The Muon:A Laboratory for Particle Physics

B.L. Roberts
Department of Physics
Boston University
roberts @bu.edu
http://physics.bu.edu/roberts.html
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Outline• Introduction to the muon
• Selected weak interaction parameters• Magnetic and electric dipole moments• Lepton Flavor Violation• Summary and conclusions.

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The Muon: Discovered in 1936

Discovered in cosmic rays bySeth Neddermeyer and Carl
AndersonB. Lee Roberts, Kyoto University - 19 July 2006

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Confirmed by Street and Stevenson

It interacted too weakly with matter tobe the “Yukawa” particle which waspostulated to carry the nuclear force
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The discovery of the muon was a
big surprise…
• Lifetime ~2.2 µs, practicallyforever• 2nd generation lepton• mµ/me= 206.768 277(24)• produced polarized– in-flight decay: both “forward” and“backward” muons are highlypolarized• Paul Scherrer Institut
has 108 µ/s in a beam

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Death of the Muon
• Decay is self analyzing

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What have we learn from the µ’s death?
• The strength of the weak interaction– i.e. the Fermi constant GF (more properly Gµ)• The fundamental nature of the weakinteraction– i.e. is it scalar, vector, tensor,pseudo-scalar, pseudo-vector or pseudo-tensor?

• Lepton flavor conservation in µ-decay• VEV of the Higgs field:• Induced form-factors in nuclear µ-capture
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A precise measurement of τµ+ leads to a precise
determination of the Fermi constantGF

from radiative corrections
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δ

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τµ helped predict the mass of the top quark

+
µe+
W
νµ+νe

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τµ helped predict the mass of the top quark

t+
µe+
WbW++

νµνe

Predictive power in weak sector of SM. Difference
between the charged current
and neutral current
propagators
The radiative correction
shown above depends on mt2. Comparisons ofcharged, vrs. neutral currents gives information on mt.
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The Electro-Weak Working Group Fits:

PredictedFm
rf o

Input: GF (17 ppm),
α (4 ppb at q2=0),αMZ (23 ppm),

G

Measured:

The µLan experiment at PSI will accumulate 1012 µ-decays andmeasure Gµ to ~1 ppm. If LHC provides a Higgs Mass, then theprecision of the confrontation with the SM will greatly improve
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The Weak Lagrangian (Leptonic Currents)• Lepton current is (vector – axial vector) “(V – A)”• It might have been: V±A or S±V±A or most general
form:
Scalar ± Vector ± Weak-Magnitism± PseudoScalar ± Axial-Vector ± Tensor
There have been extensive studies at PSI by Gerber,
Fetscher, et al. to look for other couplings in muon decay.
Search continues with TWIST at TRIUMF.
At present, none have been found.
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If the Strong Interaction is Present• Then we have a more general current, which inprinciple can have 6 induced form factors inthe current.

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Leptonic and hadronic currents• For nuclear µ− capture (and also in β-decay) there
are induced form-factors and the hadronic V-A
current contains 6 terms.
– in µ capture the induced pseudoscaler term becomes
importantβ - decay

vectorweak magnitism

scalar

2nd classaxial vector

pseudoscalar

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tensor- p. 15/52

The Muon Trio:• Muon Magnetic Dipole Momoment aµ chiral changing• Muon EDM

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The Muon Trio:• Muon Magnetic Dipole Momoment aµ chiral changing• Muon EDM• Lepton Flavor Violation
~
χi0-

µq~
lj~lj

-eq

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Magnetic Moments (Field started by Stern)(in modern language)(and in English)

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Dirac Equation Predicts g=2

Non-relativistic reduction of the
Dirac Equation for an electron in aweak magnetic field.

