Collaborating Institutions Petersburg Nuclear Physics Institute PNPI, Gatchina, Russia Paul Scherrer

1
The Rich Physics of Nuclear Muon Capture
Tom Banks, UC Berkeley What Physicists Do
Colloquium Sonoma State University October 5, 2009
2
Introduction
The purpose of this talk is to describe the
science behind MuCap, the nuclear physics
experiment on which I did my PhD research.
In order to motivate and explain the experiment,
I need to first provide some background...
3
I. Background
4
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong
5
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong
attraction between things that have mass
6
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong

• binds electrons and nuclei into atoms
• responsible for photons (light)

7
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong
binds quarks into nucleons (protons and
neutrons), and nucleons into nuclei
8
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong
responsible for radioactivity, particle decays,
and various other processes
9
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong
Electroweak
Three, actually. (Maybe two? One?)
10
The four fundamental forces
Gravitational
Electromagnetic
Weak
Strong
The MuCap experiment studies the process of
nuclear muon capture, the physics of which
involves these three forces.
11
Nuclear muon capture
Nuclear muon capture is a weak interaction
process
12
Nuclear muon capture
Nuclear muon capture is a weak interaction
process
muon just like an electron (Q-1), except 200
times heavier (mass105.7 MeV) and unstable
13
Nuclear muon capture
Nuclear muon capture is a weak interaction
process
muon just like an electron (Q-1), except 200
times heavier (mass105.7 MeV) and unstable
proton made of 2 up quarks and a down
quark (Q1), mass938.2 MeV
14
Nuclear muon capture
Nuclear muon capture is a weak interaction
process
muon just like an electron (Q-1), except 200
times heavier (mass105.7 MeV) and unstable
proton made of 2 up quarks and a down
quark (Q1), mass938.2 MeV
neutron made of 2 down quarks and an up
quark (Q0), mass939.6 MeV
15
Nuclear muon capture
Nuclear muon capture is a weak interaction
process
neutrino chargeless (Q0), almost massless
particle, rarely interacts w/anything
muon just like an electron (Q-1), except 200
times heavier (mass105.7 MeV) and unstable
proton made of 2 up quarks and a down
quark (Q1), mass938.2 MeV
neutron made of 2 down quarks and an up
quark (Q0), mass939.6 MeV
16
Nuclear muon capture
Nuclear muon capture is a weak interaction
process
The corresponding Feynman diagram looks like this
?
n
W
p
µ
17
Why is muon capture interesting?
To explain, I will have to get a little
technical... At a fundamental level, the weak
interaction has a very simple and elegant
structure, called V-A (vector minus axial
vector)
d
?
u
µ
18
Why is muon capture interesting?
However, the proton and neutron are not
fundamental particles they are made up of
strongly interacting quarks! This complicates
the nucleons weak interaction physics, which is
described by four induced form factors
?
n
p
µ
19
Why is muon capture interesting?
In other words The strong-force-interacting
substructure of the proton affects how it
participates in weak interactions.
?
n
p
µ
20
Why is muon capture interesting?
Answer One of the form factors, the induced
pseudoscalar, is far more poorly known than the
others, and muon capture offers the best way of
measuring it.
?
n
p
µ
21
The pseudoscalar coupling gP

• The other form factors are known much better
  than the pseudoscalar gP
• Modern theories make relatively precise
  predictions for gP , but past experimental
  results have been imprecise and/or inconsistent.

22
Physics of muon capture
After a negative muon stops in matter, it can
disappear via either muon capture or decay
capture
decay
23
Physics of muon capture
After a negative muon stops in matter, it can
disappear via either muon capture or decay
in H2
0.1
capture
decay
99.9
When stopped in pure hydrogen, most muons
actually decay only 1 in a 1000 undergo nuclear
capture.
24
Muon kinetics in hydrogen
e

• Muon injection in H
• Atomic capture (forms µp)
• Muon disappearance
• Decay, or
• Nuclear capture

µ
p
25
Muon kinetics in hydrogen
e

• Muon injection in H
• Atomic capture (forms µp)
• Muon disappearance
• Decay, or
• Nuclear capture

µ
p
26
Muon kinetics in hydrogen
e

• Muon injection in H
• Atomic capture (forms µp)
• Muon disappearance
• Decay, or
• Nuclear capture

