Muon Decay Parameters From TWIST

Art Olin, TRIUMF/UVic for the TWIST Collaboration

Outline •Muon decay physics •TWIST Experiment •Systematics •Results Muon decay spectrum

The energy and angle distributions of positrons following polarized muon decay obey:

2 d Γ 2 x0 ∝3−3x ρ 4x−33η 1−x  x2 dxdcos θ  3 x 2 Pμ ξ cos θ 1−x  δ 4x−3  [ 3 ] (+ rad. corr.) Ee where x= Ee,max  Lorentz invariant, local weak interaction.  SM postulates maximally parity violating V-A: ρ=δ=3/4; ξ=1;η=0.  Mediated by W boson.  Empirically based – tested in present work.

2 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Muon decay matrix element

 Most general Lorentz-invariant, local, lepton-number conserving muon decay matrix element:

= 4GF γ Γγ ν ν Γ µ M ∑ gεµ eε | | ( e )n ( µ )m | γ | µ 2 γ =S,V ,T ε ,µ=R,L

γ  The muon decay parameters are bi-linear combinations of the g εμ

V  In the Standard Model, g LL = 1, all others are zero  Pre-TWIST global fit results (all 90% c.l.):

3 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Goal of TWIST

 Search for new physics that can be revealed by order-of-magnitude

improvements in our knowledge of ρ, δ, and Pμξ

Two examples

 Model-independent limit on muon handedness   µ = 1 + 1 ξ − 16 ξδ QR 1  2  3 9 

 Left-right symmetric model: SU(2)L x SU(2)R x U(1)

3 3 W = W cosζ +W sinζ − ρ = ζ 2 L 1 2 ⇒ 4 2  2 4  = iω ( − ζ + ζ )   M   M   WR e W1 sin W2 cos − ξ = ζ 2 + ζ  1  +  1  1 Pµ 4        M2   M2  

4 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test The TWIST Experiment TRIUMF Weak Interaction Symmetry Test

5 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Muon production and transport

m 500 MeV u d o proton e n t c a a beam r y g e t

TECs

fringe field region

ν π+ μ+ ⇒ ⇒

6 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Positron tracking

Variable density gas degrader

7 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Detector Array

-4 Al and Precision (<10 ) select variable Ag In z Wire position dE/dx density targets gas for μ+ degrader in target

trigger scintilla tor R. Henderson et al., Nucl. Instr. and Meth. A548 (2005) 306-335 8 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Muon Decay Spectrum Acceptance

Pμ

9 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Spectrum Fit Procedure

•Decay spectrum linear in ∂ N ρ, P ξ, P ξδ. N Data = N MC  +  μ μ ∂ • Derivative spectra are simulated. •Offset added to parameters to blind them. •Consistency is tested and systematics determined before unblinding. ∂ N ∂ N •Spectrum edge is fit in      angle slices to the P + P ∂ P  ∂ P  simulation. A momentum – calibrated spectrum is regenerated and fit.

α = {ρ, 10 Artδ, Olin: ξ} PANIC2011 TRIUMF Weak Interaction Symmetry Test Spectrum fit quality

 All data sets: 11x109 events, 0.55x109 in (p,cosµ) fiducial  Simulation sets: 2.7 times data statistics 11 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Fringe field, solenoid entrance

Position

Angle

2 m

12 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Fringe field, solenoid entrance

Position

Angle

2 m

13 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Measured average muon positions

nominal beam  The average muon beam trajectory inside the detector is sensitive to the muon transverse momentum . Identify changes in muon beam properties between TEC measurements  Comparisons between nominal and mis-steered beams mis-steered beam . Observed muon beam trajectories within the detector . Difference in the decay asymmetry in data vs that predicted by the simulation.  Resulting uncertainties are asymmetric. 14 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Improved drift chamber calibration

Equal-time contours Chamber position resolution

 Direct determination of the effective distance vs time relation.  Accounts for small plane-to-plane fabrication differences.  Improved momentum resolution (near the endpoint) . Was ~ 69 keV/sin(θ) in simulation and ~ 74 keV/sin(θ) in data. . Now ~ 58 keV/sin(θ) in both. A. Grossheim et al., Nucl. Instrum. Methods A 623, 954 (2010).15 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Bremsstrahlung

