ν ν Relative Intensity 53 MeV Electron energy

In a muon's lifetime: From Fermi's constant to calibrating the sun Peter Winter University of Illinois at Urbana-Champaign g P L 1A / d R τ µ

The muon Mass 207 m e Lifetime ~2.2 µs Main decay µ e ν e ν µ Parity violating decay Relative Intensity µ + e + ν ν e µ 53 MeV Electron energy L. Michel

Muon physics efforts worldwide Lifetime Fermi constant 2 precision experiments: MuLan & FAST Decay parameters Michel TWIST ρ, δ, η, P µ ξ Transverse polarization (η) PSI Capture MuCap: g P, pseudoscalar coupling MuSun: basic EW interaction in 2N system Anomalous magnetic moment (g-2) New g-2finale experiment in planning Lepton Flavor Violation µ eγ MEG at PSI taking data now µe conversion µa ea Mu2e at FNAL new highpriority project EDM E821 PRD in prep ~10-21 e. cm Modest efforts toward small dedicated ring at PSI Lorentz / CPT violation tests E821 g-2 PRL 2007; precession vs. sidereal day Muonic Lamb shift in progress (QED) Finite size effects aids to hydrogen Lamb shift effort

Outline Muon Lifetime Analysis (MuLan) Motivation MuLan experiment Main systematics and result Muon capture on the proton (MuCap) Motivation and general overview MuCap experiment Systematics and results Muon capture on the deuteron (MuSun) Motivation and outlook

Three electro-weak input parameters Fine structure constant α / α 0.37 ppm [Gabrielse et al, 2008] Neutral weak boson mass M Z / M Z 23 ppm [LEP EWWG 2005] Fermi constant G F / G F 9 ppm [Giovanetti et al, 1984, Bardin et al., 1984]

Fermi constant G F Implicit to all EW precision physics Uniquely defined by muon decay q PS, QED and hadr. rad.

Brief history of τ µ / G F Before 2007, the best measurements were over 20 years old, and until 1999 G F was theory limited. G. Bardin et al., Phys. Lett. B 137, 135 (1984) K. Giovanetti et al., Phys. Rev. D 29, 343 (1984)

Extraction of G F no longer theory limited δg G F F = 1 2 2 δτ τ + δm 5 m µ µ 2 + δ q q 2 Mid 1999: Future: 90s: 17 90.5 ppm ppm 18 1 ppm 0.09 ppm <0.3 30 ppm Lifetime error is the limit 2 loop QED corrections T. van Ritbergen and R. G. Stuart, Nucl. Phys. B564, 343 (2000)

The facility: πe3 beamline at PSI http://www.psi.ch

The Kicker Kicker Design at TRIUMF MOSFET based 50 ns switching time

The Kicker +12.5 0 kv kv -12.5 0 kv kv

Other elements Separator Quadrupoles Separator: Suppression of e + or e - in beam Detector

MuLan experiment Polarized surface muon beam (28.8 MeV/c) Electrostatic beam kicker +12.5 kv -12.5 kv Thin stopping target 500 Mhz waveform digitization Symmetric, highly segmented detector MHTDC (2004) Inner/Outer tile pair

a tile... a house... the ball...

Main systematics Any early-to-late effect: Instrumental issues Pileup pulses Non-flat background PMT gain change... Physics issues Polarization Longitudinal relaxation...

Pileup corrected from the data Measured τ vs. Deadtime A MuLan detector tile pair Raw Spectrum Pileup pulses measurably distort the lifetime Shadowed and pileup pulses have the same probability distribution! Pileup Corrected Normal Time Distribution Pulse Resolving Time time Shadow window Pileup Time Distribution

Polarization µsr in 50G

How do we control polarization? Point-like symmetry + large solid angle coverage reduce effects Polarization destroying ferromagn. target AK3 in 2006 Polarization preserving quartz target in 2007 with external field Reduce errant muon stops with vacuum beam corridor to target

Error contributions (2004) Statistics: 1.8 x 10 10 (9.6 ppm) Clearly statistics limited

New world average (16 ppm) 10 ±1 ppm (11 ppm) G F = 1.166367(5) x 10-5 GeV -2 (4.1 ppm)

Summary MuLan First result with 11ppm published 2007 Data analysis of two sets with each 10 12 decays on its way Plan to publish 1ppm result end of 2009

The nucleon

Nucleon form factors µ - µ - + p n + ν ν q 2 = -0.88m 2 µ p n M ~ G F V ud ψ ν γ α (1-γ 5 )ψ µ ψ n (V α -A α )ψ p

Nucleon form factors M ~ G F V ud ψ ν γ α (1-γ 5 )ψ µ ψ n (V α -A α )ψ p V α = g V (q 2 ) γ α + i g αβ M (q 2 ) σ q β /2M N + g S (q 2 ) q α /m µ Conserved Vector Current and isospin symmetry g S (q 2 ) = 0 g V, g M : strong program JLab, Mainz,...

