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David M Webber University of Illinois at Urbana-Champaign (Now University of Wisconsin-Madison)

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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

- Motivation
- Experiment Hardware
- Analysis
- Pulse Fitting
- Fit Results

- Systematic Uncertainties
- Gain Stability
- Pileup
- Spin Rotation

- Final Results

D. M. Webber

- 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+

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

Contains all weak interaction loop corrections

Dq

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

- 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 !!

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

D. M. Webber

πE3 Beamline,

Paul Scherrer Institut, Villigen, Switzerland

Momentum

Selection

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

Parallel beam

Spatial focus

Velocity separator removes beam positrons

A kicker is used to create the time structure.

5 ms

22 ms

counts arb.

Extinction ~ 1000

Trigger Suppression

Accumulation

Period

Measuring Period

kicker

Target rotates out of beam

D. M. Webber

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

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 !

- Precession noticeable and small longitudinal polarization exists
- Magnet ring “shadows” part of detector

Quartz

450 MHz

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

The detector is composed of 20 hexagonand 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.

Waveform

Digitizers

2 Analog Pulses

1/6 of system

x2

1 clock tick = 2.2 ns

Uncertainty on lifetime from gain stability: 0.25 ppm

D. M. Webber

Checked for 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

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

D. M. Webber

>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

Fixed reference

Dtavg

perturbation

Dtavg

Estimated pull:

D. M. Webber

ppm tm + Dsecret

22 ms

Rvs fit start time

Red band is the set-subset allowed variance

Relative t (ppm)

0 9 ms

Systematics

Introduction

D. M. Webber

Challenging

Systematics:Gain Stability

D. M. Webber

Artifact from start signal

Deviation at t=0

1 ADC = 0.004 V

Sag in tube response

0 10 20 ms

D. M. Webber

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

D. M. Webber

Measured t vs. Deadtime

Normal Time

Distribution

RawSpectrum

Pileup

Corrected

Pileup Time

Distribution

- Statistically reconstruct
- pileup time distribution
- Fit corrected distribution

Fill i

Fill i+1

1/t– 2/t

2/t

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

R (ppm)

1 ppm

150 ns deadtime range

Artificial Deadtime (ct)

- 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 …

Monte-Carlo Simulation, 1012 events

agrees with truth to < 0.2 ppm

1.19 ppm statistical uncertainty

D. M. Webber

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

- 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

Systematics

Spin Precession

D. M. Webber

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

mSR 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

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

counts arb.

B

counts arb.

Sum

Difference/Sum

counts arb.

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

All 170 Detectors

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

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 !

- Precession noticeable and small longitudinal polarization exists
- Magnet ring “shadows” part of detector

Quartz

Difference between Top 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

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)

(+ blind offset)

Magnet-right data

Start-time scan

Consistency Checks

D. M. Webber

ppm tm + Dsecret

22 ms

Rvs fit start time

Red band is the set-subset allowed variance

Relative t (ppm)

0 9 ms

All 170 Detectors

85 Opposite Pairs

Difference of Individual lifetimes to average

D. M. Webber

Conclusions

D. M. Webber

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

GF &tm precision has improved by

~4 orders of magnitude over 60 years.

Achieved!

New GF

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

FAST

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

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

Shifts the MuCap result

Using previous tm world average

Using new MuLan tm average

*Chiral Perturbation Theory

64

- 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

MuLan Collaborators

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

D. M. Webber

Backup Slides

What is gP?gP is the pseudoscalar form factor of the proton

D. M. Webber

Muon capture

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

Muon capture

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

D. M. Webber

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

- In the Standard Model, h=0,
- General form of h
- Drop second-order nonstandard couplings
- Effect on GF

return

D. M. Webber