A PART-PER-MILLION MEASUREMENT OF THE POSITIVE MUON LIFETIME AND DETERMINATION OF THE FERMI CONSTANT
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A PART-PER-MILLION MEASUREMENT OF THE POSITIVE MUON LIFETIME AND DETERMINATION OF THE FERMI CONSTANT. David M Webber University of Illinois at Urbana-Champaign (Now University of Wisconsin-Madison) December 9, 2010. Outline. Motivation Experiment Hardware Analysis Pulse Fitting

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David m webber university of illinois at urbana champaign now university of wisconsin madison

A PART-PER-MILLION MEASUREMENT OF THE POSITIVE MUON LIFETIME AND DETERMINATION OF THE FERMI CONSTANT

David M Webber

University of Illinois at Urbana-Champaign

(Now University of Wisconsin-Madison)

December 9, 2010


Outline
Outline AND DETERMINATION OF THE FERMI CONSTANT

  • Motivation

  • Experiment Hardware

  • Analysis

    • Pulse Fitting

    • Fit Results

  • Systematic Uncertainties

    • Gain Stability

    • Pileup

    • Spin Rotation

  • Final Results

D. M. Webber


Motivation
Motivation AND DETERMINATION OF THE FERMI CONSTANT

  • gives the Fermi Constant to unprecedented precision (actually Gm)

  • needed for “reference” lifetime for precision muon capture experiments

    • MuCap

    • MuSun

Capture rate from lifetime difference m-and m+


The predictive power of the standard model depends on well measured input parameters
The predictive power of the Standard Model depends on well-measured input parameters

What are the fundamental electroweak parameters (need 3)?

a

GF

MZ

sin2qw

MW

0.00068 ppm

8.6 ppm

23 ppm

650 ppm

360 ppm

* circa 2000

Obtained from muon lifetime

Other input parameters include fermion masses, and mixing matrix elements:

CKM – quark mixing

PMNS – neutrino mixing


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

Contains all weak interaction loop corrections well-measured input parameters

Dq

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

In the Fermi theory, muon decay is a contact interaction where Dq includes phase space, QED, hadronic and radiative corrections

In 1999, van Ritbergen and Stuart completed full 2-loop QED corrections reducing the uncertainty in GF from theory to < 0.3 ppm (it was the dominant error before)

D. M. Webber


The push pull of experiment and theory
The push – pull of experiment and theory well-measured input parameters

  • Lifetime now largest uncertainty leads to 2 new experiments launched: MuLan & FAST

    • Both @ PSI, but very different techniques

    • Both aim at “ppm” level GF determinations

    • Both published intermediate results on small data samples

  • Meanwhile, more theory updates !!


The lifetime difference between t m and t m in hydrogen leads to the singlet capture rate l s
The lifetime difference between well-measured input parameterstm+ and tm- in hydrogen leads to the singlet capture rate LS

1.0 ppm MuLan

~10 ppm MuCap

log(counts)

MuCap nearly complete

μ+

μ –

time

The singlet capture rate is used to determine gPand compare with theory

 gP


Experiment

Experiment well-measured input parameters

D. M. Webber


For 1ppm need more than 1 trillion 10 12 muons
For 1ppm, need more than well-measured input parameters1 trillion (1012) muons ...

πE3 Beamline,

Paul Scherrer Institut, Villigen, Switzerland


David m webber university of illinois at urbana champaign now university of wisconsin madison

Momentum well-measured input parameters

Selection

The beamline transports ~107“surface” muons per second to the experimental area.

Parallel beam

Spatial focus

Velocity separator removes beam positrons


David m webber university of illinois at urbana champaign now university of wisconsin madison

A well-measured input parameterskicker is used to create the time structure.

5 ms

22 ms

counts arb.