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Schwinger

Dirac + PaulimomentB. Lee Roberts, Kyoto University - 19 July 2006

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Radiative corrections change gγµg=2 +

DiracDiracStern-Gerlachαπγµ∗µ2∗αµ + c2µ∗γ(π )µKuschand Foley,
Schwinger
Schwinger,
1947
Kusch-Foley

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γ..
∗+µe−γ e+ γ

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The SM Value for electron and muon anomalies
e*,e,e,e,e,e,e,e,e,e,e,e vrs. µ : relative contribution of heavier things
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aµ is sensitive to a wide range of new physics• substructure• SUSY (with large tanβ )• many other things (extra dimensions, etc.)
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We measure the difference frequency
between the spin and momentum precession

With an electric quadrupole field for vertical focusing

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Experimental TechniqueπProtons(from AGS)

Pions−~ 77 mmxc =µ νµ−~ 10 mrad
β=Inflector

B dl ~= 0.1 Tmv
B

p=3.1GeV/c(1.45T)

Target• Muon polarization• Muon storage ring• injection & kicking• focus by Electric Quadrupoles• 24 electron calorimeters

Injection orbit
Central orbit
KickerStorage
Modulesring
R=711.2cm
d=9cm

Electric Quadrupoles
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βRRxc
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muon (g-2) storage ring

Muon lifetimetµ = 64.4 µs(g-2) periodta = 4.37 µs

Cyclotron period

tC = 149 ns

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Detectors and vacuum chamber

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We count high-energy electrons as afunction of time.

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The ± 1 ppm uniformity in the average field
is obtained with special shimming tools.
inner coil thermal
insulation

We can shim thedipole,quadrupole
sextupole
independently

dipole correction coilwedge

YOKEpole piecepole
fixedbumpNMRprobes
beam
regionprogrammablecurrent sheet

outercoils

0.5 ppm
contours

inner coilg−2 Magnet in Cross Section

ρ = 7112 mm

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The magnetic field is measured and controlled using
pulsed NMR and the free-induction decay.
• Calibration to a sphericalwater sample that ties thefield to the Larmor frequencyof the free proton ωp.
• So we measure ωa and ωp

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When we started in 1983, theory andexperiment were known to about 10 ppm.
µ+CERNCERN µ−(9.4 ppm)

Theoryuncertainty was~ 9 ppm(10 ppm)

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−11X 10116 595 000

116 594 000

aµ116 593 000

116 591 000
Theory116 592 000

Experimental
uncertainty was
7.3 ppm

116 590 000~1983- p. 31/52

E821 achieved 0.5 ppm and the e+e- based theory isalso at the 0.6 ppm level. Both can be improved.
All E821 results
were obtainedwith a “blind”
analysis.

world average

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To compare with theory, there are two hadronic
issues:• Lowest order hadroniccontribution• Hadronic light-by-light≈

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Lowest Order Hadronic from e+e- annihilation

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Two experiments at the Budker Insitute at Novosibirsk
have measured R(s) to better than a percent.
CMD-2

SND

1994-1995
114k π+π1996
4k π+π-

95,98

1997
33k π+π-9697

ρ−ω mesoninterference

98,2000
96,98

1998~1M π+π2000~2M π+π-

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R(s) measurements at low s
Babar/Belle (ISR)
KLOE (ISR)

VEPP-2000
VEPP-2M

At low s the cross-section is measured independently for each final
state
from Davier/Höcker
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Summary of muon (g-2) (from M. Davier at LM06)aµ [exp] – aµ [SM]=(25.4 ± 8.8) × 10 –10¨ 2.9 „standard deviations“
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Electric and Magnetic Dipole Moments
Phys. Rev. 78 (1950)

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Transformation Properties of Electric and Magnetic Dipole Moments

An EDM implies both P and T are violated. An EDM ata measureable level would imply non-standard modelCP.
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However, it should be emphasized thatwhile such arguments are appealingfrom the point of view of symmetry,
they are not necessarily valid.
Ultimately the validity of all such
symmetry arguments must rest on
experiment.

N.F. Ramsey,Phys. Rev. 109, 225 (1958)

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Present EDM Limits
Particle

Present EDM limit

SM value(e-cm)(e-cm)

n3 x 10-26 (90%CL)

10-32 to 10-31

e-1.6 x 10-27 (90%CL)< 10-41µ199Hg< 10-38

2.1 x 10-28 (95%CL)*not yet final
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e EDM (e.cm)
10-22
10-24
10

n-26

199
10-28 Hg

MultiHiggs

MSSM
φ~1
Left MSSM
Right
φ ~ α/π

10-30
10-32

Excluded region(Tl atomic beam)Commins (2002)de < 1.6 x 10-27e.cm
E. Hinds’ e-EDM
experiment
at Imperial Collegewith YbF molecules
is starting
to explore this region

10-34
10-36

Standard Modelwith thanks to Ed Hinds

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Muon EDM: Naïve scaling would imply that

but in some models the dependence is greater.

