B. Lee Roberts, College of William and Mary, 24 March 2006 - p. 1/61 The Muon: A Laboratory for...

B. Lee Roberts, College of William and Mary, 24 March 2006 - p. 1/61

The Muon: A Laboratory for Particle Physics

Everything you always wanted to know about the

muon but were afraid to ask.

B. Lee RobertsDepartment of Physics

Boston University

[email protected] http://physics.bu.edu/roberts.html

mailto:[email protected]


Outline

• Introduction to the muon• Selected weak interaction

parameters• Muonium• Lepton Flavor Violation• Magnetic and electric dipole

moments• Summary and conclusions.


The Muon: Discovered in 1936

Discovered in cosmic rays by Seth Neddermeyer and Carl Anderson


Confirmed by Street and Stevenson

It interacted too weakly with matter to be the “Yukawa” particle which was postulated to carry the nuclear force


The Muon’s Discovery was a big surprise

• Lifetime ~2.2 s, practically forever• 2nd generation lepton

• mme = 206.768 277(24)

I. I. Rabi


The Standard Model (Our Periodic Table)

Interact weakly through the

Leptons e e

Interact strongly through the gluons g

Electroweak gage bosons Z0 W±

Quarksu s t

d c b


Production of The Muon

• produced polarized from the death of a pion

For decay in flight, “forward” and “backward” muons are highly polarized.

It can be produced copiously in pion decaye.g. Paul Scherrer Institut has 108 /s in a beam


Death of the Muon

• Decay is self analyzing


What can we learn from the ’s death?

• The strength of the weak interaction– i.e. the Fermi constant GF

• The fundamental nature of the weak interaction– i.e. is it scalar, vector, tensor,

pseudo-scalar, pseudo-vector or pseudo-tensor?


from radiative corrections

A precise measurement of + leads to a precise determination of the Fermi constantGF


helped predict the mass of the top quark

Predictive power in weak sector of SM. Difference between the charged and neutral current propagator:

Top quark mass prediction: mt = 177 20 GeV Input: GF (17 ppm), (4 ppb at q2=0), MZ (23 ppm),

2004 Update from D0 mt = 178 4.3 GeV


Experiment at a glance

1. Collect handful of muons in a few s2. Turn off beam3. Watch them decay4. Repeat

e+

Time in target

Accum.Period

MeasurementPeriod


Lan @ Paul Scherrer Institut aims for a factor of 20 improvement on


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.

None were found


If the Strong Interaction is Present

• Then we have a more general current, which in principle can have all 6 of these components to the current.


Leptonic and hadronic currents• For nuclear capture (and also in -

decay) there are induced form-factors and the hadronic V-A current contains 6 terms.– the induced pseudoscaler term is important

2nd classvector weak magnitism scalar

axial vector pseudoscalar tensor


An Aside:

but stop the press! new measurement of the atomic “ortho to para transition rate” seems to remove much of this problem, Clark, Armstrong, et al., PRL 96, 073401 (2006)

The induced pseudoscalar coupling in -capture

further enhanced in radiative muon capture

A new experiment at PSI MuCap hopes to resolve the present 3 discrepancy with PCAC


Muonium + e- (not +-)Hydrogen (without the proton)

Named by Val Telegdi

discovered by Vernon Hughes


Muonium

Zeeman splitting

p = 3.183 345 24(37) (120 ppb)

where p comes from proton NMR in the same B field


muonium and hydrogen hfs → proton structure


Lepton Flavor

• Remember the puzzle with -decay?– it appeared that energy conservation

did not hold in the decay n → p + e- which should have a mono-energetic e+ in the final state.

e-


Lepton Flavor

• It took Pauli to propose that energy was conserved, but there was a new neutral particle emitted in the decay (named neutrino by Fermi), so the decay was a 3-body decay with a continuous spectrum.


Lepton Flavor

• We have found empirically that lepton family number is conserved in muon decay.– e.g.

• What about or


Lepton Flavor in Muon Decay

me = 0.511 MeV

mm = 104.7 MeV

Why don’t we see → e+ ? Neutrinos oscillate – however, the predicted

Standard Model Charged Lepton Flavor Violation unmeasureably small (from loops).

The standard model gauge bosons (interactions) do not permit lepton flavor-changing interactions, i.e. there is conservation of each lepton flavor separately.


SM charged leptons do not mix

• Expect charged lepton flavor to be enhanced if there is new dynamics at the TeV scale, in particular if there is Supersymmetry


In Standard Model we have:

antiparticles

particles

supersymmetric partners(spartners)

SUSY:

(with thanks to Bruce Winstein)


Supersymmetry Permits Charged Lepton Mixing

• In supersymmetry there is mixing between the charged sleptons

• Many people believe that SUSY is the new physics which will be found at LHC


Beyond the SM: The Muon Trio:• Lepton Flavor Violation

• Muon MDM (g-2) chiral changing

• Muon EDM


The First -N e-N Experiment Steinberger and Wolf

• After the discovery of the muon, it was realized it could decay into an electron and a photon or convert to an electron in the field of a nucleus.

