era Symposium at the Institute of Nuclear Theory Seattle, October 008

2 Outline Origin of the asymmetry Prior results, TWIST and other experiments Depolarization and asymmetry experimental features important for P μ ξ measurement simulation methods and tests fringe field depolarization and beam characterization stopping target depolarization other issues: detector response and symmetry expectations for final precision Application of decay asymmetry for SM tests Summary: what are the limitations for TWIST?

3 Pion decay: the polarizer Prototype of a polarization experiment For SM with massless ν: RH anti-ν (LH ν) and μ - (μ + ) result when π - (π + ) decay. μ + created with P μ P π μ = -.0 with respect to muon momentum. 3

4 Asymmetric decay: the analyzer Muon decay parameters ρ, η, P μ ξ, δ muon differential decay rate vs. energy and angle: d Γ dx d cos θ = q 4 m μw 4 μe G F x x 0 where and {F IS (x, ρ, η) +cosθ P μ F AS (x, ξ, δ)} + R.C. F IS (x, ρ, η) = x( x) + 9 ρ(4x 3x x 0 )+ηx 0( x) F AS (x, ξ, δ) = 3 W μe = m μ+m e m μ q x x 0 "ξ { x} + 3 ξδ n 4x 3+ ³q x0 o#, x = E e W μe, x 0 = m e W μe. θ p P μ 4

5 Results to date Direct measurements: P μ ξ =.007 ± ± (Beltrami et al., 987) P μ ξ =.0003 ± (stat) ± (sys) (TWIST, Jamieson et al., 006) (TWIST precision goal: <0.0008) Indirect from P μ (ξδ/ρ)> (Jodidio et al., 986) < P μ ξ <.0040 (TWIST, Gaponenko et al., 006) < P μ ξ <.0009 (TWIST, MacDonald et al., 006) Beltrami et al., 987 Jamieson et al. (TWIST), 006 TWIST final result? P μπ ξ 5

6 Systematics for TWIST result Systematic uncertainties Depolarization in fringe field (ave) Depolarization in muon stopping material (ave) Chamber response (ave) Spectrometer alignment Positron interactions (ave) Depolarization in muon production target Momentum calibration Upstream-downstream efficiency Background muon contamination (ave) Beam intensity (ave) Decay η parameter Theoretical radiative correction Total in quadrature P μ ξ ( 0-4 ) Jamieson et al., 006 6

7 Systematics for TWIST result Systematic uncertainties Depolarization in fringe field (ave) Depolarization in muon stopping material (ave) Chamber response (ave) Spectrometer alignment Positron interactions (ave) Depolarization in muon production target Momentum calibration Upstream-downstream efficiency Background muon contamination (ave) Beam intensity (ave) Decay η parameter Theoretical radiative correction Total in quadrature P μ ξ ( 0-4 ) Jamieson et al., 006 7

8 Depolarization and asymmetry Two classes of systematic uncertainty: Depolarization: relate P μ at decay to P μπ at production P μ impossible to measure via decay, independent of ξ. polarizer and analyzer depend on weak interaction. Two main sources fringe field requires accurate field model and simulation of beam characteristics, motion: P μ < P μ π stopping target spin interactions with high-purity metal (Al, Ag) lead to small time-dependence and extrapolation: P μ = P μ e - λ t. Asymmetry Detector asymmetries (chamber response and efficiency, material interactions, alignment). 8

9 Muon production and transport 500 MeV proton beam muon decay detector TEC fringe field region muon production elements used for additional beam steering 9

10 Simulation quality is essential Simulation based on GEANT3 contains: precise geometry output format same as data Thomas-BMT spin tracking muons sampled from data distributions verified via: special data sets special analyses of standard sets comparison to G4 y Ten muon decay events simulated in the TWIST detector. z 0

11 Fringe field depolarization The problem: For SM with massless ν, μ + produced with P μ P μπ = with respect to muon momentum. <P μ > with respect to physical axis (beam direction, magnetic field) is less, due to finite beam acceptance (angular divergence). effective <P μ > of a muon beam changes as beam divergence changes, e.g. due to B field in a beam line or detector. The TWIST solution: Simulate μ + with P μπ =, in realistic B field, sampling from measured beam characteristics (position, divergence, momentum). Apply Thomas equation (BMT) for spin evolution, GEANT3 physics processes (scattering, energy loss, etc. ). Carefully assess systematic effects due to limitations in field map, detector stability, beam size and stability, simulation precision,...

