arXiv:nucl-ex/0404013v1 8 Apr 2004

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PAST, PRESENT AND FUTURE OF MUONIUM

KLAUS P. JUNGMANN
Kernfysisch Versneller Instituut
Rijksuniversiteit Groningen
Zernikelaan 25,
Groningen, 9747 AA, The Netherlands
E-mail: jungmann@KVI.nl
Muonium, the atom which consists of a positive muon and an electron, has been
discovered by a team led by Vernon W. Hughes in 1960. It is in many respects themost ideal atom available from nature. Due to the close confinement in the boundstate muonium can be used as an ideal probe of electro-weak interaction, including
particularly Quantum Electrodynamics, and to search for additional yet unknown
interactions acting on leptons. Recently completed experiments cover the groundstate hyperfine structure, the 1s-2s interval and a search for spontaneous conversionof muonium to antimuonium. The experiments yield precise values for the finestructure constant, the muon mass and its magnetic moment. The results fromthese precision measurements have provided restrictions for a number of theories
beyond the Standard Model of particle physics. Future precision experiments will
require new and intense sources of muons.

1. Muonium - The Atom discovered by Vernon Hughes
Atomic hydrogen is generally considered the simplest and most fundamental
atom in nature. Its role in development of modern physics is outstanding.
Our physical picture of atoms, the success of quantum mechanics and thestart of quantum field theories such as Quantum Electrodynamics (QED)
are just a few examples for insights which go back to careful analysis ofwhat had been observed in this atom. Hydrogen has been exploited innumerous precision measurements to determine fundamental constants andto reconfirm fundamental concepts such as, e.g. the equality of the electron
and proton charge units.
Unfortunately, the presence of the proton as the nucleus in this one electron atom reduces the possibilities for a complete theoretical description.
Precise measurements are at present orders of magnitude more accurate
than calculations can be performed. Proton properties such as its meansquare charge radius or its magnetic radius or even the dynamics of the1

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2 P3/22

2 S1/2F=2
F=174 MHz10922 MHz

F=1
558 MHz

1047 MHzF=0
λ= 244nm

F=1
187 MHz

22P1/2F=0

2 455 THz
λ= 244nm

F=1
2

1 S1/24463 MHz

F=0

Figure 1. Energy levels of the hydrogen-like muonium atom for states with principal
quantum numbers n=1 and n=2. The indicated transitions could be induced to date bymicrowave or laser spectroscopy. High accuracy has been achieved for the transitions
which involve the ground state. The atoms can be produced most efficiently for n=1.

charge and spin carrying constituents inside the proton are not known tosufficient accuracy.
High energy scattering experiments have shown for leptons no structure
down to dimensions of 10−18 m. They may therefore be considered ”pointlike”. As a consequence, complications as those arising from the structureof the nucleus in natural atoms and such artificial systems that containhadrons are absent in the muonium atom (M = µ+ e− ), which is the boundstate of two leptons, a positive muon (µ+ ) and an electron (e) 1,2 . It may
be considered a light hydrogen isotope.
The dominant interaction within the muonium atom (see Fig. 1) is electromagnetic. In the framework of bound state Quantum Electrodynamics(QED) the electromagnetic part of the binding can be calculated to sufficiently high accuracy for modern high precision spectroscopy experiments.
There are also contributions from weak interactions arising through Z 0 boson exchange and from strong interactions owing to vacuum polarization

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loops containing hadrons. The corresponding energy level shifts can beobtained to the required level of precision using standard theory. Precision experiments in muonium can therefore provide sensitive tests of theStandard Model of particle physics and sensitive searches for new and yet
unknown forces in nature become possible. Parameters in speculative theories can be restricted. In particular, such speculations which try to expand
the Standard Model in order to gain deeper insights into some of its notwell understood features, i.e. where the standard theory gives well a fulldescription, but lacks a fully satisfactory explanation of the observed facts.
In addition, fundamental constants like the muon mass mµ , its magnetic
moment µµ and magnetic anomaly aµ and the fine structure constant α
can be measured precisely by muonium spectroscopy.
In 1960 a team led by Vernon W. Hughes has observed the muonium
atom for the first time 3 . The details of the exciting circumstances aroundthis discovery and the research in the early years are described in thisvolume by an eye witness, Richard Prepost 4 . They are also available fromthe viewpoint of the leader, Valentin Telegdi, of the very group, which wascompeting in muonium research with the Yale team of Vernon Hughes formore than a decade 5 .