Extinction ~ 1000

Trigger Suppression

Accumulation

Period

Measuring Period

kicker


David m webber university of illinois at urbana champaign now university of wisconsin madison
ARNOKROME™ III well-measured input parameters(AK-3) high-field target used in 2006- Rapid precession of muon spin - mSR studies show fast damping


The target was opened once per day to view the beam profile

Target rotates out of beam well-measured input parameters

The target was opened once per day to view the beam profile.

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

In 2006, The ferromagnetic target dephases the muons during accumulation.

  • Arnokrome-3 (AK3) Target (~28% chromium, ~8% cobalt, ~64% iron)

  • 0.5 T internal magnetic field

  • Muons arrive randomly during 5 ms accumulation period

  • Muons precess by 0 to 350 revolutions

D. M. Webber


2007 target crystal quartz surrounded by an external 135 g magnetic field
2007 target: crystal quartz, surrounded by an external ~ 135 G magnetic field

Installed

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

Quartz


David m webber university of illinois at urbana champaign now university of wisconsin madison

450 MHz G magnetic field

WaveForm

Digitization

(2006/07)

MHTDC

(2004)

The experimental concept…

170 Inner/Outer

tile pairs

Real data

Kicker On

Measurement Period

Number (log scale)

time

Fill Period

-12.5 kV

12.5 kV


David m webber university of illinois at urbana champaign now university of wisconsin madison

The detector is composed of 20 hexagon G magnetic fieldand 10 pentagon sections, forming a truncated icosahedron.

Each section contains either 6 or 5tile elements

a

Each element is made from two independentscintillator tiles with light guides and photomultiplier tubes.


170 scintillator tile pairs readout using 450 mhz waveform digitizers

Waveform G magnetic field

Digitizers

2 Analog Pulses

1/6 of system

170 scintillator tile pairs readout using 450 MHz waveform digitizers.

x2

1 clock tick = 2.2 ns

Uncertainty on lifetime from gain stability: 0.25 ppm

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

Checked G magnetic fieldfor consistency throughout the run.

Compared to Quartzlock A10-R rubidium frequency standard.

Compared to calibrated frequency counter

Different blinded frequencies in 2006 and 2007

The clock was provided by an Agilent E4400B Signal Generator, which was stable during the run and found to be accurate to 0.025 ppm.

Agilent E4400 Function Generator

f = 450.87649126MHz

f = 451.0 +/- 0.2

Average difference = 0.025 ppm


Mulan collected two datasets each containing 10 12 muon decays
MuLan collected two datasets, each containing 10 G magnetic field12 muon decays

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

Datasets agree to sub-ppm

Ferromagnetic Target, 2006

Quartz Target, 2007


Analysis

Analysis G magnetic field

D. M. Webber


Raw waveforms are fit with templates to find pulse amplitudes and times
Raw waveforms are fit with templates to find pulse amplitudes and times

>2 x 1012pulses in 2006 data set

>65 TBytes raw data

inner

A difficult fit

Normal Pulse

ADT

Template

outer

Two pulses close together

D. M. Webber


Nearby pulses perturb the time of main pulses studied with simulations
Nearby pulses perturb the time of main pulses. amplitudes and timesStudied with simulations

Fixed reference

Dtavg

perturbation

Dtavg

Estimated pull:

D. M. Webber


2006 fit of 30 000 ak 3 pileup corrected runs

ppm amplitudes and timestm + Dsecret

22 ms

Rvs fit start time

Red band is the set-subset allowed variance

2006: Fit of 30,000 AK-3 pileup-corrected runs.

Relative t (ppm)

0 9 ms


David m webber university of illinois at urbana champaign now university of wisconsin madison
2007 amplitudes and times: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish.


