± 1 10 part-per-million precision

Size: px

Start display at page:

Download "± 1 10 part-per-million precision"

Theresa Lynne Parrish
5 years ago
Views:

1 Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant to Part-per-Million Precision David Hertzog University of Washington τ μ ± 1 10 part-per-million precision Motivation MuLan: τ μ + MuCap: m - p capture Plus: Final results on: Nucleon s Weak Induced Pseudoscalar Coupling Results & Summary Seminar: Cornell 2014

Positive and Negative Muon Lifetimes Free muon decay is a pure weak process

if free, or form atomic-bound muonium with a lifetime shift expected at the ~ ppb

muonic atoms and either decay or, undergo nuclear capture.

2 Positive and Negative Muon Lifetimes Free muon decay is a pure weak process determines G m, often called G F Muons stopped in matter: Positive muons decay as if free, or form atomic-bound muonium with a lifetime shift expected at the ~ ppb level e - most precise Fermi Constant m + Negative muons form 1-electron-like muonic atoms and either decay or, undergo nuclear capture. The decay and capture rates add; lifetime is shorter 1 τ = Λ total = Λ decay + Λ capture Z m- Extract physics here

τ μ + Positive muon lifetime motivation:

wellmeasured input parameters G F a M Z 9 ppm 0.

6 ppm Hanneke, Fogwell, Gabrielse PRL 100,

427:257-454,2006 MuLan Collaboration PRL 106,

3 τ μ + Positive muon lifetime motivation: Predictive power of the SM depends on wellmeasured input parameters G F a M Z 9 ppm 0.37 ppb 23 ppm 0.6 ppm Hanneke, Fogwell, Gabrielse PRL 100, (2008) Phys.Rept.427: ,2006 MuLan Collaboration PRL 106, (2011) This work G F = (7) x 10-5 GeV -2 α 1 = ± M Z = ± GeV

The Fermi constant is related to the electroweak gauge coupling g by

muon decay is a contact interaction where Dq is phase space and both

and Stuart completed full 2-loop QED corrections reducing the

4 The Fermi constant is related to the electroweak gauge coupling g by Contains all weak interaction loop corrections In the Fermi theory, muon decay is a contact interaction where Dq is phase space and both QED and hadronic and radiative corrections q In 1999, van Ritbergen and Stuart completed full 2-loop QED corrections reducing the uncertainty in G F from theory to < 0.3 ppm (it was the dominant error before)

5 τ μ + Example: connection from t m to sin 2 θ W Momentum transfer q 2 = (p μ p νμ ) 2 = (p e + p νe ) 2 < m m 2 much smaller than M W 2 Thus, W propagator shrinks to a point and can be well approximated through a local four-fermion interaction, MuLan: G F = ( ± ) 10 5 GeV 2. (there are further quantum corrections here not included)

The push pull of experiment and theory Lifetime now largest uncertainty leads to 2 new experiments launched: MuLan & FAST Both @ PSI, but very

6 The push pull of experiment and theory Lifetime now largest uncertainty leads to 2 new experiments launched: MuLan & FAST PSI, but very different techniques Both aimed at ppm level G F determinations Both published intermediate results on small data samples Meanwhile, more theory updates

7 log(counts) τ μ + Further motivation: Take difference between t m + and t m - in hydrogen to infer singlet capture rate L S τ μ m - + p n + m D - t 0.16% m + -m 1.0 ppm MuLan ~15 ppm MuCap L S L m μ μ L + - m 1 t m - time 1 t m + g P

8 World avg dt m /t m is 18 ppm, but is it right? Lessons from History m+ Neutron Lifetime Precision vs Accuracy 10 ±1 ppm? Goal of MuLan is 1 ppm.

9 The Experiments Generic design considerations MuLan MuCap τ μ + τ μ

10 PSI: a 1.3 MW facility with many secondary muon beams. Example: pe3 beamline at PSI MuSun MuCap MEG MuLan PiBeta + new p/m area Lamb shift below

τ μ + Design Considerations counts and systematic control τ μ Need: 10 12 m + decays

2 ma protons @ 590 MeV pe3 low-energy muon beamline Time structured custom Kicker

11 τ μ + Design Considerations counts and systematic control τ μ Need: m + decays (1 ppm) & m - decays (10 ppm) PSI: 2.2 ma 590 MeV pe3 low-energy muon beamline Time structured custom Kicker MuLan: ~10 7 m+ /s Beam-on / Beam-off periodic cycles Multiple decays per cycle MuCap: ~10 5 m - /s Muon-on-demand 1 measurement at a time