2. Muonium Formation
In the early years muonium research concentrated on measurements thatwere possible with atoms created by stopping muons in a material andstudying them in this environment (see Fig. 2). Besides important workon condensed matter in the framework of muon spin rotation (µSR) there
were in particular precision experiments which concerned the ground state
hyperfine structure and a search for muonium-antimuonium conversion. In
the 1980ies the spectrum of possible experiments could be significantly expanded when methods where developed which allowed to have the atoms
in vacuum 1,2 .
All high precision experiments in muonium up to date atom have involved the 1s ground state (see Fig.1), in which the atoms can be producedin sufficient quantities. The most efficient mechanism is e− capture after
stopping µ+ in a suitable noble gas, where yields of 80(10) % were achieved
for krypton gas. This technique was used in the most recent precision measurements of the atom’s ground state hyperfine structure splitting ∆νHF S
and µµ at the Los Alamos Meson Physics Facility (LAMPF) in Los Alamos,
USA 6 .

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Methods of Muonium Production• Gas Stop
Kr, Arµ+
Yields up to 100%
Polarization up to 50% (B=0)
100% (B>>1T)µ++e−→Μ

foreign gas effects• Beam Foilµ+Muonium in Vacuo
n=2 state populated
fast muonium• SiO2 Powderµ+thermal Muonium in Vacuo
Yields up to 12%
Polarization 39(9)%

µ+

50%

µ+e−

1%

µ+e−e−

0.01%

keV energyMM(2s) /M(1s) < 10-4
velocity 1.5 cm/ τµFigure 2. Muonium atoms for precision experiments have been produced by three different methods. Stopping muons in a noble gas gives atoms at thermal energies which are
subject to collisional effects. Due to velocity a beam foil technique yields muonium atoms
in vacuum at keV energies. Muonium atoms diffuse at thermal velocities in vacuum after
being produced by muon stopping in a fluffy SiO2 powder.

Muonium at thermal velocities in vacuum can be obtained by stoppingµ+ close to the surface of a SiO2 powder target, where the atoms are formed
through e− capture and some of them diffuse through the target surface into
the surrounding vacuum. This process has an efficiency of a few percent andwas an essential prerequisite for Doppler-free two-photon laser spectroscopyof the 12 S1/2 -22 S1/2 interval ∆ν1s2s at the Rutherford Appleton Laboratory(RAL) in Chilton, United Kingdom 7 , which yields an accurate value formµ .

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5Electromagnetic transitions in excited states, particularly the 22 S1/2 2 P1/2 classical Lamb shift and 22 S1/2 -22 P3/2 fine structure splitting could
be induced by microwave spectroscopy, too. Only moderate numbers of
atoms in the metastable 2s state can be produced with a beam foil technique. Because furthermore these atoms have keV energies due to a velocity
resonance in their formation, the experimental accuracy is now the 1.5 %level 8,9 , which represents not yet a severe test of theory.
2

3. Muonium Ground State Hyperfine Structure
3.1. The Last LAMPF Experiment
The most recent experiment at LAMPF had a krypton gas target inside ofa microwave cavity at typically atmospheric density and in a homogeneous
magnetic field of 1.7 T. Microwave transitions between the two energeticallyhighest respectively two lowest Zeeman sublevels of the n=1 state at thefrequencies ν12 and ν34 (Fig. 3) involve a muon spin flip. Due to parity
violation in the weak interaction muon decay process the e+ from µ+ decays
are preferentially emitted in the µ+ spin direction. This allows a detectionof the spin flips through a change in the spatial distribution of the decay e+ .
As a consequence of the Breit-Rabi equation, which describes the behaviourof the muonium ground-state Zeeman levels in a magnetic field B, the sumof ν12 and ν34 equals at any value of B the zero field splitting ∆νHF S . For
sufficiently well known B the difference of these two frequencies yields themagnetic moment µµ . The latest LAMPF experiment 6 has utilized the

Figure 3.

The muonium ground state Zeeman splitting.