Systematics

Systematics amplitudes and times

Introduction

D. M. Webber


Leading systematic considerations

Challenging amplitudes and times

Leading systematic considerations:


Systematics gain stability

Systematics: amplitudes and timesGain Stability

D. M. Webber


Gain is photomultiplier tube type dependent
Gain is photomultiplier tube type dependent amplitudes and times

Artifact from start signal

Deviation at t=0

1 ADC = 0.004 V

Sag in tube response

0 10 20 ms

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison
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

0 10 20 ms

Carefully studied over the summer. Gain correction is 0.5 ppm shift with 0.25 ppm uncertainty.

33


Systematics pileup

Systematics: peak (MPV) of the fit to pulse distributionPileup

D. M. Webber


Leading order pileup to a 5x10 4 effect

Measured peak (MPV) of the fit to pulse distributiont vs. Deadtime

Normal Time

Distribution

RawSpectrum

Pileup

Corrected

Pileup Time

Distribution

Leading order pileup to a ~5x10-4 effect

  • Statistically reconstruct

  • pileup time distribution

  • Fit corrected distribution

Fill i

Fill i+1

1/t– 2/t

2/t


Introducing higher order pileup
Introducing higher-order pileup peak (MPV) of the fit to pulse distribution

A

B

C

D

E

F

G

triple

hit

hit

pileup

Inner tile

Artificial deadtime

Artificial deadtime

Artificial deadtime

time

time

Outer tile

Artificial deadtime

D. M. Webber


Pileup to sub ppm requires higher order terms

R (ppm) peak (MPV) of the fit to pulse distribution

1 ppm

150 ns deadtime range

Artificial Deadtime (ct)

Pileup to sub-ppm requires higher-order terms

  • 12 ns deadtime, pileup has a 5 x 10-4 probability at our rates

    • Left uncorrected, lifetime wrong by 100’s of ppm

  • Proof of procedure validated with detailed Monte Carlo simulation

uncorrected

Pileup terms at different orders …


The pileup corrections were tested with monte carlo
The pileup corrections were tested with Monte-Carlo. peak (MPV) of the fit to pulse distribution

Monte-Carlo Simulation, 1012 events

agrees with truth to < 0.2 ppm

1.19 ppm statistical uncertainty

D. M. Webber


Lifetime vs artificially imposed deadtime window is an important diagnostic
Lifetime vs. artificially imposed deadtime window is an important diagnostic

A slope exists due to a pileup undercorrection

1 ppm

150 ns deadtime range

Extrapolation to 0 deadtime is correct answer

D. M. Webber

39

Pileup Correction Uncertainty: 0.2 ppm


Explanations of r vs adt slope
Explanations of R vs. ADT slope important diagnostic

  • Gain stability vs. Dt?

    • No. Included in gain stability systematic uncertainty.

  • Missed correction?

    • Possibly

    • Extrapolation to ADT=0 valid

  • Beam fluctuations?

    • Likely

    • Fluctuations at 4% level in ion source exist

    • Extrapolation to ADT=0 valid

D. M. Webber


Systematics1

Systematics important diagnostic

Spin Precession

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

The decay positron energy and angular distributions are not uniform, resulting in position dependant measurement rates.

Highest Energy Positrons

Lowest Energy Positrons

q

e+

Ee = Emax = 52.83 MeV

Positron energy distribution

  • Lowest energy positron when neutrinos are anti-parallel.

  • Neutrino helicities add so that they have angular momentum of 2.

  • Positron spin must compensate to bring total to 1.

  • Chiral suppression (not well justified at this energy) makes positron most likely right handed.

  • Most probable positron direction is opposite muon spin

  • Highest energy positron when neutrinos are parallel.

  • Neutrino helicities cancel angular momentum.

  • Positron spin must be in the same direction as muon spin.

  • Chiral limit dictates right handed positrons.

  • Most probable positron direction is same as muon spin

Ee = 26.4 MeV

Ee = 13.2 MeV

Detectionthreshold


David m webber university of illinois at urbana champaign now university of wisconsin madison

m uniform, resulting in position dependant measurement rates.SR rotation results in an oscillation of the measurement probability for a given detector.