• Without any flavor conservation, the expected branching fraction for +e+ is about 10-5.

• Steinberger and Wolf

looked for -N e-N for the first time, publishing a null result in 1955, with a limit Re < 2 10-4

Absorbs e- from - decay

Conversion e- reach this

counter

9”


The MECO Experiment

Muon Beam Stop

Superconducting Production Solenoid

(5.0 T – 2.5 T)

Superconducting Transport Solenoid

(2.5 T – 2.1 T)

Straw Tracker

Crystal Calorimeter

Muon Stopping Target

Superconducting Detector Solenoid

(2.0 T – 1.0 T)Collimators

10-17 BR single event sensitivity

p beam


Past and Future of LFV Limits

+e-→-e+

MEG → e – 10-13 BR

sensitivity• under

construction at PSI, first data in 2006

MECO ++A→e+

+A– 10-17 BR

sensitivity• Was approved

at Brookhaven, not funded

Bra

nchi

ng R

atio

Lim

it


Electric and Magnetic Dipole Moments

In 1950, Purcell and Ramsey propose to search for a neutron EDM to check parity violation

In 1957, Landau and Ramsey independently point out that an EDM violates both P and T


Electric and Magnetic Dipole Moments

Transformation properties:

An EDM implies both P and T are violated. An EDM at a measureable level would imply non-standard model CP. The baryon/antibaryon asymmetry in the universe, needs new sources of CP.


Present EDM Limits

Particle Present EDM limit(e-cm)

SM value(e-cm)

n

future exp

10-24 to 10-25

*projected


Magnetic Dipole Moments

The field was started by Otto Stern


Z. Phys. 7, 249 (1921)


(in modern language)


Dirac + Pauli moment


Dirac Equation Predicts g=2

• radiative corrections change g

Schwinger


The CERN Muon (g-2) Experiments

The muon was shown to be a point particle obeying QED (Quantum Electrodynamics)

The final CERN precision was 7.3 ppm


Standard Model Value for (g-2)

relative contribution of heavier things


Lowest Order Hadronic from e+e- annihilation

Cauchy’s theorem and the optical theorem


aμ is sensitive to a wide range of new physics

• muon substructure

• anomalous couplings• SUSY (with large tanβ )

• many other things (extra dimensions, etc.)


SUSY connection between a , Dμ , μ → e


Spin Precession Frequencies: in B field


If we use an electric quadrupole field for vertical focusing we get

0


Inflector

Kicker Modules

Storagering

Central orbitInjection orbit

Pions

Target

Protons

π

(from AGS) p=3.1GeV/c

Experimental Technique

π

μνS

Spin

Momentum

B

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

R=711.2cm

d=9cm

(1.45T)

Electric Quadrupoles

polarized


muon (g-2) storage ring


Detectors and vacuum chamber

Detector acceptance depends on radial position of the when it decays.


Where we came from:


Today with e+e- based theory:All E821 results were obtained with a “blind” analysis.


Can we do better and confront theory more strongly?

• With a 2.7 discrepancy, you’ve got to go further.

• A new upgraded experiment to go from ±0.5 ppm to ± 0.2 ppm was approved by the BNL PAC in September 2004

• It will be considered by the Particle Physics Project Prioritization Panel (P5) next Monday.


Courtesy K.Olivebased on Ellis, Olive, Santoso, Spanos

In CMSSM, a can be combined with b → s, cosmological relic density h2, and LEP Higgs searches to constrain mass

Allowedband a(exp) – a(e+e- theory)

Excluded by direct searches

Excluded for neutral dark matter

Preferred

same discrepancy no discrepancy

With expected improvements in ahad + E969 the error on the difference


aμ implications for the muon EDM


An EDM can also cause spin precession

The EDM causes the spin to precess out of plane.

The motional E - field, β X B, is much stronger than laboratory electric fields (MV/m)


Muon EDM• use radial E field to “turn off” g-2 precession

so the spin follows the momentum.• look for an up-down asymmetry which builds

up with time • Needs 1018 muons


Summary and Outlook

• The muon has provided us with much knowledge on how nature works. V-A, GF, induced weak couplings, lepton flavor

conservation, a a precision test of the SM

• New experiments on the horizon may continue this tradition.

• Muon (g-2), with a precision of 0.5 ppm, has a 2.7 discrepancy with the standard model.

• This new physics, if confirmed, could also show up as a muon EDM, as well as in Lepton flavor violation in decay.


Like most science, this is a work in progress

Stay tuned !


