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David M. Webber For the MuLan Collaboration 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

For the MuLan Collaboration

University of Wisconsin-Madison

Formerly University of Illinois at Urbana-Champaign

August 12, 2011

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

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

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

Challenging

Waveform

Digitizers

2 Analog Pulses

1/6 of system

x2

1 clock tick = 2.2 ns

D. M. Webber

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

>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

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

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

13

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

ppm tm + Dsecret

22 ms

2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish.

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

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)

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

20

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

- 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

D. M. Webber

πE3 Beamline,

Paul ScherrerInstitute, Villigen, Switzerland

Artifact from start signal

Deviation at t=0

1 ADC = 0.004 V

Sag in tube response

0 10 20 ms

D. M. Webber

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

- 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 !!