New Muon Lifetime
and the
Fermi Coupling Constant GF
Kevin Giovanetti
James Madison University
HallC meeting, JLAB, Aug 10, 2007
aµ = (gµ − 2) /2
Precision
Muon Phyiscs
FUNDAMENTAL
SYMMETRIES
Precision Measurements of Standard
“Of all
the recent
muon
experiments,
the measurement
of the
“The
weak
mixing
angle
θW, parametrizes
the mixing
Model
Properties
“The
Fermi
constant,
, measured
via
thebyµ+
lifetime
muon
anomalous
magnetic
moment,
experiment
µ-2)/2bosons
U(1)aYµ=(g
gauge
in the
between neutral
SU(2)GL Fand
Precision
Measurements
E821be
atElectroweak
BNL
stands
out
experimentally
and
theoretically. “
“High
precision
electroweak
experiments
provide
will
improved
aboth
factor
of
20
PSI.
That
Standard
Model.
Itby
is,
arguably,
theatmost
important
stringent
of the
Model
(SM)
at the current
tree
and
parametertests
is used
to Standard
normalize
all When
weak
charged
parameter
in
electroweak
physics.
combined
with
“That measurement
was statistics limited and could be further
quantum
loop
levels.”
and most measurements
weak neutral current
amplitudes.
Itconstant)
is also and
precision
of
a,
G
(the
Fermi
F
improved. Indeed, an upgrade proposal by the collaboration
instrumental
for
comparison
with
and
other
precision
,
it
can
be
used
to
probe
quantum
loop
corrections
m
outlines
a
plan
to
reduce
the
error
in
by
a
about
factor
of 2.” from
Z
electroweak
measurements.”
heavy
fermions,
the Higgs scalar, and various new physics
effects.”
HallC meeting, JLAB, Aug 10, 2007
aµ = (gµ − 2) /2
Precision
Muon Phyiscs
FUNDAMENTAL
SYMMETRIES
MUONS
PSI
TRIUMF
BNL
FNAL ?
Michel parm
Lifetime
µ−p capture
µ−d capture
g-2
µA->eA
ρ, δ, η, Pµξ
GF (1 ppm)
ΛS -> gP
L1A
SUSY, BSM
LFV, BSM
HallC meeting, JLAB, Aug 10, 2007
MUON Physics
Physical Review Letters, 20 July 2007,Volume 99, Number 3
Improved Measurement of the Positive-Muon Lifetime and
Determination of the Fermi Constant
D. B. Chitwood et al. (MuLan Collaboration)
Published 16 July 2007
Measurement of the Muon Capture Rate in Hydrogen Gas and
Determination of the Proton's Pseudoscalar Coupling gP
V. A. Andreev et al. (MuCap Collaboration)
Published 16 July 2007
032002
Electroweak Radiative Corrections to Muon Capture
Andrzej Czarnecki, William J. Marciano, and Alberto Sirlin
Published 16 July 2007
032003
HallC meeting, JLAB, Aug 10, 2007
Standard Model Electroweak Interaction
(4 parameters)
g’
U(1)
g
SU(2)
MH (Higgs)
v
expectation value
of the Higgs field
α
Fine structure constant
00.045 ppm
GF
Fermi coupling constant
09.000 ppm
Mz
Mass of the Z boson
23.000 ppm
MH
Higgs mass
constrained
mi masses of quarks and leptons (12)
CKM quark mass mixing matrix, [Cabbibo] Kobayashi-Maskawa (4)
MKS mass matrix for neutrinos, Maki-Nakagawa-Sakata matrix (4)
Cosmological Constant (1)
QCD Coupling (1)
26 dimensionless constants for standard model
•Ritenbergen and Stuart, Nucl. Phys. B564 (2000)
•PDG, Particle Data Group
Electroweak Interaction
e
νµ
µ+
µ + → e+ + ν e + ν µ
νµ
+
νe
µ+
e+
νe
W+
2 2GF
(
LF = −
u (ν e )γ α (1 − γ 5 )u ( e + ) )(u (ν µ )γ β (1 − γ 5 )u( µ + ) )
4
kα kα
− gαβ + 2
2
g
MW
+
+
β
α
(
ν
γ
γ
µ
LW = − (u (ν e )γ (1 − γ 5 )u ( e ) ) 2
u
(
)
(
1
−
)
u
(
))
5
µ
2
8
k − MW
gαβ
g2
+
α
LW = − (u (ν e )γ (1 − γ 5 )u ( e ) ) 2 (u (ν µ )γ β (1 − γ 5 )u ( µ + ) )
8
MW
Fermi Coupling constant
2
F
55
11 G mµµ
=
((11++ δ )
33
ττ 192π
νµ
µ
+
νe
+
e
γ
+…
νµ
GF
g 22
(1 ++ ∆r)
=
22
2 8M WW
µ+
Z0
W+
e+
+…
νe
The theoretical uncertainty on GF as extracted from
the muon lifetime is < 0.3 ppm.