12 Generic Design Considerations counts and systematic control τ μ + Gain stability Pileup e 2t/τ Spin (msr) Symmetry; Dephasing Stability of Detector early-to-late Minimize precession amplitude Maximize precession frequency Background: small and constant τ μ Avoid impurities Fiducial volume Interference of m & e tracks Capture rate Z 4 must stop in target μ a TPC specific effect e

tile pairs Measurement Period Fill Period time Extinction ~ 1000

13 Number (log scale) τ μ + The MuLan experimental concept Real data Kicker On 450 MHz WaveForm Digitization 170 Inner/Outer tile pairs Measurement Period Fill Period time Extinction ~ 1000 Accumulation Measuring Period Detector has symmetric design around stops

14 Stopping Target 14

15 Stopping Target

τ μ + Stopping targets selected to control spin AK-3 Internal B

arrival times Quartz Form muonium 90% Precession period few ns

16 τ μ + Stopping targets selected to control spin AK-3 Internal B ~ 0.5 T Quartz + Halbach Array Quartz Start Accumulation P 0 Start Measurement AK-3* Internal 0.5 T transverse field Precess rapidly Dephase owing to different arrival times Quartz Form muonium 90% Precession period few ns Control 10% free muon spins by symmetry of detector *Arnokrome-3 (~28% chromium, ~8% cobalt, ~64% iron)

MuLan collected two datasets, each containing 10 12 muon decays

data sets Different blinded clock frequencies used Revealed only

17 MuLan collected two datasets, each containing muon decays Ferromagnetic Target, 2006 Quartz Target, 2007 Two (very different) data sets Different blinded clock frequencies used Revealed only after all analyses of both data sets completed Most systematic errors are common

18 The detector is composed of 20 hexagon and 10 pentagon sections, forming a truncated icosahedron. Each section contains either 6 or 5 tile elements a Each element is made from two independent scintillator tiles with light guides and photomultiplier tubes.

19 170 scintillator tile pairs readout using 450 MHz waveform digitizers. 2 Analog Pulses Waveform Digitizers x2 1 clock tick = 2.2 ns

20 Raw waveforms for 170 inner and outer scintillators are fit using calibrated pulse templates >2 x decays 130 TB data at NCSA Normal Pulse artificial deadtimes Two pulses close together A difficult fit

21 τ μ + Leading order pileup is a ~5x10-4 effect, yet Fill i Statistically reconstruct pileup time distribution Fit corrected distribution Fill i+1 Normal Time Distribution Pileup Time Distribution This is only the 1 st order effect

22 τ μ + Pileup to sub-ppm requires higher-order terms Pileup terms at different orders R (ppm) 1 ppm 150 ns deadtime range Artificial Deadtime (ct) Time ns

23 The pileup corrections were tested with Monte-Carlo. Monte-Carlo Simulation, events agrees with truth to < 0.2 ppm 1.19 ppm statistical uncertainty

24 24

25 Gain variation vs. time is derived from the stability of the peak (MPV) of the fit to pulse distribution Real δn N 4 Artificial Test threshold 25

26 Gain variation vs. time is derived from the stability of the peak (MPV) of the fit to pulse distribution If MPV moves, implies greater or fewer hits will be over threshold δn N ms Gain(t) is PMT type dependent. Carefully studied and reduced to 0.25 ppm uncertainty. Gain correction gives a 0.5 ppm shift in result vs uncorrected 26

27 0 9 ms τ μ + MuLan fit of 30,000 AK-3 pileup-corrected runs ppm t m + D secret 22 ms Relative t (ppm) tau vs fit start time Red band is the set-subset allowed variance

28 τ μ + Varying the fit start and stop time shows good selfconsistency. R c 2 /NDF R c 2 /NDF

Installed Quartz Halbach Array 90% muonium formation Test of

free Rapid spin precession not observable by us 10% free

29 Crystal quartz is really different. This was meant to challenge the otherwise easy AK3 target Installed Quartz Halbach Array 90% muonium formation Test of lifetime in muonium vs. free Rapid spin precession not observable by us 10% free muons Precession noticeable and small longitudinal polarization exists Creates analysis challenges! Magnet ring shadows part of detector

30 msr relaxation results in a reduction of the polarization magnitude. T1 is independent of magnetic field. T2 is from an inhomogeneous field.