12 Measuring beam characteristics Need to know x, y, θ x, θ y, and correlations, for incident muon beam. Measure in two modules of low pressure (80 mb) time expansion chambers (TEC). Correct for multiple scattering ( 0 mrad rms). Simulate by sampling corrected distributions. Decay parameters measured with TEC removed; multiple scattering reduces polarization. J. Hu et al., NIM A566 (006)

13 Simulating the muon beam Comparison of TEC data and corresponding simulation of beam profiles 3

14 Fringe field, solenoid entrance Yoke entrance TEC decay detector region region of next plots The central field is T, with a strong gradient near the solenoid yoke entrance. Muon tracks are measured by the TEC, to establish incident beam parameters. Muons are also tracked in the upstream part of the decay detector 4

15 Muon entrance paths muon position (cm) nominal beam single track x y average position (cm) decay nominal beam detector x y region average of many tracks z muon position (cm) z (cm) 5 x 4 mis-steered beam y single track average position (cm) z (cm) mis-steered beam y x average of many tracks z (cm) z (cm)

16 Measured average muon positions plots courtesy of J. Bueno average position (cm) average position (cm) z (cm) nominal beam mis-steered beam x y x y Each point represents the average muon beam position at a detector plane. Simulated data can be analyzed in the same way. Fit both to shrinking helix. Comparison of fits of data and simulation is a powerful way to verify the simulation, e.g., influence of fringe field on muon beam, detector-field alignment z (cm) 6 Use internal beam to test fringe field depolarization limitations.

17 Muon beam in decay detector Average muon beam: position (run-by-run) shows beam (in)stability. Typical sets stable to ±0.03 cm. Outliers discarded. Internal beam parameters (position, amplitude, etc. ) compared with simulation to verify effect of fringe field. systematic uncertainties derived, especially from mis-steered sets. Data taken under different conditions: beam steering, stopping target material, solenoid field (± %), muon stop position, material in detector (symmetry), initial muon momentum. Average position of helix, with respect to detector axis, for internal muon beam for all runs in each of ten data sets. Set 76 and set 86 are intentionally mis-steered. 7

18 Depolarization in stopping target μsr effect -- minimize by use of high-purity metal targets: main mechanism at room temperature is via interaction with conduction electrons (Korringa relaxation), studied in μsr experiments. asymmetry is a function of time: P μ (t) = P μ exp (- λt ). different targets, Al (76 μm) and Ag (8 μm) provide test of possible systematic bias. Stopping target forms anode of adjacent MWPC detectors: energy loss (ionization charge) information discriminates against muons stopping in other detector materials, to reduce depolarization from (μ + e -) formation (e.g. in MWPC gas, He), which depolarizes muons (depolarization also reduced by high longitudinal field). chemical reactions (analogous to hydrogen atom). 8

19 Systematic correction for relaxation TWIST detector is a very powerful μsr device: uniform field, excellent background rejection. e + momentum available for weighting the asymmetry.... but not very versatile... Observed relaxation rate is included in the simulation: accounts realistically for relaxation. statistical uncertainty in λ is a source of target depolarization systematic uncertainty in P μπ ξ. Ag λ Ag = 0.73(7) 0-3 μs - Al λ Al =.8(7) 0-3 μs - 9