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technique of ”Old Muonium”, which allowed to reduce the line width of
the signals below half of the ”natural” line width ∆νnat = 1/(2πτµ ) (Fig.
4)12 , where τµ = 2.2µs is the muon lifetime. For this purpose an essentiallycontinuous muon beam was chopped by an electrostatic kicking device into
4 µs long pulses with 14 µs separation. Only decays of atoms which had
been interacting coherently with the microwave field for periods longer thanseveral muon lifetimes were detected. Here, the first quoted uncertainty is
due to the accuracy to

Figure 4. Samples of conventional and ”Old Muonium” resonances at frequency ν12 .
The narrow ”old” lines exhibit a larger signal amplitude. The signals were obtained withmagnetic field sweep (left column, magnetic field in units of proton NMR frequencies)
and by microwave frequency scans (right column).

The magnetic moment was measured to be µµ = 3.183 345 24(37) (120ppb) which translates into a muon-electron mass ratio µµ /me =206.768 277(24) (120 ppb). The zero-field hyperfine splitting is determinedto ∆νHF S (exp) = 4 463 302 765(53) Hz (12 ppb) which agrees well with theFebruary 4, 2008

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theoretical prediction of ∆νHF S (theo) = 4 463 302 563(520)(34)(<100) Hz(120 ppb).
which mµ /me is known, the second error is from the knowledge of aas extracted from Penning trap measurements of the electron magnetic
anomaly, and the third uncertainty corresponds to estimates of uncalculated higher order terms. Among the non-QED contributions is the strong
interaction through vacuum polarization loops with hadrons (250 Hz) anda parity conserving axial vector-axial vector weak interaction (-65 Hz).
For the muonium hyperfine structure the comparison between theory
and experiment is possible with almost two orders of magnitude higher
precision than for natural hydrogen because of the not sufficiently known
proton charge and magnetism distributions. The achieved – some six orders of magnitude higher – experimental precision in hydrogen maser experiments can unfortunately not be exploited for a better understanding offundamental interactions. Among the possible exotic interactions, which
could contribute to ∆νHF S , is muonium-antimuonium conversion 10 . Here,an upper limit of 9 Hz could be set from an independent experiment described in section 6.

Figure 5. The absence of a significant siderial oscillation confirms CPT invariance atthe best level tested for muons.

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3.2. Search for CPT violation
Recently, generic extensions of the Standard Model, in which both Lorentz
invariance and CPT invariance are not assumed, have attracted widespreadattention in physics.
Diurnal variations of the ratio (ν12 − ν34 )/(ν12 + ν34 ) are predicted (seeFig. 5). An upper limit could be set from a reanalysis of the LAMPF
data at 2 · 10−23 GeV for the Lorentz and CPT violating parameter. In
a specific model by Kostelecky and co-workers a dimensionless figure of
merit for CPT tests is sought by normalizing this parameter to the particle
mass. In this framework ∆νHF S provides a significantly better test of CPT
invariance than electron g-2 and the neutral Kaon oscillations11 .
3.3. The Fine Structure ConstantFine Structure Constant α

×10-5

R∞ & mn/h

Krueger et al.

R∞ & mn/h

601

Krueger et al.

Quant.Hall∆νHFS∼ α4 me/h c2 F()

Jeffery et al.

R∞ & mCs/h

Quant.Hall-1

α - 137.03

The hyperfine splitting is proportional to α2 · R∞ with the very precisely
known Rydberg constant R∞ . Comparing experiment and theory yields
α−1 = 137.035 996 3(80) (58ppb). If R∞ is decomposed into even more
fundamental constants, one finds ∆νHF S = α4 me /h. With h/me as de-Chu et al. prel.

Cage et al.

600(g-2) e(g-2) eKinoshita599∆νHFS∼ α2 R∞ 2F()(g-2) eacJosep. & γp

Kinoshita

Kinoshita

Williams et al.

HFS Muonium
Yale-Heidelberg

598
HFS Muonium

597

Figure 6.

Kinoshita

1990

1992

1994

1996

1998

2000

2002

2004

year

Various determinations of the fine structure constant α.