Nucleon form factors M ~ G F V ud ψ ν γ α (1-γ 5 )ψ µ ψ n (V α -A α )ψ p A α = g A (q 2 ) γ α γ 5 + i g αβ T (q 2 ) σ q β /2M N γ 5 + g P (q 2 ) q α /m µ γ 5 Second class current suppressed by isospin g T (q 2 ) = 0 g A (q 2 ) measured in neutron decay

Pseudoscalar form factor g P A α = g A (q 2 ) γ α γ 5 + g P (q 2 ) q α /m µ γ 5 µ ν Dominant diagram ~ -f π g πnn q α γ 5 / (q 2 -m π2 ) f π W π p g πnn n PCAC: µ A µ = 0 for m π 0

Pseudoscalar form factor g P N ¹ 1 g - g A (0)m N m µ r 2 P (q 2 ) = - 2m Nm µ g A (0) q 2 -m 2 A ¼π 3 PCAC pole term (Adler, Dothan, Wolfenstein) g P = (8.74 ± 0.23) - (0.48 µ f π W NLO (ChPT) π ν Bernard, Kaiser, Meissner PR D50, 6899 (1994) g πnn solid QCD prediction via ChPT (2-3% level) NNLO < 1%: N. Kaiser, PRC67 (2003) basic test of QCD symmetries (0.48 ± 0.02) = 8.26 ± 0.23 p Recent reviews: T. Gorringe, H. Fearing, Rev. Mod. Physics 76 (2004) 31 V. Bernard et al., Nucl. Part. Phys. 28 (2002), R1 n

Values of relevant quantities g q 2 =0 q 2 = -0.88m 2 µ g V 1 0.9755(5) from e+p scat. g M 3.71 3.5821(25) from e+p scat. g A 1.2695(29) 1.245(4) n decay, r A from νn (PDG) scat. and π elect.prod. g P 8.3 ± 50% V UD 0.97377(27) 0.97377(27) superallowed 0 + 0 + beta decay

Sensitivity of Λ S δλ S Λ S δg P g P g P 2.4% 13.6% 1.0% 6.1% Λ S [s -1 ] 0.5% 3.8% Contributes 0.45% uncertainty to Λ S theory Λ S x x Λ S from Govaerts, Lucio-Martinez, Nucl.Phys.A678 (2000), 110

Calculation of S 1% Inclusion of radiative corrections later

How to access g P? In principle any process directly involving axial current: - β decay: Not sensitive since g P term ~ q - ν scattering difficult to measure Muon capture most direct source for g P

Experiments: Observed Processes - Ordinary muon capture (OMC): µ - p ν n - BR = ~10-3, 8 exps with 4-15% precision in Λ S - Liquid or gaseous hydrogen target - Neutron counting or "lifetime" method - Radiative muon capture (RMC): µ - p ν n γ - BR = ~10-8 for E γ >60 MeV - Theoretical connection to g P more complicated - 279 ± 25 events (Wright et al., 1998) - µ - 3 He ν 3 H or other nuclei - Pion electroproduction

OMC: Methods to measure Neutron experiments: - Measure outgoing neutrons N N - Requires knowledge of neutron efficiency - Separation of decay γ's from neutrons - Typical experiments 8-13% precision in Λ S Lifetime method: - Λ S = 1/τ - - 1/τ + General requirements: - Good muon stop identification - Avoid Z>1 and deuterium contamination

Muon kinetics φ: Hydrogen density, (LH 2 : φ=1) Λ T ~ 12s -1 pµ µ p φ>0.01 <100ns pµ Λ S ~ 700s -1

Muon kinetics φλ OF ppµ ortho (J=1) Λ OM ~ ¾ Λ S pµ λ OP Λ S ~ 700s -1 φλ PF ppµ Λ PM ~ ¼ Λ S para (J=0) ppµ formation depends on density φ Interpretation requires knowledge of Λ OM, Λ PM and λ OP

φλ OF ppµ ortho (J=1) Λ OM ~ ¾ Λ S pµ λ OP Λ S ~ 700s -1 φλ PF ppµ Λ PM ~ ¼ Λ S φ = 1 (Liquid) para (J=0) φ = 0.01 (~10 bar gas) Rel. Population Rel. Population Time after µp Formation Time after µp Formation