B

B = 34 G

B = 1 G

counts arb.

counts arb.

This oscillation is not easily detectedand systematic errors may arise

This oscillation is easily detected


David m webber university of illinois at urbana champaign now university of wisconsin madison

The sum cancels muSR effects; the difference accentuates the effect.

counts arb.

B

counts arb.

Sum

Difference/Sum

counts arb.


David m webber university of illinois at urbana champaign now university of wisconsin madison

2006 target: AK3 ferromagnetic alloy with high internal magnetic field

  • Arnokrome-3 (AK3) Target (~28% chromium, ~8% cobalt, ~64% iron)

  • 0.4 T transverse field rotates muons with 18 ns period

  • Muons arrive randomly during 5 ms accumulation period

  • Muons precess by 0 to 350 revolutions  DEPHASED  small ensemble avg. polarization

Ensemble Averge Polarization


David m webber university of illinois at urbana champaign now university of wisconsin madison

All 170 Detectors magnetic field

85 Opposite Pairs

Lifetime

Opposite pairs summed

Front

Back

“front-back folded”

A small asymmetry exists front / back owing to residual longitudinal polarization

When front / back opposite tile pairs are added first, there is no distortion


2007 target crystal quartz surrounded by an external 135 g magnetic field1
2007 target: crystal quartz, surrounded by an external ~ 135 G magnetic field

Installed

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

Quartz


David m webber university of illinois at urbana champaign now university of wisconsin madison

Difference between G magnetic fieldTop of Ball and Bottom of Ball to Sum, vs time-in-fill

We directly confront the mSR. Fit each detector for an “effective lifetime.” Would be correct, except for remnant longitudinal polarization relaxation.

Illustration of free muon precession in top/bottom detector differences


David m webber university of illinois at urbana champaign now university of wisconsin madison

Longitudinal polarization G magnetic field 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)

(+ blind offset)

Magnet-right data


2007 consistency against many special runs where we varied target magnet ball position etc
2007: Consistency against MANY special runs, where we varied target, magnet, ball position, etc.

Start-time scan


Consistency checks

Consistency Checks varied target, magnet, ball position, etc.

D. M. Webber


2006 fit of 30 000 ak 3 pileup corrected runs1

ppm varied target, magnet, ball position, etc.tm + Dsecret

22 ms

Rvs fit start time

Red band is the set-subset allowed variance

2006: Fit of 30,000 AK-3 pileup-corrected runs

Relative t (ppm)

0 9 ms


2006 ak 3 target consistent fits of individual detectors but opposite pairs summed is better

All 170 Detectors varied target, magnet, ball position, etc.

85 Opposite Pairs

2006: AK-3 target consistent fits of individual detectors, but opposite pairs – summed – is better

Difference of Individual lifetimes to average


David m webber university of illinois at urbana champaign now university of wisconsin madison
2007 varied target, magnet, ball position, etc.: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish


Variations in t m vs fit start time are within allowed statisical deviations
Variations in varied target, magnet, ball position, etc.tmvs. fit start time are within allowed statisical deviations

D. M. Webber


Conclusions

Conclusions varied target, magnet, ball position, etc.

D. M. Webber


Final errors and numbers
Final Errors and Numbers varied target, magnet, ball position, etc.

ppm units

t(R06) = 2 196 979.9± 2.5 ± 0.9 ps

t(R07) = 2 196 981.2 ± 3.7 ± 0.9 ps

t(Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm)

Dt(R07 – R06) = 1.3 ps


David m webber university of illinois at urbana champaign now university of wisconsin madison

G varied target, magnet, ball position, etc.F &tm precision has improved by

~4 orders of magnitude over 60 years.

Achieved!