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termined in measurements of the neutron de Broglie wavelength we have
α−1 = 137.036 004 7(48) (35 ppb). In the near future a small improvementin this figure can be expected from ongoing determinations of h/me in measurements of the photon recoil in Cs. A better determination of the muon
mass, e.g. will result in a further improvement and may contribute to resolving the situation of various poorly agreeing determinations of the finestructure constant, which is important in many different fields of physics.
It should be mentioned that the present agreement between α as determined from muonium hyperfine structure and from the electron magnetic
anomaly is generally considered the best test of internal consistency of
QED, as one case involves bound state QED and the other one QED of freeparticles.

3.4. Future Possibilities for ∆νHF S
The results from the LAMPF experiment are mainly statistics limited andimprove the knowledge of both ∆νHF S and µµ by a factor of three overprevious measurements. This gain could be significantly surpassed withan experiment based on the ”Old Muonium” technique at a future highflux muon source (see section 7). As a useful starting point one would liketo have 5 · 108 µ+ /s at below 28 MeV/c momentum with typically 1 %momentum width. The beam should be pulsed with 1µs wide pulses of up
to several 10 kHz repetition frequency. One can expect that theory will
be continuously improved to allow the extraction of fundamental physics
information from a precision experiment13 .

4. Muonium 1s-2s Two-photon Spectroscopy
In muonium the 1s-2s energy difference is essentially given by the relevant
quantum numbers, R∞ and a reduced mass correction. Therefore, thistransition may be regarded ideal for a determination of the muon-electronmass ratio. QED corrections are well known for the needs of presently
possible precision experiments and do not play an important role here.
Doppler-free excitation of the 1s-2s transition has been achieved in pioneering experiments at KEK 14 and at RAL 15 . In all these experiments
two counter-propagating pulsed laser beams at 244 nm wavelength were
employed to excite the n=2 state. The successful transitions were thendetected by photo-ionization with a third photon from the same laser field.
The released µ+ was then registered on a micro-channel plate detector.

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Events per Laser Pulse [10 ]

10

1.4
1.2
1

Muonium

Signal

F=1 → F=1

Theory

0.8
0.6
0.4
0.2
0
640

660

680

700

720

νLaser-νIodine [MHz]Figure 7. Muonium 1s-2s signal. The frequency corresponds to the offset of theTi:sapphire laser from the iodine reference line. The open circles are the observed signal,
the solid squares represent the theoretical expectation based on measured laser beam
parameters and a line shape model.

4.1. The recent RAL Experiment
The accuracy of the early measurements was limited by the ac-Stark effect and rapid phase fluctuations (frequency chirps), which were inherent properties of the necessary pulsed high power laser systems (see Fig.
8). The key feature for the latest high accuracy measurement at RAL
was a shot by shot recording of the spatial laser intensity profile as wellas the time dependences of the laser light intensity and phase. This together with a newly developed theory of resonant photo-ionization 16 allowed a shot-by-shot prediction of the transition probability as a basis forthe theoretical line shape (Fig. 7). The latest RAL experiment 7 yields∆ν1s2s (exp)= 2 455 528 941.0(9.8) MHz in good agreement with a theoretical value ∆ν1s2s (theo)=2 455 528 935.4(1.4) MHz 17 . The muon-electronmass ratio is found to be mµ+ /me− = 206.768 38(17).
Alternatively, with mm+ /me− as extracted from ∆νHF S , a comparison of experimental and theoretical values for the 1s-2s transition canbe interpreted in terms of a µ+ – e− charge ratio, which results as
qm+ /qe− + 1 = −1.1(2.1) · 10−9 . This is the best verification of chargeFebruary 4, 2008

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ν1s2s - 2 455 520 000 [MHz]

11

9100
9000

HORSSY
V. Meyer et al

HORSSY

8900

TheoryF. Maas et al.

HORSSYK. Pachucki
S. Karshenboim

K. Jungmann et al.

8800
KEK
K. Danzmann et al.

8700
8600

KEK
S. Chu et al.

