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 For the MuLan Collaboration University of Wisconsin-Madison Formerly University of Illinois at Urbana-Champaign August 12, 2011.

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David M. Webber For the MuLan Collaboration University of Wisconsin-Madison

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David m webber for the mulan collaboration university of wisconsin madison

A part-per-million measurement of the positive muon lifetime and determination of the Fermi constant

David M. Webber

For the MuLan Collaboration

University of Wisconsin-Madison

Formerly University of Illinois at Urbana-Champaign

August 12, 2011


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

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


David m webber for the mulan collaboration university of wisconsin madison

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


Mulan collected two datasets each containing 10 12 muon decays

MuLan collected two datasets, each containing 1012 muon decays

Two (very different) data sets

Different muon stopping targets

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


Leading systematic considerations

Challenging

Leading systematic considerations:


170 scintillator tile pairs readout using 450 mhz waveform digitizers

Waveform

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

D. M. Webber


David m webber for the mulan collaboration 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 of 2010. Gain correction is 0.5 ppm shift with 0.25 ppm uncertainty.

8


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


Leading order pileup to a 5x10 4 effect

Measured t 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


Pileup to sub ppm requires higher order terms

R (ppm)

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.

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

13

Pileup Correction Uncertainty: 0.2 ppm


Explanations of r vs adt slope

Explanations of R vs. ADT slope

  • 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


2006 fit of 30 000 ak 3 pileup corrected runs

ppm tm + Dsecret

22 ms

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

2007: 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 statistical deviations

Variations in tmvs. fit start time are within allowed statistical deviations

D. M. Webber


Final errors and numbers

Final Errors and Numbers

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


Results

Results

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

The Result

New GF

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


The lifetime difference between t m and t m in hydrogen leads to the singlet capture rate l s

The lifetime difference between 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: (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

20


David m webber for the mulan collaboration university of wisconsin madison

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


Conclusions

Conclusions

  • MuLan has finished

    • PRL published. Phys. Rev. Lett. 106, 041803 (2011)

    • 1.0 ppm final error achieved, as proposed

    • PRD in preparation

  • Most precise lifetime

    • Most precise Fermi constant

  • Influence on muon capture

    • Shift moves gP to better agreement with theory

    • “Eliminates” the error from the positive muon lifetime, needed in future m- capture determinations (e.g. MuCap and MuSun)

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


Backup

Backup

D. M. Webber


For 1ppm need more than 1 trillion 10 12 muons

For 1ppm, need more than 1 trillion (1012) muons ...

πE3 Beamline,

Paul ScherrerInstitute, Villigen, Switzerland


Gain is photomultiplier tube type dependent

Gain is photomultiplier tube type dependent

Artifact from start signal

Deviation at t=0

1 ADC = 0.004 V

Sag in tube response

0 10 20 ms

D. M. Webber


Introducing higher order pileup

Introducing higher-order pileup

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


The push pull of experiment and theory

The push – pull of experiment and theory

  • Muon lifetime is now the largest uncertainty on GF ; 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 !!


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