31 Lifetime Opposite pairs summed τ μ + A small asymmetry exists front / back owing to residual longitudinal polarization 85 Opposite Pairs All 170 Detectors m Front Back front-back folded

32 τ μ + Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The msr remnants vanish. Start-time scan

33 τ μ + MuLan Systematics and Final Numbers ppm units Effect Comment Kicker extinction stability Voltage measurements of plates Upstream muon stops Upper limit from measurements Overall gain stability: MPV vs time in fill; includes: Timing stability Laser with external reference ctr. Pileup correction Extrapolation to zero ADT Residual polarization Long relax; quartz spin cancelation Clock stability Calibration and measurement Total Systematic Highly correlated for 2006/2007 Total Statistical t(r06) = ± 2.5 ± 0.9 ps t(r07) = ± 3.7 ± 0.9 ps AK-3 Quartz Dt(R07 R06) = 1.3 ps Both measurements were separately blinded

34 MuLan Final Results on t m : MuLan FAST PSI The most precise particle or nuclear or atomic lifetime ever measured t(mulan) = ± 2.2 ps (1.0 ppm) G F precision improved by factor of 30 compared to 1999 PDG G F (MuLan) = (6) x 10-5 GeV -2 (0.5 ppm) PRL 106, (2011) Phys. Rev. D 87, (2013) DOE Comparative Review, 25 June

35 G F & t m precision has improved by ~4 orders of magnitude over 60 years. Achieved!

36 Some recent Press

37 Muon Capture on the Proton The Black Sheep of Form Factors T. Hemmert quark level u m g m (1- g 5 ) W d g P g P nucleon level m q W q relevant degrees of freedom? DL L S S DgP 1% 6.1% g P

38 Muon Capture on the proton and Axial Nucleon Structure Capture rate L S : m - + p n+ m Lorentz, T invariance gives these possibilities How does L S depend on precision of the form factors? Well known L LS L L L L S S S S S Dg V Dg Dg A M 0.024% 0.01% 0.38% DL L S S DgP 1% 6.1% g The least well known is g P P

39 Pseudoscalar form factor g P τ μ N ¹ 1 g - g A (0)m N m m r 2 P (q 2 ) = - 2m Nm m g A (0) f p q 2 -m 2 A ¼p 3 PCAC pole term (Adler, Dothan, Wolfenstein) m p NLO (ChPT) Bernard, Kaiser, Meissner PR D50, 6899 (1994) p g P = 8.26 ± 0.23 g pnn n L S = ± 4.6 s -1 (0.65%) ChPT based on the spontaneous symmetry breaking QCD prediction via 2-3% precision level Basic test of chiral symmetries and low-energy QCD Recent review: Kammel, P. and Kubodera, K., Annu. Rev. Nucl. Part. Sci. 60 (2010), 327

40 The experimental determinations of g P prior to MuCap were far less precise τ μ Ordinary Muon Capture (OMC) Radiative LH 2 LH 2 LH 2 LH 2 GH 2 GH 2 LH 2 LH 2 Liquid H 2 target Gas (low density) H 2 target

41 The MuCap Experimental Concept Stop in pure hydrogen (gas) Gas impurities < 10 ppb Isotopic impurity < 6 ppb Image muon stop with TPC Measure the disappearance rate (effective lifetime) τ μ m - E e - m - p

42 Muon kinetics τ μ f: Hydrogen density, (LH 2 : f=1) L T ~ 12s -1 μ- p pμ < 100ns fl OF ppμ ortho (J=1) L OM ~ ¾ L S pμ l OP L S ~ 700s -1 fl PF ppμ L PM ~ ¼ L S para (J=0)

43 Capture from mp singlet is in competition with capture from ppm molecular states: depends on density and time τ μ fl OF ppμ ortho (J=1) L OM ~ 540 s -1 RMC pμ L S ~ 700s -1 l OP fl PF L PM ~ 210 s -1 Liquid hydrogen experiments Molecular-states dominate ppμ para (J=0) MuCap conditions Singlet-state dominates

44 MuCap Negative Muon Lifetime Spectra τ μ Typical fit normalized residuals

45 Start- and stop-time-scans τ μ Rate versus run duration Data run number (~3 minutes per run)

46 Fit Rate (s -1 ) The disappearance rate is independent of azimuth (non trivial since TPC is asymmetric vertically owing to drift direction) τ μ Beam View of MuCap Detector Azimuthal Element 4/6/2012

47 Precise and unambiguous MuCap result solves longstanding puzzle Verifies Basic Prediction of Low-Energy QCD τ μ Phys.Rev.Lett. 110 (2013) g P (MuCap) = 8.06 ± 0.55 g P (theory) = 8.26 ± 0.23

48 τ μ + Free m+ Effective* m- Difference: Compare Lifetimes! (If you believe cpt more than CPT ) t MuLan = ± 2.2 ps t MuCap = τ + τ +/- 42 ps τ avg = 7 ± 19 ppm τ μ *Important assumptions Assume cpt prediction is exact Correct for mp atomic shift (easy) 4/30/2012 Correct for impurity distortion (expt. errors are included) 48