8500
1988

1990

1992

1994

1996

1998

2000

year
Figure 8. Evolution of muonium 1s-2s measurements. The two results labeled KEK accelerator facility refer to one single measurement by a Japanese - American collaborationand its reanalysis. The newer measurements were made by the Heidelberg - Oxford Rutherford - Sussex - Siberia - Yale collaboration and have reached a level of accuracy
comparable to theory, where the limitation arises primarily to the muon mass.

equality in the first two generations of particles. The existence of one single universal quantized unit of charge is solely an experimental fact andno underlying symmetry could yet be revealed. The interest in such a
viewpoint arises because gauge invariance assures charge quantization only
within one generation of particles.
4.2. Slow Muons from Muonium Ionization
A new development aims at providing low energy (<1 eV energy spread)muons for condensed matter research. At RIKEN-RAL facility a new muonsource is being set-up which bases on the laser photo-ionization of muonium.
The atoms are produced from hot metal foils which they leave at thermalvelocities. The ionization process involves one-photon excitation of the 1s2p transition and subsequent ionization with a second laser. At present theyield is a few µ+ /s. 18

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4.3. Future Muonium Laser Spectroscopy
Major progress in the laser spectroscopy of muonium can be expected from acontinuous wave laser experiment, where frequency measurement accuracy
does not present any problem because light phase fluctuations are absent.
For this an intense source of muons will be indispensable (see section 7).
which provides at least a factor of 1000 higher flux of (pulsed) surface
muons. As a promising starting point one would like to have a pulsed
beam 5 · 108 µ+ /s below 20 MeV/c with typically 3 % momentum widthand about 100 Hz repetition rate.
5. Muonium and the Muon Magnetic Anomaly
The muon magnetic anomaly aµ (see contributions by Francis Farley and
Ernst Sichtermann to this volume 19 ) is given, like in case of the electron,
mostly by virtual photon and electron-positron fields. However, the effectsof heavier particles can be enhanced by the square of the muon - electronmass ratio mµ /me ≈ 4 · 104 .
At the level of present experimental accuracy there are contributions to
the muon magnetic anomaly which are absent in the electron case. For themuon the contributions of the strong interaction, which come in throughvacuum polarization loops with hadronic content, can be determined using
a dispersion relation and the input from experimental data on e+ -e− annihilation into hadrons and hadronic τ -decays. They amount to 58 ppm. The
weak interactions contributing through W or Z boson exchange give a 1.3
ppm correction. At present standard theory yields aµ to about 0.7 ppm.
Contributions from physics beyond the Standard Model could arise from,e.g., supersymmetry, compositeness of fundamental fermions and bosons,
CPT violation and many other sources. They could be at the ppm level.
The experimental values for the magnetic anomaly of µ+ and µ havebeen determined very recently by a collaboration headed by Vernon Hughesat the Brookhaven national Laboratory (BNL). It is a ”g-2” experiment inwhich the difference of the spin precession and the cyclotron frequencies
is measured. The experimental results for muons of both sign of electriccharge are accurate to 0.7 ppm and agree well. Assuming CPT invariancethey yield a combined value of aµ to 0.5 ppm 20 . At this time it is unclear,whether there is a small difference between theory and experiment at thelevel of 2 to 3 standard deviations due to unresolved issues in the theory of
hadronic corrections.

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Figure 9. The spectroscopic experiments on the hyperfine structure of muonium andthe 1s-2s energy interval are closely related to a precise measurement of the muon muon
magnetic anomaly. The measurements put a stringent test on the internal consistency of
the theory of electroweak interaction and on the set of fundamental constants involved.

The microwave and laser spectroscopy of muonium are closely related
to the measurement of the muon magnetic anomaly. The fundamental constants such as mµ , µµ , α and qµ+ /qe− are indispensable input for the theory
and the experiment on aµ . It should be noted that prior to a future significant experimental improvement of aµ , such as planned at the Japanese
J-PARC accelerator complex 21 , an improvement in the knowledge of muon
related fundamental constants would be required. Muonium spectroscopy
offers a clean way to obtain them.
6. Muonium-Antimuonium Conversion
In addition to the indirect searches for signatures of new physics in the muon
magnetic anomaly and in electromagnetic interactions within the muonium
atom the bound state offers also the possibility to search more directly forpredictions of speculative models.