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Spin Frequencies: µ in B field with MDM & EDM

0spin
difference
ThemotionalE - field, frequency = ωs - ωcβ X B, is much stronger
than laboratory electric(not to scale)fields (~GV/m).
The EDM causes thespin to precess outof plane.

ωωaBωη

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βx B- p. 45/52

Dedicated EDM Experiment0
Use a radial E-field to turn off the ωa precession(not to scale)ωWith ωa = 0, the EDM causes
ωa the spin to steadily
precess out of the plane.
ωηωη

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B
βx B
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“Frozen spin” technique• Turn off the (g-2) precession with radial E• Look for an up-down asymmetry building up with timeEµ+v+µB0(a)

E+µθ

2θ

B
12Time [arb.]

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Lepton Flavor Violation (the transition moment)• The standard-model gauge bosons do not permit
leptons to mix, but new physics at the TeV scale such
as SUSY does.
~χi0-µ~lj~ljqB. Lee Roberts, Kyoto University - 19 July 2006

e-q
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SUSY connection between aµ , Dµ , µ → eµ→eMDM, EDM~µ~µ~µ~eµµµe~B~
B

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Branching Ratio Limit

Past and Future of LFV Limitsµ+e-→µ-e+

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MEG Experiment (@PSI)

Discovery Potential:µ+ → e+ γSingle event sensitivity ~ 1 X 10-13
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Summary and Outlook• The muon has provided us with much knowledge on how
nature works.
• New experiments on the horizion continue this tradition.
• Muon (g-2), with a precision of 0.5 ppm, has a 2.9 σdiscrepancy with the standard model.
– Upgrade, E969 waits for funding decision in 10/06• This new physics, if confirmed, would show up in an EDM andperhaps LFV as well.
• MEG is set to turn on and collect data in the next year.
• Muon-electron conversion holds the best experimental
prospect for going much further on LFV.

• There is plenty of room for new surprises!
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µ → e γ branching ratio (typical example)
SUSY seesaw modelJ.Hisano and D.Nomura,2000

SU(5) and SO(10) SUSY GUTK.Okumura

MEGASO(10)SU(5)

Right-handed selectron mass

The branching ratio can be large
in particular for SO(10) SUSY GUT model.

Right-handed neutrino mass

thanks to Y. Okada- p. 54/52

B. Lee Roberts, Kyoto University - 19 July 2006

Comparison of three muon processes in various new physics
modelsSUSY
GUT/Seesaw

B( µ→e γ ) >> B(µ→3e) ~SUSY withlarge tan βµ→e conv. can be enhanced. Z-dependence in µ→econv. branching ratio.

Triplet Higgsfor neutrino

B(µ→3e) > or ~ B(µ→eg) ~B(µA→eA)

RL modelB(µ→3e) >> B(µ→eg) ~B(µA→eA)
Asymmetry in µ→3e

RPV SUSY

Various patterns of branching ratios andasymmetries

B(µA→eA)

Various asymmetries in polarized µ decays.

want to measure all three LFV processes to disentangle the models
thanks to Y. Okada- p. 55/52

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µLan @ PSI aims for a factor of 20improvement

Fit to 2004 data set,σstat ≈ 8.2 ppm

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Recent Developments:
The induced pseudoscalar coupling in nuclear µ -capture

further enhanced in radiative muon capture (RMC).
TRUIMF experiment saw a 3σ discrepancy with
PCAC prediction.
A new ordinary muon capture (OMC) experiment at
PSI, MuCap, hopes to resolve this 3 σ discrepancy.