20 Previous results 17.5 15 12.5 g P 10 7.5 µcap precision goal ChPT 5 2.5 exp theory TRIUMF 2005 20 40 60 80 100 120 λ OP (ms -1 ) no overlap theory, OMC & RMC large uncertainty in λ OP g P ± 50%

Requirement of clean target µz Λ Z ~ Λ S Z 4 c Z Λ Z φλ OF ppµ ortho (J=1) Λ OM ~ ¾ Λ S µd c d λ pd pµ λ OP Λ d diffusion Λ S ~ 700s -1 φλ PF ppµ para (J=0) Λ PM ~ ¼ Λ S Isotopically and chemically pure H 2, ideally: c d <1 ppm, c Z <10 ppb

MuCap: General overview Lifetime method: 10 10 µ decays Λ S to 1% precision Low gas density Capture mostly from F=0 Active gas target (TPC) Clean µ stop Ultra pure gas system with in-situ monitoring c Z ~ 10-30 ppb (Z = N 2, H 2 O) Isotopically pure "protium" c d ~ 0.1-2 ppm (deuterium separation)

µ e

Muon-On-Demand Muon entrance counter Target 0 kv µ beam µ 0 kv

Muon-On-Demand kicked Muon entrance counter Fig will be improved Target +12.5 kv µ beam µ DC -12.5 kv ~3 times higher rate Pileup protection for 25 µs

TPC - the active target 10 bar ultra-pure hydrogen, φ = 1.16% 2.0 kv/cm drift field ~ 5.4 kv on 3.5 mm anode half gap bakeable glass/ceramic materials Operation with pure H 2 challenging, R&D @ PNPI, PSI

TPC - the active target µ entrance: lower energy loss µ stop: Bragg peak µ - e - µp E y x z xz projection from anodes and strips zy projection from anodes and drift time xy projection from strips and drift time 3d tracking without material in fiducial volume Clean muon stop definition

The clean µ stop definition strips Connected muon pixels Clear Bragg peak anodes Only muon stops well away from the wall accepted Reject pileup events

Electron detectors Timing from scintillator (esc) Temporal and spatial coincidences with wire chamber planes (epc1 and epc2) Full 3d tracking of electron The impact parameter b is the distance of closest approach of the muon stop and electron track

Drift chamber

Lifetime spectra Normalized residuals

Consistency checks

6 mm Inside TPC Non overlapping TPC volume shells

µ + as reference µsr in 50G Measurement with µ + has identical detector systematics Cross check with world average τ + : ~1ppm precision in the future (MuLan and FAST @ PSI)

What do we have so far? µ lifetime: τ - Consistency checks µ + lifetime: τ + Is that it for Λ S = 1/τ - - 1/τ +? Not yet...... but almost!

Internal corrections to λ - (statistical uncertainty of λ - : 13.7 s -1 )

Continous H 2 CHUPS Ultra-Purification System c N2 N2, c O2 < 10 ppb NIM A578 (2007), 485

Impurity monitoring Imp. Capture: µ Z (Z-1) n ν 2004 run: c N, c O < 7 ppb, c 2006/2007 runs: c N, c < 7 ppb, c H2O ~30 ppb, c O < 7 ppb, c H2O ~10 ppb

Final high-z impurity correction Production Data λ Calibration Data (oxygen added to production gas) Extrapolated Result 0 Observed capture yield Y Z Lifetime deviation is linear with the Z>1 capture yield.

Internal corrections to λ - (statistical uncertainty of λ - : 13.7 s -1 )

µd d diffusion (Monte Carlo) Ramsauer-Townsend minimum in the scattering cross section µd d can diffuse ~10 cm before muon decay, possibly into walls

Deuterium correction Again zero extrapolation procedure Production Data (d-depleted Hydrogen) Calibration Data (Natural Hydrogen) λ from fits to data (f = Nλe -λ t + B) λ Extrapolated Result 0 d Concentration (c d ) This must be determined.