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+

p
p
p
p
p

e

p
p
p

++

p
p


e+

(a)

+

p
p
p
p
p

e

p
p
p
p
p

(c)

N

e+

j  j

+
e

L

p

p

p

WR

+

p

p

p

p

p

p

p

p

p

p

p

p

p

p
p
p
p

e

p

p

p

R

p

p

p

p

W

p

p

p

L

p



p

p

j e jL

R
(b)

p

p
p
p
p
p

X ++


e+

e+

(d)

Figure 10. Muonium-antimuonium conversion in theories beyond the standard model.
The interaction could be mediated by (a) a doubly charged Higgs boson ∆++ , (b) heavy
Majorana neutrinos, (c) a neutral scalar ΦN , e.g. a supersymmetric τ -sneutrino ν̃τ , or(d) a bileptonic gauge boson X ++ .

The process of muonium to antimuonium-conversion (M-M)violates additive lepton family number conservation. It would be an analogy in the
lepton sector to the well known K 0 -K 0 and B 0 -B 0 oscillations in the quark
sector. Muonium-antimuonium conversion appears naturally in many theories beyond the Standard Model. The interaction could be mediated,e.g., by a doubly charged Higgs boson ∆++ , Majorana neutrinos, a neutral
scalar, a supersymmetric τ -sneutrino , or a doubly charged bileptonic gaugeboson.
There have been a number of attempts to observe M-M conversion. The
pioneering work was again performed by a group guided by Vernon Hughes
already in the 1960ies 22 . The early experiments 22,23 relied on the X-rays
which would follow a µ− -transfer to a heavy element upon contact of M
with matter as part of their signature. A breakthrough was the availabilityof thermal muonium in vacuum 24 which led to a significant increase insensitivity 25 .
6.1. The latest M-M Experiment at PSIAt PSI an experiment was designed to exploit a powerful new signature,
which requires the coincident identification of both particles forming theanti-atom in its decay 10 . The technique had been pioneered by an international collaboration led by Vernon Hughes at LAMPF 25 .
Thermal muonium atoms in vacuum from a SiO2 powder target, are observed for decays. Energetic electrons from the decay of the µ− in the atom

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pump
iron
MCP
CsI

+

magnetic field coils
hodoscope
MWPC
annihilation
beam counter photons
SiO2-targeteacceleratorironcollimator

+

µ

1m
Figure 11.

separatore

The Muonium-Antimuonium Conversion Spectrometer at PSI.

can be identified in a magnetic spectrometer (Fig. 11). The positron in theatomic shell of M is left behind after the decay with 13.5 eV average kinetic
energy. It has been post-accelerated and guided in a magnetic transportsystem onto a position sensitive micro-channel plate detector (MCP). Annihilation radiation can be observed in a segmented pure CsI calorimeteraround it. The decay vertex can be reconstructed. The measurements were
performed during a period of 6 months in total over 4 years during which
5.7 · 1010 muonium atoms were in the interaction region. One event fellwithin a 99% confidence interval of all relevant distributions. The expectedbackground due to accidental coincidences is 1.7(2) events (Fig. 12). Depending on the interaction details one has to account for a suppression of theconversion in the 0.1 T magnetic field in the spectrometer. This amounts
maximally to a factor of about 3 for V±A type interactions. Thus, theupper limit on the conversion probability is 8.2 · 10−11 (90% C.L.). The
coupling constant is bound to below 3.0 · 10−3 GF , where GF is the weakinteraction Fermi coupling constant.
This new result, which exceeds limits from previous experiments by afactor of 2500 and one from an early stage of the experiment by 35, has

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Rdca [cm]Rdca [cm]

16

2.5

5
2.5

0

0

-2.5

-2.5

-5

-5

-20

-10

0

10

20

TOF - TOFexpected [ns]

-20

-10

0

10

20

TOF - TOFexpected [ns]Figure 12. Time of Flight (TOF) and vertex quality for the final 4 month of integrated
search data for antimuonium (left) and for a single 20 minutes measurement of muonium (right). In the antimuonium case one event falls into the indicated area, whichcorresponds to 3 standard deviations for the parameters of an expected antimuonium
signature, which were calibrated with muonium decays when all electro-magnetic fields
in the apparatus were reversed.