Normal muon stopping target

Leading systematic for ρ and δ. Separately determined from upstream stops and broken decay tracks. Larger in Ag target. Both consistent with GEANT3 simulation at 2.5% level. 16 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Consistency of data sets

) Ag Al

4 110

-

0 100 Key:

1

( 90 68 – zstop shifted

Δρ

m s 80 70 – B = 1.96 T

o

r

r e 70 71 – B = 2.04 T

f

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t a 70 74 – Nominal

a r 60

d a 75 – Nominal

p Δδ 50

f 40 76 – Mis-steered

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e i 20

c t material

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ΔP ξ μ

D n 60 91 – Low momentum

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d 40 92 – Low momentum

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i 68 70 71 72 74 75 76 83 84 86 87 91 92 93 93 – Low momentum

h 14 data sets for ρ and δ, χ2 of 14.0 and 17.7 respectively 2 9 data sets used for Pμξ, χ = 9.7 statistical uncertainties only, after corrections

17 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Decay parameter results

ρ = 0.74977 ± 0.00012 (stat) ± 0.00023 (syst) (<1σ from SM, -1.4x10-4 from blind)

δ = 0.75049 ± 0.00021 (stat) ± 0.00027 (syst) (+1.4σ from SM, -2.3x10-4 from blind)

+0.00165 π P μξ = 1.00084 ± 0.00029 (stat)-0.00063 (syst) (+1.2σ from SM, same as blind)

Pπ ξδ/ρ > 0.99909 (90%CL) μ from global analysis

R. Bayes et al., Phys. Rev. Lett. 106, 041804 (2011). J. Bueno et al., Phys. Rev.D (August). Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test 18 Decay parameter results

ρ = 0.74977 ± 0.00012 (stat) ± 0.00023 (syst) -4 Implies(<1σ from a negative SM, -1.4 decayx10 fromrate! blind) Triggered a full analysis review. Identifiedδ = 0.75049 sensitivity ± 0.00021 to (stat) stop ± position,0.00027 (syst)target-dependent systematics.(+1.4σ from SM, -2.3x10-4 from blind) Final results are slightly modified.

+0.00165 π P μξ = 1.00084 ± 0.00029 (stat)-0.00063 (syst) (+1.2σ from SM, same as blind)

Pπ ξδ/ρ > 0.99909 (90%CL) μ from global analysis

Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test 19 Implications for the Weak Couplings

 The final TWIST results have been included in a new muon decay global analysis together with all previous muon decay parameter measurements  Find significantly tighter 90% c.l. upper limits on the coupling of right-handed muons to right- or left-handed electrons: . S | g RR| < 0.031 Factor of ~2 smaller than V . | g RR| < 0.015 pre-TWIST values . | gS | < 0.041 LR Factor of ~3 smaller than . | gV | < 0.018 LR pre-TWIST values T . | g LR| < 0.012

μ -4  New limit on right-handed muon couplings: Q R < 5.8x10 (90% c.l.) – Factor of ~9 smaller than pre-TWIST value  Uncertainty for η reduced by 1/3 compared to 2005 global analysis – η = -0.0033 ± 0.0046

. Important for the determination of GF 20 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Left-Right Symmetric limit comparison

“manifest” LRS, 90%CL generalized or non-manifest LRS, 90%CL

2 2 m2 > 592 GeV/c (gL/gR)m2 > 578 GeV/c

-0.020 < ζ < +0.017 -0.020 < (gR/gL)ζ < +0.020  Other W’ direct search mass limits . ATLAS: >1.49 TeV/c2, 95%CL (LLWI11)  Other limits on mixing angle ζ . CMS: >1.58 TeV/c2, 95%CL (LLWI11) . Hardy and Towner: <0.0005 (MLRS), <0.04 . CMS: >1.36 TeV/c2, 95%CL (2011) (generalized) 2 . CDF: >1.12 TeV/c , 95%CL (2011) . K decay: <0.004 (MLRS) . D0: >1.0 TeV/c2, 95%CL (2008)

Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test 21 Inclusive Limits on μ→e X0

 Limits when X0 is undetectable. Massive X0 Decays  First search for two-body decays with possible asymmetries.  Order of magnitude improvement for massive isotropic decays.  Peak structures at the endpoint are produced by small momentum scale mismatches, so this sets the systematic limit. Decay Massless  Jodidio more sensitive to Anisotropy B 90% CL isotropic signal but completely -6 insensitive to asymmetric decay. A= -1 52x10 -6  Limits on 3-body X0 decays are A=0 20x10 obtained from decay parameter A=+1 10x10-6 values. -6 Jodidio A=0 2.6x1022 Art Olin: PANIC2011 TRIUMF Weak Interaction SymmetryPRD34,1967(1986) Test Limits for heavy sterile neutrinos

 Muon decay spectrum shape places limits on heavy neutrino mass and mixing in a mass region inaccessible with π or K decays.