20 Other depolarization mechanisms? Multiple muon scattering at exit of production target: use narrow momentum range ( MeV/c); small energy loss quantifies possible depolarization ( 0-4 systematic correction). Radiative processes in pion decay calculated to be negligible for our kinematics. In-flight interactions with magnetic moments magnetic scattering, estimated to be negligible. (g ), laboratory E fields, relativistic E fields, non-zero neutrino mass all estimated to be negligible. 0

21 Chamber response Improvements benefit three parameters, ρ, δ, and P μ ξ. Detector position response: use drift chamber Space Time Relationships as determined from data, individually for each plane. Use same procedure with simulated data to reduce bias in fit of data to simulation. Upstream/Downstream tracking inefficiency differences: Test with positrons from Upstream stops tracking inefficiency difference between simulation and data: 0.6() 0-4 US 0.3() 0-4 DS. cosθ Momentum (MeV/c) DS inefficiency, data

22 Preliminary estimates: final uncertainties Systematic uncertainties Depolarization in fringe field (ave) Depolarization in muon stopping material (ave) Chamber response (ave) Momentum calibration Decay η parameter Theoretical radiative correction Positron interactions (ave) Depolarization in muon production target Upstream-downstream efficiency Total systematic in quadrature Statistical uncertainty Total uncertainty in quadrature P μ ξ ( 0 4 ) Several of the previous systematic uncertainties are now too small to be included.

23 SM extension: Left-Right Symmetric Weak eigenstates in terms of mass eigenstates and mixing angle: W L = W cos ζ + W sin ζ, W R = e iω ( W sin ζ + W cos ζ) Assume possible differences in left and right couplings and CKM character. Use notation: t = g R m, t gl θ = t V ud R m Vud L, ζ g = g R ζ gl Then, for muon decay, the Michel parameters are modified: ρ = 3 4 ( ζ g ), ξ = (t + ζ g ), P μ = t θ ζ g 4t θζ g cos(α + ω) manifest LRS assumes g R = g L, V R = V L, ω = 0 (no CP violation). pseudo-manifest LRS allows CP violation, but V R = (V L )* and g R = g L. LRS non-manifest or generalized LRS makes no such assumptions. Many experiments must make assumptions about LRS models! 3

24 Limits on LRS parameters: PDG08 Observable m (GeV/c ) ζ m(k L 0)- m(k S 0) >700 reach (P)MLRS Direct W R searches >000 (D0) >788 (CDF) clear signal (P)MLRS decay model Electroweak fit <0.03 fit (P)MLRS β decay >30 <0.040 both parameters (P)MLRS light ν R μ decay*, TWIST >475 (>530) <0.0 (<0.06) model independence light ν R * in generalized LRS model; to be interpreted as m (g L /g R ), ζ(g R /g L ). 4

25 Muon decay LRS limits Exclusion (90% cl) plots for left-right symmetric model mixing angle ζ and W mass m. Generalized LRS model; no assumptions on RH CKM matrix elements. 5

26 Handedness of the muon Diagonal represents exactly lefthanded muon decay. Shaded regions represent comparison of current and proposed TWIST limits, compared to previous PDG limits. Q μ R = [ + 3 ξ 6 9 ξδ] 0 < 0.004(90%CL) (Global analysis; R.P. MacDonald et al., 008) Final TWIST result with global analysis could reduce the limit to <

27 Summary TWIST has completed data taking; analysis well underway. Systematic and statistical precision should meet or exceed initial expectations. The polarization measurement has unique challenges; Depolarization systematics especially. TWIST was successful, but could be improved upon: higher luminosity beams, better field characterization, higher precision detectors (beam and decay). or some better ideas? 7

28 Thank you to: - INT and the organizers, for the opportunity to speak here -the TWIST collaboration (especially J. Bueno and R. Mischke) - our support agencies: NSERC, DOE, TRIUMF - WestGrid, for lots of CPU power - the audience, for your attention 8

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