some impact on speculative models. For example: A certain Z8 model isruled out. It had more than 4 generations of particles and where masses
could be generated radiatively with heavy lepton seeding. A new lower limitof 2.6 TeV/c2 × g3l (95% C.L.) on the masses of flavour diagonal bileptonic
gauge bosons in GUT models is extracted, which lies well beyond the value
derived from direct searches, measurements of the muon magnetic anomaly
or high energy Bhabha scattering. Here, g3l is of order unity and depends
on the details of the underlying symmetry. For 331 models the experimental
result can be translated into 850 GeV/c2 × g3l which excludes some of theirminimal Higgs versions, where an upper bound of 600 GeV/c2 has been
extracted from an analysis of electro-weak parameters. The 331 models
need now to refer to a less attractive and more complicated extensions.
In the framework of R-parity violating supersymmetry the bound on therelevant coupling parameters could be lowered by a factor of 15 to λ132 ·λ231 ≤ 3 · 10−4 for assumed super-partner masses of 100 GeV/c2 .
6.2. Future Possibilities for M-M Experiments
A future experiment to search for M-M conversion could particularly takeadvantage of high intensity pulsed beams. In contrast to other lepton (family) number violating muon decays, the conversion through its nature as

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particle-antiparticle oscillation has a time evolution in which the probability for finding a system formed as muonium decaying as M increases
quadratically in time. This gives the signal an advantage, which grows intime over exponentially decaying background. E.g., with a twofold coincidence as part of a signature: after a time ∆T = 2τµ beam related accidental
background has dropped by almost two orders of magnitude, whereas a MM-signal would not have suffered significantly at all. An almost ideal beamwould have 1 · 1010 µ+ /s at below 23 MeV/c with typically 1-2 % momentum width. The beam should be pulsed with up to 1µs wide pulses of up
to several 10 kHz repetition frequency.
Such efforts appear well motivated among other reasons through theconnection to numerous speculative models involving, e.g., lepton flavour
violation in general or a possible Majorana nature of the neutrinos 27 .

7. Future Possibilities for Fundamental Interaction
Research with Muons
It appears that the availability of particles limits at present progress in research with muonium. This includes better fundamental constants as wellas the possibility to find very rare processes and to impose significantly
improved limits in continuation of the search program of dedicated experiments.
Therefore significant measures to boost the muon fluxes at existing accelerator centers and to create future facilities with orders of magnitude
higher muon currents is indispensable prior to any significant progress. Thisrequirement matches well with the demand of several communities within
physics which request an intense particle accelerator. Such interest exists,e.g., worldwide for a Neutrino Factory and a Muon Collider 26 , in Japanfor the J-PARC facility and in Europe for EURISOL facility 28 . The perspectives for muonium research have beam worked out for such a scenario
in some detail 26 .
Examples of tailored intense muon sources at existing facilities are theπ −µ converter at PSI, the planned muon production of the planned MECO
experiment at BNL or the projected phase rotated intense source of muons(PRISM) 29 in connection with the upcoming J-PARC facility.
The design goal for such a new machine should be a minimum of 1 MW
proton beam on a production target. This could become a reality at various
places including BNL, CERN, GSI and J-PARC.

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Figure 13. Vernon W. Hughes keeping contact with his colleagues during the Lepton
Moments I conference in Heidelberg in 1999. Effective communication is a key to operate
simultaneously several challenging large experiments at different research centers aroundthe world.

8. Conclusions
More than 70 years after the muon was discovered 30 , its properties still
remain puzzling. The mysteries include not less than the reason for theFebruary 4, 2008

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muon’s existence, the size of its mass, its charge and the fact of lepton
number (and for charged species) lepton family number conservation. All
precision experiments to date have confirmed that the muon is a heavy copyof the ”point-like” electron. Standard theory appears to be an adequate
description of all measurements, although it cannot answer some of the
deeper questions.
Searches for a violation of the Standard Model were not blessed with asuccessful observation yet. However, both the theoretical and experimental
work in this connection have led to a much deeper understanding of particle
interactions. One special value of the precision experiments are their continuous contributions towards guiding theoretical developments by excluding
various speculative models. The research of Vernon Hughes has most significantly added to shaping our knowledge about nature in this way. Researchon muonium has contributed quite some essential facets to the picture offundamental particles and fundamental interactions in physics.
9. Final Remarksa

The author owes his heartily gratitude to Vernon Willard Hughes for along fruitful collaboration in the framework of a number of international
collaborations. The measurements we could carry out together all involvedmuons. In particular, many of them involved centrally the fundamental
atom we could find for our research:Thank You Vernon for introducing muonium to the scientific community.
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