R.R. Schrock, Phys. Rev. D 24, 1275 (1981).

P. Kalyniak and J.N. Ng, Phys. Rev. D 25, 1305 (1982).

M.S. Dixit et al., Phys. Rev. D 27, 2216 (1983).

Heavy sterile neutrino model

Art Olin: PANIC2011 TRIUMF Weak InteractionS.N. Symmetry Gninenko, Test arXiv:1009.5536v3, Jan 2011 LLWI2011, Feb 20−26 2011 23 G.M. Marshall, Muon Decay Parameters fromTWIST Summary and Outlook

TWIST has significantly improved the measurements of ρ, δ, and Pπ ξ. These results μ are in agreement with the Standard Model. The value of Pπ ξδ/ρ >1 disagrees even with μ the general weak interaction. We have reexamined all of our key assumptions and repeated the analysis, leading only to small changes. Constraints on the weak couplings and LRS models are significantly improved. New inclusive bounds on μ→e X0 μ-Al decay spectrum – not presented.

24 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test TWIST Collaboration

Kurchatov Institute TRIUMF Alberta Ryan Bayes § Vladimir Selivanov Andrei Gaponenko Yuri Davydov Texas A&M Peter Kitching Jaap Doornbos Robert MacDonald Wayne Faszer Carl Gagliardi Nate Rodning Makoto Fujiwara Jim Musser David Gill British Columbia Alexander Grossheim Bob Tribble James Bueno Peter Gumplinger Mike Hasinoff Anthony Hillairet § Valparaiso Blair Jamieson Robert Henderson Don Koetke Jingliang Hu Shirvel Stanislaus Montréal Glen Marshall Pierre Depommier Dick Mischke Mina Nozar Regina Konstantin Olchanski Ted Mathie Art Olin § Roman Tacik Robert Openshaw Graduated student Jean-Michel Poutissou § also U Vic Renée Poutissou Grant Sheffer £ also Saskatchewan Bill Shin £ Supported by NSERC, DOE, RMF, Westgrid 25 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Extras

26 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Early  Decay Measurements

27 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Uncertainties in ρ and δ

Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test 28 P ξ uncertainties μ

Uncertainties P ξ (x10-4) μ Depolarization in fringe field +15.8, -4.0 Depolarization in stopping material 3.2 Background muons 1.0 Depolarization in production target 0.3 Chamber response 2.3 Resolution 1.5 Momentum calibration 1.5 External uncertainties 1.2 Positron interactions 0.7 Beam stability 0.3 Spectrometer alignment 0.2 Systematics in quadrature +16.5, -6.2 Statistical uncertainty 3.5

Total uncertainty +16.9, -7.2 29 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Depolarization in target material

- Estimate of relaxation is included in simulation;small 2.0 correction is made to polarization parameter. 1.5 - μSR experiment establishes no fast relaxation. 1.0 - Statistical uncertainty in ¸ is included in decay 0.5 Aluminum Silver parameter systematic uncertainty. 0.0 Previous μSR New μSR New TWIST (E1111) TWIST (E1111) TWIST 30 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Ensuring muons stop in the metal target

stops in gas foil wiresStopping target (Ag or Al)

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PC5 signal amplitude  Muons that stop in gas can depolarize through muonium formation PC5 PC6 PC7  Use muon energy depositions near the stopping target to reject those that stop in gas 31 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Energy Resolution

Energy calibration procedure matches the position of data and simulation edges MC Ag Data Resolution 59.5±0.2 keV/c MC Resolution 59.5±0.2 keV/c Data Response func diff 1.2 keV/c

Al Data Resolution 58.5±0.2 keV/c MC Resolution 58.4±0.2 keV/c Response func diff 2.0 keV/c 2004 analysis Data Resolution 65 keV/c MC resolution 60 keV/c

32 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Reconstruction Inefficiency

33 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Left-Right Symmetric Models

 Weak eigenstates in terms of mass eigenstates and mixing angle:

 Assume possible differences in left and right couplings and CKM character. Use notation:

 Then, for muon decay, the Michel parameters are modified:

R L ω . “manifest” LRS assumes gR = gL, V = V , = 0 (no CP violation). R L . “pseudo-manifest” LRS allows CP violation, but V = (V )* and gR = gL. . LRS “non-manifest” or generalized LRS makes no such assumptions.