γHowever, a new TRIUMF measurement of the atomic“ortho to para transition rate” seems to remove
much of this problem.
Clark, et al., PRL 96, 073401 (2006)
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Muonium

Hydrogen (without the proton)
Zeeman splittingµµ/µp= 3.183 345 24(37) (120 ppb)

where µp comes from proton NMR in the same B field
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Pion formfactor (CMD-2)

published

Analysis finished.
Not published yet.

Systematic error
ρ−ω interference
0.7%
0.6% (95)/ 0.8% (98) from:
1.2-4.2%I Logashenko
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Implications for aµ
Davier,Marciano-2004:∆aµ = (23.9 ± 7.2had,LO ± 3.5other ± 5.8exp)·10−10• 0.610<√s<0.960 GeV
CMD-2 (95):379.7 ± 2.6 ± 2.3 (3.5)

CMD-2 (98):374.3 ± 1.8 ± 3.0 (3.5)

CMD-2 (comb): 377.05 ± 2.2 ± 1.5 (2.7)
SND:

376.7 ± 1.3 ± 4.9 (5.1)

KLOE:

375.6 ± 0.8 ± 4.9 (5.0)

aµ(had;0.6<√s<1.0 GeV)

S.Eidelman, private communicationfrom I. Logaseheko
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a(had) from hadronic τ decay?

• Assume: CVC, no 2nd-class currents, isospin breaking
corrections.
– e+e- goes through neutral ρ– while τ-decay goes through charged ρ• n.b. τ decay has no isoscalar piece, e+e- does
• Many inconsistencies in comparison of e+e- andτ decay:

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Testing CVC with one number
Infer τ branching fractions (more robust than spectral functions) from e+e– data:

Difference: BR[τ ] – BR[e+e – (CVC)]:Mode∆(τ – e+e –)`Sigma‘τ – → π – π 0 ντ

+ 0.92 ± 0.21

4.5

τ – → π – 3π 0 ντ

– 0.08 ± 0.110.7

τ – → 2 π – π + π 0 ντ

+ 0.91 ± 0.25

3.6

ee data on π – π + π 0π 0 not satisfactoryfrom Michel Davier
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τ – → π –π 0ντ: preliminary results from BELLE• preliminary results from BELLE on τ ππ spectral function presented at EPS 2005
• high statistics: see dip at 2.4 GeV2 for first time in τ data
• discrepancies with ALEPH/CLEO at large mass and ee data at low mass

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The use of τ-decay is in question• Until the discrepancies between the individualτ data sets can be resolved, and CVC can beshown to hold independently it’s clear that
only the e+e- data can be used to determineaµ(had)¾The agreement between SND and CMD-2 invalidates

the use of τ data until a better understanding of thediscrepancies is achieved (an interesting question assuch)
Michel Davier at Lepton Moments, June 2006
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Model calculations of µ EDMµ EDM may be enhanced
above mµ/me × e EDM

Magnitude increases withmagnitude of ν Yukawa couplings
and tan βµ EDM greatly enhanced
when heavy neutrinosB.non-degeneratefrom John Ellis
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aµ implications for the muon EDMFeng et al.

Old E821
bounds−93(1) X 10+ 2σ−+ 1σ−B. Lee Roberts, Kyoto University - 19 July 2006

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Future Experiments:• MECO Experiment @ BNLµ- + N → e- + N– 10-17 single event sensitivity

mu2e @ FNAL???

EM calorimeter

straw trackerµ- stopping target
protonbeamπ-/µ- collection
solenoid

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Future Experiments:• MECO Experiment @ BNLµ- + Ne- + N→– 10-17 single event sensitivity

Cancelled• MEG Experiment @PSIµ+ → e+ γ– Under Construction Data Begins in 2006

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Comparison of three processes

If the photon penguin process dominates, there are simple relations among
these branching ratios.

This is true in many, but not all SUSY modes.

thanks to Y. Okada- p. 74/52

B. Lee Roberts, Kyoto University - 19 July 2006

LFV Experiments:• MECO Experiment @ BNLµ- + Ne- + N→
– 10-17 single event sensitivity

Cancelled• MEG Experiment– Under Construction Data Begins in 2006

• PRISM-PRIMEµ- + N → e- + N– LOI to J-PARC FFAG under construction– 10-18 – 10-19 single event sensitivity
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