?e
µ
p
?µ
99.9
27
Muon kinetics in hydrogen
?µ

• Muon injection in H
• Atomic capture (forms µp)
• Muon disappearance
• Decay, or
• Nuclear capture

µ
p
0.1
n
28
Exponential disappearance law
The muon decay probability vs. time follows an
exponential law
time
The decay rate, ?decay, is well-known from µ
lifetime measurements.
29
Exponential disappearance law
The muon decay probability vs. time follows an
exponential law
time
The decay rate, ?decay, is well-known from µ
lifetime measurements.
For negative muons in matter, the exponential
disappearance rate is simply the sum of the muon
decay rate and the nuclear capture rate
30
Measuring muon capture
So how is muon capture measured? Historically
there have been two basic approaches

• Detect the capture neutrons (and the absence of a
  decay electron), and then calculate the fraction
  of muons that underwent capture
• Measure the exponential time spectrum of decay
  electrons to get the overall muon disappearance
  rate, then subtract the muon decay rate

31
Complication 1 pµp formation
triplet
µ
para (L0)
ortho (L1)
singlet
In pure hydrogen, µp atoms tend to form pµp
molecules over time, at a rate proportional to
the hydrogen density f.
32
Muon kinetics in H2 pµp formation
Complication 1 pµp formation
tµ
In fact, muons stopped in liquid hydrogen
actually spend most of their time in pµp
molecules.
33
Complication 1 pµp formation
triplet
µ
para
ortho
singlet

• This is a serious problem because each muonic
  state has a unique nuclear capture rate!
• The overall capture rate is a time-dependent
  combination of these rates
• The key pµp ortho ?para transition rate ?op is
  poorly known

34
Complication 2 impurities

triplet
µ
para
ortho
singlet

• Muons preferentially irreversibly transfer to
  Zgt1 and isotopic impurities, which provide
  additional capture pathways with unique rates
• Small amounts of impurities can severely distort
  the observed capture rate
• µd atoms can (i) rapidly diffuse away from
  stopping point, (ii) participate in pµd fusion

35
Complications kinetics
This is a pretty complicated situation... for
example, heres the solution to the system of
differential equations describing it!
36
Complications kinetics

triplet
µ
para
ortho
singlet
In order to correctly interpret experimental
results, its essential to know the occupation
numbers of these muonic states vs. time!
37
Past experimental results
OMC
RMC
LH2
LH2
LH2
LH2
LH2
LH2
GH2
GH2
38
Past experimental results
OMC
RMC
LH2
LH2
LH2
LH2
LH2
LH2
GH2
GH2
Plotting the gP values in this way does not tell
the entire story, however...
39
Past experimental results
? 8.26 0.23

• Prior to MuCap, the situation surrounding gP
  was inconclusive the two best experiment
  results and the precise theoretical prediction
  were mutually inconsistent.
• The experimental results were sensitive to
  uncertainties in the kinematics of muonic
  molecules.

40
II. MuCap
41
MuCap experiment
We measure the rate of nuclear muon capture by
the proton by stopping negative muons in hydrogen
gas and observing the time spectrum of decay
electrons.
42
MuCap experimental concept
The Lifetime Technique
e
Data Acquisition
Telectron
µ
H2
Tmuon
DT
counts

• Fill histogram with muons lifetime ?T
• Repeat N times for a 1/vN precision
  lifetime measurement

DT
0
43
MuCap experimental concept
The Lifetime Technique
log(counts)
muon decay time

• Negative muons can disappear via decay or
  nuclear capture
• Positive muons can only decay
• The muon capture rate can be obtained from the
  small (0.16) difference between the
  disappearance rates of the two species

44
MuCap experimental concept
TeSC-TµSC (ns)

• This is a high-precision experiment In order to
  accurately determine the muon capture rate,
  its necessary to collect 1010 decay events!
• In high-precision experiments like this, the
  primary challenge lies in controlling
  systematic effects, which skew measured values
  away from the true values.

45
MuCap experimental strategy

• We cant eliminate systematic effects (e.g., from
  pµp molecules or hydrogen gas impurities), but
  our unique
• hydrogen target, and
• detector setup
• enable us to minimize and characterize such
  effects, and to correct for them in the measured
  lifetime.