µd: MuCap's unique capability Data: λ versus impact parameter cut On site purification since 2006 c d = 1.49 ± 0.12 ppm AMS, ETH Zurich c d = 1.44 ± 0.15 ppm World Record: c d < 100 ppb

External corrections to λ - molecular formation bound state effect

Here we are... Λ S = 725.0 ± 13.7 stat ± 10.7 10.7 syst s -1 V.A. Andreev et al., Phys. Rev. Lett. 99, 032002 (2007)

MuCap and Λ S calculations Rad. corrections: R = 2.8% A. Czarnecki, W.J. Marciano, A. Sirlin, PRL99, 032003 (2007) Λ S = 725.0 ± 13.7 stat ± 10.7 10.7 syst s -1 V.A. Andreev et al., Phys. Rev. Lett. 99, 032002 (2007)

MuCap and g P g P = 7.3 ± 1.1 First precise and unambigous result

Summary for µ p capture Active hydrogen target for clean muon stop Muon-On-Demand mode for pileup rejection Ultra clean running conditions In-situ high-z capture monitoring First precise result and almost independent of λ OP Final precision of g P /g P = 7% in progress

MuSun: "Calibrating" the sun µ + d n + n + ν model-independent connection via EFT & L 1A Aim: Measure rate Λ d from µd( d( ) to < 1.5 %

Motivation: µ - d n n ν Aim: Measure rate Λ d from µd( d( ) to < 1.5 % Simplest weak interaction in a nucleus allowing for precise theory & experiment Close relation to neutrino/astrophysics Broader Impact on modern nuclear physics EFT relates µd d to strong processes like πd γnn, a nn nn

Axial current reaction (Gamov-Teller 3 S 1 1 S 0 ) Theory One body currents well defined Two body currents not well constrained by theory (short dist.) Methods: Potential model + MEC hybrid EFT (L 1A / d R ) Muon capture soft enough to relate to solar reactions MEC EFT L 1A, d R

Precise experiment needed hybrid EFT Potential Model + MEC consistent ChPT pionless, needs L 1A

µd d kinetics µd µ + t + p µ dµd µ + 3 He + n µd µz µ 3 He + n Λ D n + n + ν

Energy spectrum (from MCF exp.) µn capture

Approved proposal by PSI µd( ) µ 3 He µd( ) time (µs) 1% LD 2 300 K 30K, 5% 10% LD 2 30 K Stage 1: MuCap setup with 1% LD 2 and 300 K Prove excellent energy resol. Understand fusion and impurity events Measure nitrogen transfer rate Run finished end of 2008 Stage 2: Measure Λ D at >5% LD 2 and 30 K Cryo TPC development

Cryo-TPC development Aluminum shell Rear neon collector Be window flange Be window Front neon collector

Cryo-TPC development Cold head Vibration-free support Neon condensor Cryo-TPC Vacuum vessel Neon heat pipe

MuLan: Overall summary First G F update in 23 years 2.5x improvement Factor 10 additional improvement on the way MuCap: First precise g P with clear interpretation Consistent with ChPT expectation, clarifies long-standing puzzle Factor 3 additional improvement on the way MuSun Muon-deuteron capture with 10x higher precision Calibrates basic astrophysics reactions and provides new benchmark in axial 2N reactions

Parts of the MuLan collaboration Parts of the MuCap collaboration Petersburg Nuclear Physics Institute, Gatchina, Russia Paul Scherrer Institute, CH University of California, Berkeley, USA University of Illinois at Urbana-Champaign, USA Université Catholique de Louvain, Belgium University of Kentucky, Lexington, USA Boston University, USA James Madison University, USA Regis University, Colorado, USA

Science and arts belong to the whole world, and before them vanish the barriers of nationality. J. W. von Goethe

EXTRA Slides Non flat background: MuLan - kicker

Phenomenological calculation dw = δ(e p -E n +E µ E ν )d 3 p ν M 2 /4π 2 ¹p p spin dependence Λ S = W F=0 = 690.0 s -1 Λ T = W F=1 = 11.3 s -1

Muon vacuum corridor

The MuCap detector Target Pressure Vessel (Pulled Back) Magnet coil for µ +

Stopping distribution E σ Z = 8 cm σ x = σ y = 3.1 cm

FAST Experiment Fast imaging target of 4x4x200 mm 3 scintillators, PSPMs Trigger: L1 selects π, L2 selects π µ e decay chain Essentially many small decay detectors in parallel Proof-of-principle measurement 16 ppm published 2008, 30 khz L2 One year run in 2008 to obtain 2 ppm τ result (with improved L2)

Connection to Neutrino/Astrophysics Basic solar fusion reaction p + p d + e + + ν Key reactions for Sudbury Neutrino Observatory ν e + d p + p + e - (CC) ν x + d p + n + ν x (NC) Intense theoretical studies, scarce direct data EFT connection to m+d capture via LEC L 1A with Muon L 1A ~ capture 6 fm 3 soft enough to relate to solar reactions

More fit consistency Other fit parameters Target magnetic environment Run-by-run consistency Beam extinction factor Target material Discriminator threshold... and a host of other variables argue for consistency of the global fit.

Cryo-TPC development

Neutrino flux SNO

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