 Many experiments must make assumptions about LRS models! 34 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test

¹ µ g µ g P = 1 ¡ 2t2 ¡ 2³ 2 ¡ 4t ³ 2 cos(®+ ! ) W L = W 1 cos ³ + W 2 sin ³ ; W R = e (¡ W 1 sin ³ + W 2 cos ³ ) ½= 4(1 ¡ 2³ g ); » = 1 ¡ 2(t +i ! ³ g); 3 2 2 2

L 2 u d L g2 m 2 µ jV L j g g2 t = R 1 ; t = t u d ; ³ 2 = R ³ 2 g2 m 2 jV R j g2 BSM Physics

 Right-Left Symmetric Models . Spontaneous breaking of parity . Herczeg, Phys Rev. D34,3449 (1986).  R-Parity Violating Supersymmetric Models . Profumo et al, Phys. Rev. D75, 075017 (2007).  Lepton Flavour Violating 2-body decays μ⇨ e X0 . Strong limits exist when X0 or it's products are detectable . μ decay limits interesting when X0 is not detectable. . Hirsch et al, Phys Rev D 79,055023 (2009)

35 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Estimating field component effects

Estimate of error

36 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Coupling constants and Michel parameters  The Michel parameters are bilinear combinations of the coupling constants:

37 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Limits on LRS parameters

Observabl m (GeV/c ) | ζ | e 2 2 + -

m(KL – KS) >1600 reach (P)MLRS

Direct >1000 (D0) clear (P)MLRS WR >652 (CDF) signal decay model CKMsearches (P)MLRS <10-3 sensitivity ν unitarity heavy R both (P)MLRS β decay >310 <0.040 ν parameters light R µ decay model >420 <0.022 light ν ( TWIST independenc R ) e 38 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Selecting muons in metal target foil wires stops in gas

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PC5 signal amplitude

Place cut on 2-d distribution so that PC5 PC6 <0.5% of “stops in gas” contaminate “stops in target” region (zone 1). 39 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Electron spectrum from ¹-Al

One week of data with μ- beam Precise measure of muonic aluminum (μ-Al) decay in orbit (DIO) changes phase space, initial KE competes with nuclear muon capture comparison with calculation consistency above 53 MeV, but limited to p<75 MeV (below μe conversion signal) mismatch near peak and excess events at lower energies higher order corrections required?

A. Grossheim et al., Phys. Rev. D 80, 052012 (2009) 40 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Radiative corrections

Arbuzov et al., Phys. Rev. D66 (2002) 93003. Arbuzov et al., Phys. Rev. D65 (2002) 113006. Arbuzov et al., JHEP03:063(2003). Anastasiou et al, JHEP0709:014, (2007).

Included in TWIST simulation Full O(α) radiative corrections with exact electron mass dependence. Leading and next-to-leading large log terms of O(α2). Corrections for soft pairs, virtual pairs, and an ad-hoc exponentiation. Uncertainty is non-log O(α2) term recently calculated. 41 Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test Decay parameter results

ρ = 0.74977 ± 0.00012 (stat) ± 0.00023 (syst) (<1σ from SM, -1.4x10-4 from blind)

δ = 0.75049 ± 0.00021 (stat) ± 0.00027 (syst) (+1.4σ from SM, -2.3x10-4 from blind)

+0.00165 π P μξ = 1.00084 ± 0.00029 (stat)-0.00063 (syst) (+1.2σ from SM, same as blind)

Jodidio Pπ ξδ/ρ > 0.99909 (90%CL) μ 90% CL from global analysis

R. Bayes et al., Phys. Rev. Lett. 106, 041804 (2011). J. Bueno et al., Phys. Rev.D (August). Art Olin: PANIC2011 TRIUMF Weak Interaction Symmetry Test 42