46
Detectors
e
µ

• Muon detectors
• µSC fast timing of muon arrivals
• µPC1, TPC 3D tracking of incoming muon
  trajectories
• Electron detectors
• ePC1, ePC2 3D tracking of outgoing electron
  trajectories
• eSC fast timing of outgoing decay electrons

47
Hydrogen target TPC detector

• TPC Time Projection Chamber
• Active target H2 gas is both muon stopping
  target and chamber gas
• First TPC of its kind
• Provides three-dimensional tracking of incoming
  muons, enabling identification of clean
  muon stops
• Can directly observe muon captures by Z gt1 gas
  impurities

48
Hydrogen target
µp??
triplet
pµp
pµp
µ
para
ortho
singlet

• We use low-density (1 of LH2) hydrogen gas,
  which is an optimal compromise among competing
  demands
• preservation of substantial muon stopping power
• minimization of µp diffusion
• suppression of pµp molecule formation

49
Hydrogen target
µp??
triplet
pµp
pµp
µ
para
ortho
singlet

• To minimize effects from Zgt1 impurities, we
• Use a bakeable TPC pressure vessel
• Pass the H2 through palladium filter when
  filling the pressure vessel
• Use a custom-built system to continuously
  circulate clean the H2

50
Hydrogen target
µp??
triplet
pµp
pµp
µ
para
ortho
singlet
To minimize µd effects, we use deuterium-depleted
H2 (protium) with cd 1.5 ppm. (Natural
hydrogen has a deuterium concentration of cd
140 ppm.)
51
Experimental goal
?
A precise (7) determination of gP that is
relatively insensitive to ambiguities arising
from pµp molecule formation.
52
Experimental sequence
1010 µ- decay events in pure hydrogen gas
10 ppm measurement of µ- disappearance rate
1 determination of (µp)singlet nuclear capture
rate ?S
7 determination of gP
53
Experiment location
Paul Scherrer Institut
Villigen, Switzerland
PSI Experimentierhalle, home to a cyclotron and
muon beamlines
54
Experimental apparatus
Overhead view of the MuCap detector in the pE3
beamline at PSI, October 2004.
55
Experimental apparatus
The MuCap detectors assembled at the Paul
Scherrer Institut, Switzerland, OctoberNovember,
2004.
56
Experimental apparatus
The MuCap detectors assembled at the Paul
Scherrer Institut, Switzerland, OctoberNovember,
2004.
57
The lifetime spectrum

• We recorded roughly 1.6 x 109 negative muon
  decay events during our first physics run
  in 2004.

58
The lifetime spectrum

• We recorded roughly 1.6 x 109 negative muon
  decay events during our first physics run
  in 2004.
• The muon disappearance rate is obtained by
  fitting the measured decay time spectrum
  with an exponential function of the form

59
Fit result

• The result for the fitted µ disappearance rate
  is
• However, the lifetime spectrum is not a pure
  exponential...

60
Correction Zgt1 impurities

triplet
para
ortho
singlet
Although the circulation system did a great job
of suppressing impurity levels in 2004, there was
still a nonnegligible level of contaminationprima
rily oxygen from humidity that outgassed from the
pressure vessel walls.
61
Correction Zgt1 impurities

The TPC can detect Zgt1 nuclear captures.
62
Correction Zgt1 impurities

• The effect of impurities on the muon
  disappearance rate is proportional to the
  number of TPC-observed captures per good muon
  stop.
• The proportionality for contaminants N,O is
  established by calibration measurements in
  which we intentionally doped the gas.
• The capture-yield-based correction is

63
Correction muon scatters
muon scatter signature

• Sometimes a muon scatters off a proton,
  mimicking a stop in the TPC
• Scatter events are dangerous because the
  scattered muons can stop in surrounding Zgt1
  detector materials
• We can catch some of these events, but the
  signature is not always robust

64
Correction muon scatters

• Differential study of scatter events indeed
  exhibits a higher disappearance rate
• Unfortunately, we must rely on simulations to
  estimate our identification efficiency
• We remove the scatters we find, and
  conservatively assume 50 inefficiency

65
Correction deuterium µd diffusion
µd
µp
r 1 mm

• Muons preferentially transfer from µp ? µd
• H2 gas is more transparent to µd atoms, so
  they diffuse faster farther
• The rapid diffusion can raise the observed muon
  disappearance rate in two ways
• muons can diffuse out of the decay vertex
  reconstruction radius
• muons can diffuse into surrounding detector
  materials and capture there