49 Summary MuLan has finished and published 1.0 ppm final error achieved, as proposed The most precise particle or nuclear lifetime ever measured Most precise Fermi constant Modest check of muonium versus free muon MuCap has finished and published First unambiguous determination of g P Excellent agreement with theory Method paves way for future MuSun expt on md capture MuCap MuLan

50 MuLan at PSI

51 Backups

52 MuSun: muon capture on the deuteron Goal: Measure rate L d from md( ) to < 1.5 % Several fundamental astrophysics processes depend on weak interaction in deuterium Basic solar fusion: p + p d + e + + Sudbury Neutrino e + d p + p + e - (CC) x + d p + n + x (NC) EFT L 1A, d R Experiment In Progress at PSI DOE Comparative Review, 25 June

53 MuSun Detector System Electron Tracker Liquid Ne Circulation CryoTPC TPC Digitizer Electronics Impurity filtering DOE Comparative Review, 25 June

54 CENPA and MuSun Cryo-PreAmps, Local TPC optimization, MWPC support Pictures from PSI and from our UW MuSun Lab setup. Cryo PreAmp design and construction Summer PSI Summer PSI 3D local design work UW MuSun Prep Lab DOE Comparative Review, 25 June 2013 Kammel et al 54

0 +/- 0.2 MHz Checked for consistency throughout the run.

55 The clock was provided by an Agilent E4400B Signal Generator, which was stable during the run and found to be accurate to ppm. Agilent E4400 Function Generator f f = /- 0.2 MHz Checked for consistency throughout the run. Compared to Quartzlock A10- R rubidium frequency standard. Compared to calibrated frequency counter Average difference = ppm

56 EW Phenomenology In the gauge and scalar sectors, the SM Lagrangian contains only four parameters: g, g, μ 2 and h. One could trade them by α, θ W, M W and M H. Alternatively, we can choose as free parameters: G F = ( ± ) 10 5 GeV 2 α 1 = ± M Z = ( ± ) GeV and the Higgs mass M H. Uses the three most precise experimental determinations to fix the interaction. The Standard Model of Electroweak Interactions A. Pich (València) arxiv: v1 [hep-ph] 2 Jan 2012

57 MuCap systematic corrections, uncertainties and final capture rate Systematic errors Run 2006 Run 2007 Comment L (s -1 ) dl (s -1 ) L (s -1 ) dl(s -1 ) High-Z impurities mp scatter * * * = prelim. mp diffusion Fiducial volume cut Entrance counter inefficiencies Choice of electron detector def. 1.8* 1.8* * =prelim. Total = correlated L 0 (06) = 455,857.3 ± 7.7 ± 5.2 s -1 L 0 (07) = 455,853.1 ± 8.3 ± 3.9 s -1 Measured disappearance rates Apply mp atomic correction Subtract m+ decay rate: L m+ = ± 0.46 s % increase in the uncertainty because of ppm correction τ μ L S (06) = ± 8.0 ± 5.7 s -1 L S (07) = ± 8.6 ± 4.5 s -1 DL S (06 07) = 4.4 s -1

58 Gas impurities are monitored directly. Correction is based on measurement. Calibration done at high concentation τ μ Production Data L Calibration Data (nitrogen added to production gas) Extrapolated Result 0 Observed capture yield Y Z Imp. Capture: m - Z (Z-1) n 2004 run: c N < 7 ppb, c H2O ~30 ppb 2006 / 2007 runs: c N < 7 ppb, c H2O ~10 ppb

59 External corrections to L τ μ MuCap Λ obs disappearance = Λ μ decay + Λ S + Λ ppμ MuLan Λ free μ + + Λ μp molecular formation Atomic bound state effect L S (MuCap) = ± 5.4 stat ± 5.0 syst s -1 * Small revision of molecular correction might affect L S < 0.5 s -1 and syst. error L S (theory) = ± 3.5 ± 3 s -1

60 τ μ + Quartz visible msr. Fit each detector for an effective lifetime. Would be correct, except for remnant longitudinal polarization relaxation. Difference between Top of Ball and Bottom of Ball to Sum, vs time-in-fill Illustration of free muon precession in top/bottom detector differences

61 τ μ + Longitudinal polarization distorts result in predictable manner depending on location. The ensemble of lifetimes is fit to obtain the actual lifetime. (Method robust in MC studies) Relative effective lifetime (ppm) Magnet-right data (+ blind offset)

Blind Measurements and Precision Muon Physics. David Hertzog University of Washington

Blind Measurements and Precision Muon Physics David Hertzog University of Washington A word about the Evolution of Precision Time "our future discoveries must be looked for in the sixth place of decimals."