ELectroweak
• Basic parameters [2006] (e.g. PDG)
Standard Model Electroweak Interaction
α
Fine structure constant
00.045 ppm
GF
Fermi coupling constant
(Before current effort)
09.000 ppm
Mz Mass of the Z boson
δGF
GF
=
1 δτ
−
2 τ
9 ppm
5 δmµ
−
2 mµ
0.08 ppm
23.000 ppm
1 δ (1 + q)
−
2 (1 + q)
0.3 ppm
MuLan Collaboration
University of Illinois at Urbana Champaign (UIUC)
Boston University (BU)
University of California, Berkeley (UCB and LBNL)
University of Kentucky, Lexington
TRIUMF, Vancouver
James Madison University, (JMU)
KVI Groningen, Netherlands
HallC meeting,
JLAB,
Aug 10,University,
2007
Istanbul
Technical
Turkey
HallC meeting, JLAB, Aug 10, 2007
The experimental concept
Number (log scale)
Real dataKicker On
Measurement Period
time
Fill Period
5
-12.
kV
kV
12.5
Rates
• 1ppm requires at least 1012 observed decays
• Probability for a set of measurements (t1, t2,…)
dP(t1 , t2 ... | τ ) = ρ ( t1 | τ ) ρ ( t2 | τ )...dt1dt2 ...
• Probability that a parameter has a value based on (t1, t2,…)
L(τ | t1 , t2 ...) = ρ ( t1 | τ ) ρ ( t2 | τ )
Rates and Uncertainty
• For a simple distribution one can find the value for τ
that make the experimental result highly probable and
estimate the uncertainty. (same result from fitting)
dL(τ | t1 , t2 ...)
=0
dτ
t
1 −τ
ρ (t ) = e
τ
t1 + t2 + ...
τ=
N
 1  ∂ρ  2 
 ∫   dt 
 ρ  ∂τ  
∆τ =
N
∆τ =
τ
N
−
1
2
Uncertainty with Background
Assume measurement period of 10τ
.
001-.002
Uncertainty
• Uncertainty is increased due to new terms in the
distribution
• Lifetime is distorted due to an incorrect distribution
•The average is no longer an unbiased estimator
for the lifetime when there is background
•Reduce your uncertainty through statistics therefore
an unbiased measurement of t is critical
•Individual precise measurements are not critical
KNOW YOUR DISTRIBUTION
REMOVE SYSTEMTICS
Rates
• To accumulate the statistics necessary in a one
month period
– 4.0x105 muon decays/sec
– 1 muon every 3 µs
• Need more than 1 muon in target at a given
time.
– Granularity (FAST approach)
– Pulsed beam (µLAN Approach)
• Duty facor (35 µs -total ) /(5 µs –on)
[factor of 7]
– 3x106 muons/sec
Beam rate of a FEW MHz
MuLan Experiment at the
Paul Scherrer Institut
1.8 mA cyclotron,
Villigen, Switzerland
590 MeV protons
Neutrons
SINQ
Swiss Light Source
πe3 beamline
Surface Muon Beam 29 MeV/c
•Dedicated beam studies for several years
•A Beam Rate > 11 MHz;
•Spot at target, only few cm2.
•Separator leaves about 5–10% positron background.
•Many elements to tune. Straight beam is tricky.
•Extinction fraction looks reasonable. (1000)
quads
kicker plates
separator
Expt.
+12.5 kV
0
-12.5 kV
11.3 m
triplet
slits
triplet
Subsystem #1
PSI πE3 4.2 MeV
muon source
Quads
Kicker Plates
N
S
+10 kV
0
-10 kV
Kicker HV supply; 50 kHz cycle time
Subsystem #2
Subsystem #6
LEDs
Simulations:
outer
t
Tunes
inner
GEANT 4
Systematics
Fitting
outer
500 MHz WFD Bank
Online DAQ and Analysis Farm
Subsystem #3
#4
Subsystem #3
inner
e+
Subsystem #5
25 kV (+/- 12.5 on each plate) kick, 12 cm gap, 30 kHz: a gift from TRIUMF
Extinction ~ 1000
Trigger
Suppression
Adjustable
Accumulation
Measuring Period
2-sided, soccer-ball geometry
Hex-house
Inner (larger)
Outer (smaller)
Pent-house
(
ea
Ar
lse
Pu
ter
ou
)
2 Analog Pulses
Pulse Area (inner)