66
Correction deuterium µd diffusion
?
Production Data
Deuterium-doped data
??µd
cd (ppm)
122(5)
1.44(13)
0
Extrapolated Result
We perform a zero extrapolation to correct for
the effects of µd diffusion.
67
Correction deuterium µd diffusion

• The deuterium concentrations were determined
  using two complementary methods
• External measurements of gas samples
• From data analysis of the ? vs. impact
  parameter dependence
• The results from the two approaches were
  consistent
• The zero extrapolation yields

68
Correction µp diffusion
actual
observed

• Although µp diffusion distances are small ( 1
  mm), the scattering of outgoing decay
  electrons by the aluminum pressure vessel
  magnifies the behavior
• By combining the electron scattering
  distribution with a simple model of isotropic
  µp diffusion, we calculate the correction

69
Correction pµp molecule formation

• Even in perfectly clean, pure hydrogen gas,
  muons will slowly form pµp molecules
• The nuclear capture rates in pµp molecules are
  lower than in the µp atom

70
Correction pµp molecule formation

• In order to extract the µp singlet capture rate,
  we have to make some assumptions about pµp
  kinetics...
• We used conservative averages of published pµp
  formation and transition rates to obtain

71
Systematics table (2004 data)
Source Uncorrected rate Zgt1 gas impurities Muon
scatter events µd diffusion µp diffusion pµp
molecule formation Muon detector
inefficiencies Analysis consistency µp bound
state decay rate Adjusted µ- disappearance rate
455 886.6 19.2 3.1 10.2 2.7 23.5 12.3 455
887.2
12.6 5.0 3.0 1.6 0.5 7.3 3.0
5.0 16.8

72
Results (2004 data) capture rate
Subtracting the positive muon lifetime measured
by our sister experiment, MuLan, yields the µp
singlet capture rate
This result is consistent with the latest
theoretical calculations, which predict 711.5
4.5 Hz. All of these results appeared in the
July 20, 2007 issue of Physical Review Letters
(PRL 99, 032002 and 032003 (2007)).
73
Results (2004 data) gP
From the measured capture rate we extracted the
pseudoscalar value
which is consistent with the theoretical
prediction of 8.260.23, and thus corroborates
our modern understanding of the role of the
strong force.
74
Status future

• During 2005 ? 2007, MuCap collected more data of
  superior quality, with higher statistics
  (1.5 1010 decays), cleaner hydrogen, and
  enhanced detectors.
• Analysis is in progress the primary challenge
  now is systematics.
• We expect to reduce the statistical and
  systematic errors by at least a factor of 2,
  reaching the design goal of a 1 capture
  measurement.

75
The next phase...
MuSun

• Goal measurement of the µd capture rate to 1
• Calibrating the sun
• Determines L1A, of relevance to astrophysical
  studies

76
Closing remarks
I hope Ive succeeded in conveying the rich
variety of physics involved in studying this
particular, little-considered process of muon
capture
For me, working on MuCap was a unique
opportunity I was able to participate in a
reasonably sized experiment, and to learn about a
wide range of physics.
77
Closing remarks
I hope Ive succeeded in conveying the rich
variety of physics involved in studying this
particular, little-considered process of muon
capture
For me, working on MuCap was a unique
opportunity I was able to participate in a
reasonably sized experiment, and to learn about a
wide range of physics.
Good physics is not only found in the obvious
places!
78
MuCap Collaboration
Thanks to the many hard-working members of the
MuCap Collaboration!
79
Petersburg Nuclear Physics Institute (PNPI),
Gatchina, RussiaPaul Scherrer Institute (PSI),
Villigen, SwitzerlandUniversity of California,
Berkeley (UCB and LBNL), USAUniversity of
Illinois, Urbana-Champaign (UIUC), USAUniversite
Catholique de Louvain, BelgiumUniversity of
Kentucky, USABoston University, USA
MuCap Collaboration
The MuCap experiment is supported in part by the
United States Department of Energy and the
National Science Foundation.
www.npl.uiuc.edu/exp/mucapture
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81
Weak interaction historical personalities
Lee and Yang
Pauli
Wu
Sudarshan
Marshak
Fermi
Gell-Mann and Feynman
82
The pseudoscalar coupling gP
?
n
W
p
µ
p