Two Hadronic Issues:

• Lowest order hadronic contribution• Hadronic light-by-light


The error budget for E969 represents a continuation of improvements already made

during E821

• Field improvements: better trolley calibrations, better tracking of the field with time, temperature stability of room, improvements in the hardware

• Precession improvements will involve new scraping scheme, lower thresholds, more complete digitization periods, better energy calibration

Systematic uncertainty (ppm)

1998 1999

2000 2001

E969

Goal

Magnetic field – p 0.5 0.4 0.24 0.17 0.1

Anomalous precession – a

0.8 0.3 0.31 0.21 0.1

Statistical uncertainty (ppm)

4.9 1.3 0.62 0.66 0.14

Total Uncertainty (ppm) 5.0 1.3 0.73 0.72 0.20


Hadronic light-by-light

• This contribution must be determined by calculation.

• the knowledge of this contribution limits knowledge of theory value.

+/- Signs are Important!


Better agreement between exclusive and inclusive (2) data than in 1997-1998 analyses

Agreement between Data (BES) and pQCD (within correlated systematic errors)

use QCD

use data

use QCD

Evaluating the Dispersion Integral

from A. Höcker ICHEP04


Tests of CVC (A. Höcker – ICHEP04)


Shape of F from e+e- and hadronic decay

zoom

Comparison between t data and e+e- data from CDM2 (Novosibirsk)

New precision data from KLOE confirms

CMD2


MEG @ PSI (10-13 BR sensitivity)

MEG will start running in 2006


Experimental Experimental boundbound

Largely favouredLargely favoured and confirmed by and confirmed by KamlandKamland

Additional contributionAdditional contribution toto slepton mixingslepton mixing fromfrom VV2121, matrix element , matrix element responsible responsible forfor solar neutrino deficit solar neutrino deficit. (. (J. Hisano & N. Nomura, Phys. Rev. J. Hisano & N. Nomura, Phys. Rev. D59D59 (1999) (1999) 116005)116005)..

All All solar solar experimentsexperiments combinedcombined

tan(tan() = ) = 3030

tan(tan() = 0) = 0

MEG MEG goalgoal

AfterAfterKamlandKamland

Connection with oscillations


E821 ωp systematic errors (ppm)

E969

(i)(I)

(II)

(III)

(iv)

*higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time-

varying stray fields.


Systematic errors on ωa (ppm)

σsystematic 1999 2000

2001

E969

Pile-up 0.13 0.13 0.08 0.07

AGS Background 0.10 0.10 *

Lost Muons 0.10 0.10 0.09 0.04

Timing Shifts 0.10 0.02 0.02

E-Field, Pitch 0.08 0.03 * 0.05

Fitting/Binning 0.07 0.06 *

CBO 0.05 0.21 0.07 0.04

Beam Debunching 0.04 0.04 *

Gain Change 0.02 0.13 0.13 0.03

total 0.3 0.31 0.21 0.11Σ* = 0.11


a(had) from hadronic decay?

• Assume: CVC, no 2nd-class currents, isospin breaking corrections.

• n.b. decay has no isoscalar piece, while e+e- does• Many inconsistencies in comparison of e+e- and decay:

- Using CVC to predict branching ratios gives 0.7 to 3.6 discrepancies with reality.

- F from decay has different shape from e+e-.


The Storage Ring Magnet

r = 7112 mmB0 = 1.45 T

cyc = 149 ns

(g-2) = 4.37 s

= 64.4 s

p = 3.094 GeV/c

B Field Measurement

2001


E969: Systematic Error Goal

• Field improvements will involve better trolley calibrations, better tracking of the field with time, temperature stability of room, improvements in the hardware

• Precession improvements will involve new scraping scheme, lower thresholds, more complete digitization periods, better energy calibration

Systematic uncertainty (ppm)

1998 1999

2000 2001

E969

Goal

Magnetic field – p 0.5 0.4 0.24 0.17 0.1

Anomalous precession – a

0.8 0.3 0.3 0.21 0.1


Improved transmission into the ring

InflectorInflector aperture

Storage ring aperture

E821 Closed End E821 Prototype Open End


E969: backward decay beam

Pions @ 5.32 GeV/c

Decay muons @ 3.094 GeV/c

No hadron-induced prompt flash

Approximately the same muon flux is realized

x 1 more

muons

Expect for both sides

Pedestal vs. Time

Near side Far side

E821

E821: Pions @ 3.115 GeV/c

momentum

collimator


μ EDM may be enhancedabove mμ/me × e EDM

Magnitude increases withmagnitude of ν Yukawa couplings

and tan β

μ EDM greatly enhanced when heavy neutrinos non-degenerate

Model Calculations of EDM


Beam Needs: NP2

• the figure of merit is Nμ times the polarization.

• we needto reach the 10-24 e-cm level. • Since SUSY calculations range from 10-22 to

10-32 e cm, more muons is better.

= 5*10-7

(Up-

Dow

n)/(

Up+

Dow

n)

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