Lifetime history

New G varied target, magnet, ball position, etc.F

GF(MuLan) = 1.166 378 8(7) x 10-5 GeV-2 (0.6 ppm)

Lifetime “history”

FAST

The most precise particle or nuclear or (we believe) atomic lifetime evermeasured


The lifetime difference between t m and t m in hydrogen leads to the singlet capture rate l s1
The lifetime difference between varied target, magnet, ball position, etc.tm+ and tm- in hydrogen leads to the singlet capture rate LS

1.0 ppm MuLan

~10 ppm MuCap

log(counts)

MuCap nearly complete

μ+

μ –

time

The singlet capture rate is used to determine gPand compare with theory

 gP


In hydrogen 1 t m 1 t m l s g p now in even better agreement with chpt
In hydrogen: varied target, magnet, ball position, etc.(1/tm-)-(1/tm+) = LS gPnow in even better agreement with ChPT*

Shifts the MuCap result

Using previous tm world average

Using new MuLan tm average

*Chiral Perturbation Theory

64


Conclusions1
Conclusions varied target, magnet, ball position, etc.

  • MuLan has finished

    • PRL accepted and in press. (see also arxiv:1010.0991)

    • 1.0 ppm final error achieved, as proposed

  • Most precise lifetime

    • Most precise Fermi constant

    • “Modest” check of muonium versus free muon

  • Influence on muon capture

    • Shift moves gP to better agreement with theory

    • “Eliminates” the error from the positive muon lifetime, needed in future MuCap and MuSun capture determinations

t(R06) = 2 196 979.9± 2.5 ± 0.9 ps

t(R07) = 2 196 981.2 ± 3.7 ± 0.9 ps

t(Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm)

Dt(R07 – R06) = 1.3 ps


David m webber university of illinois at urbana champaign now university of wisconsin madison

MuLan Collaborators varied target, magnet, ball position, etc.

2004

Institutions:

University of Illinois at Urbana-Champaign

University of California, Berkeley

TRIUMF

University of Kentucky

Boston University

James Madison University

Groningen University

Kentucky Wesleyan College

2006

2007

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

D. M. Webber varied target, magnet, ball position, etc.


Backup slides

Backup Slides varied target, magnet, ball position, etc.


What is g p g p is the pseudoscalar form factor of the proton

What is g varied target, magnet, ball position, etc.P?gP is the pseudoscalar form factor of the proton

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

Muon capture varied target, magnet, ball position, etc.

At a fundamental level, the leptonic and quark currents possess the simple V−A structure characteristic of the weak interaction.

ν

d

μ

u

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

Muon capture varied target, magnet, ball position, etc.

In reality, the QCD substructure of the nucleon complicates the weak interaction physics. These effects are encapsulated in the nucleonic charged current’s four “induced form factors”:

ν

n

μ

p

Return

D. M. Webber


Miscellaneous

Miscellaneous varied target, magnet, ball position, etc.

D. M. Webber


David m webber university of illinois at urbana champaign now university of wisconsin madison

The decay positron energy and angular distributions are not uniform, resulting in position dependant measurement rates.

Highest Energy Positrons

Lowest Energy Positrons

q

e+

Ee = Emax = 52.83 MeV

Positron energy distribution

  • Lowest energy positron when neutrinos are anti-parallel.

  • Neutrino helicities add so that they have angular momentum of 2.

  • Positron spin must compensate to bring total to 1.

  • Chiral suppression (not well justified at this energy) makes positron most likely right handed.

  • Most probable positron direction is opposite muon spin

  • Highest energy positron when neutrinos are parallel.

  • Neutrino helicities cancel angular momentum.

  • Positron spin must be in the same direction as muon spin.

  • Chiral limit dictates right handed positrons.

  • Most probable positron direction is same as muon spin

Ee = 26.4 MeV

Ee = 13.2 MeV

Detectionthreshold


Effect of h on g f
Effect of uniform, resulting in position dependant measurement rates.h on GF

  • In the Standard Model, h=0,

  • General form of h

  • Drop second-order nonstandard couplings

  • Effect on GF

return

D. M. Webber