• Pion pole is dominant contributor to the
  pseudoscalar form factor
• PCAC yielded an expression for the pseudoscalar
  more than 30 years ago
• Modern chiral perturbation theories (ChPT),
  which are low-E effective QCD, reproduce
  the PCAC result in systematic expansions gP(q02)
  8.26 0.23
• Very recent progress in numerical lattice QCD
  calculations of form factors

83
Measuring gP

• The pseudoscalar form factor participates in any
  process involving the nucleons charged
  current, including
• beta decay
• neutrino scattering
• pion electroproduction
• muon capture
• Muon capture is the most attractive because of
  its
• large momentum transfer
• comparative ease of measurement
• model-independent connection to gP
• Muon capture offers a unique probe of the
  nucleons electroweak axial structure

n
W
p
84
PSI experimental hall facilities
Muon Source PSI accelerator (ring cyclotron)
generates 590 MeV proton beam (v
0.8c) protons strike a spinning graphite
target and produce pions pions decay to muons
Muon Beam Properties µ or µ selectable
Momentum 30-40 MeV/c Max intensity 50 kHz
85
PSI experimental hall facilities
86
Measuring gP via muon capture
Muon capture can take place in any nucleus, but
there are trade-offs involved...
Hydrogen
Z gt 1 nuclei
No nuclear environment
High capture rate
Low capture rate 10-3 of decay rate ?0 455 kHz
Complications from nuclear environment
Complications from muon kinetics
All-neutral final state
87
Capture experiments in H2 19601980
Bubble chambers
Neutron counters

• Observed 5.2 MeV final-state neutrons,
  absence of decay electrons
• Measured capture time distribution
• Limited by calibration efficiency of
  scintillating neutron detectors

• Observed 5.2 MeV final-state neutrons,
  absence of decay electrons
• Measured time-integrated capture rate
• Statistics limited

• E. Bleser et al., Phys. Rev. Lett. 8, 288 (1962)
• J.E. Rothberg et al., Phys. Rev. 132, 2664
  (1963)
• A.A. Quaranta et al., Phys. Rev. 177, 2118
  (1969)
• V.M. Bystritsky et al. Sov. Phys. JETP 39, 19
  (1974)

• R.H. Hildebrand, Phys. Rev. Lett. 8, 3437
  (1962)
• Bertolini et al. (1962)

88
Capture experiments in H2 1980s
Lifetime technique
The 1981 Saclay experiment used a novel approach
instead of directly observing capture events by
detecting final-state neutrons, they measured the
time spectrum of µ- decay electrons in liquid
hydrogen and compared it to the µ time spectrum.
G. Bardin et al., Nucl. Phys. A352, 365378 (1981)
89
Capture experiments in H2 RMC
Radiative muon capture (RMC) in hydrogen provides
yet another avenue
Variable momentum transfer ? more sensitive to
pion pole than ordinary muon capture (OMC)
Less sensitive to molecular effects than OMC
experiments
Branching ratio 108 (compared to OMC 103)
Only 1 RMC measurement to date 1996 TRIUMF
experiment counted photons with E gt 60 MeV
D. H. Wright et al., Phys. Rev. C 57, 373390
(1998)
90
Hydrogen target
Zgt1 Impurities
Deuterium

• Use bakeable TPC pressure vessel
• Pass H2 through palladium filter
• Use custom-built Circulating Hydrogen
  Ultra-high Purification System (CHUPS) to
  continuously clean H2, maintain impurity
  levels at 510-8

• Use deuterium-depleted H2 with cd 1.5 ppm
  (protium)
• More recently, a cryogenic system the
  Deuterium Removal Unit (DRU) was built to
  produce maintain deuterium levels at lt 6
  ppb (!)

CHUPS and DRU systems built by PNPI
Strategy
We cant eliminate gas impurities and molecular
effects, but we can minimize and characterize
them, and then perform small corrections to the
measured lifetime.
91
Time Projection Chamber (TPC)
x
y,t
muon stop (Bragg peak)
z
y,t
muon entrance (low energy loss)
92
Lifetime spectrum

• The signal-to-background ratio of the lifetime
  histogram is enhanced by
• imposing a 25 µs separation between muon
  arrivals
• requiring coincident hits in all 3 electron
  detectors
• imposing an impact cut on the muon/electron
  vertex

93
Hydrogen target
tµ
tµ