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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

roberts@bu.edu http://physics.bu.edu/roberts.html

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Outline

• Introduction to the muon

• Selected weak interaction parameters

• Muonium

• Lepton Flavor Violation

• Magnetic and electric dipole moments

• Summary and conclusions.

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The Muon (“Who ordered that?”)

• Lifetime ~2.2 s, practically forever

• 2nd generation lepton

• mme = 206.768 277(24)

• produced polarized

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

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The Muon – ctd.

• Decay is self analyzing

• It can be produced copiously in pion decay– PSI has 108 /s in a new beam

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A precise measurement of + leads to a precise determination of GF

Predictive power in weak sector of SM:

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

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Lan @ PSI aims for a factor of 20 improvement

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The Leptonic Currents

• Lepton current is (V – A)

There have been extensive studies at PSI by Gerber, Fetscher, et al. to look for other couplings in muon decay.

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Leptonic and hadronic currents• For nuclear capture there are induced

formfactors and the hadronic current contains 6 terms.– the induced pseudoscaler term is important

further enhanced in radiative muon capture

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

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Muonium

Hydrogen (without the proton)

Zeeman splitting

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

where p comes from proton NMR in the same B field

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muonium and hydrogen hfs → proton structure

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Lepton Flavor

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

• What about

or

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General Statements

• We know that oscillate– neutral lepton flavor violation

• Expect charged lepton flavor violation at some level– enhanced if there is new dynamics at the TeV

scale• in particular if there is SUSY

• We expect CP in the lepton sector (EDMs as well as oscillations)– possible connection with cosmology

(leptogenesis)

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The Muon Trio:• Lepton Flavor Violation

• Muon MDM (g-2) chiral changing

• Muon EDM

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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• approved at

Brookhaven, not yet funded (Needs Congressional approval)

Bra

nchi

ng R

atio

Lim

it

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Magnetic Dipole Moments

The field was started by Stern

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Z. Phys. 7, 249 (1921)

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(in modern language)

673 (1924)

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Dirac + Pauli moment

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Dirac Equation Predicts g=2

• radiative corrections change g

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The CERN Muon (g-2) Experiments

The muon was shown to be a point particle obeying QED

The final CERN precision was 7.3 ppm

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Standard Model Value for (g-2)

relative contribution of heavier things

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Two Hadronic Issues:

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

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Lowest Order Hadronic from e+e- annihilation

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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-.

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• Comparison with CMD-2 in the Energy Range 0.37 <s<0.93 GeV2

(375.6 0.8stat 4.9syst+theo) 10-10

(378.6 2.7stat 2.3syst+theo) 10-10

KLOECMD2

1.3% Error0.9% Error

a= (388.7 0.8stat 3.5syst

3.5theo) 10-10

2 contribution to ahadr

• KLOE has evaluated the Dispersions Integral for the 2-Pion-Channel in the Energy Range 0.35 <s<0.95 GeV2

• At large values of s (>m) KLOE is consistent with CMD and therefore

They confirm the deviation from -data!.

Pion Formfactor

CMD-2KLOE

0.4 0.5 0.6 0.7 0.8 0.9

s [GeV2]

45

40

35

30

25

20

15

10

5

45

0

KLOE Data on R(s)

Courtesy of G. Venanzone

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A. Höcker at ICHEP04

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ahad [e+e–

] = (693.4 ± 5.3 ± 3.5) 10 –10

a SM

[e+e–

] = (11 659 182.8 ± 6.3had ± 3.5LBL ± 0.3QED+EW) 10 –10

Weak contribution aweak = + (15.4 ± 0.3) 10

–10

Hadronic contribution from higher order : ahad [( /)3] = – (10.0 ± 0.6) 10

–10

Hadronic contribution from LBL scattering: ahad [LBL] = + (12.0 ± 3.5) 10

–10

a exp – a

SM =(25.2 ± 9.2) 10

–

10

2.7 ”standard deviations“

Observed Difference with Experiment:

BNL E821 (2004):a

exp =(11 659 208.0 5.8) 10 10

not yet published

not yet published

preliminary

SM Theory from ICHEP04 (A. Höcker)

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Hadronic light-by-light

• This contribution must be determined by calculation.

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

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aμ is sensitive to a wide range of new physics

• muon substructure

• anomalous couplings• SUSY (with large tanβ )

• many other things (extra dimensions, etc.)

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SUSY connection between a , Dμ , μ → e

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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

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Spin Precession Frequencies: in B field

The EDM causes the spin to precess out of plane.

The motional E - field, β X B, is much stronger than laboratory electric fields.

spin difference frequency = s - c

0

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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

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muon (g-2) storage ring

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The Storage Ring Magnet

r = 7112 mm

B0 = 1.45 T

cyc = 149 ns

(g-2) = 4.37 s

= 64.4 s

p = 3.094 GeV/c

B Field Measurement

2001

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Detectors and vacuum chamber

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

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Fourier Transform: residuals to 5-parameter fit

beam motion across a

scintillating fiber – ~15 turn period

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Where we came from:

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

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Life Beyond E821?

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

• A new upgraded experiment was approved by the BNL PAC in September

E969• Goal: total error = 0.2 ppm

– lower systematic errors– more beam

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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

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Improved transmission into the ring

InflectorInflector aperture

Storage ring aperture

E821 Closed End E821 Prototype Open End

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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

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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.

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Present EDM Limits

Particle Present EDM limit

(e-cm)

SM value

(e-cm)

n

future exp 10-24 to 10-25

*projected

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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

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aμ implications for the muon EDM

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Recall

The EDM causes the spin to precess out of plane.

EDM Systematic errors are huge in E821 because of (g-2) precession!

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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

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Beam Needs: NP2

• the figure of merit is Nμ times the polarization.

• we need

to 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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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 2.7 discrepancy with the standard model.

• This new physics, if confirmed, would show up in an EDM as well.

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Outlook• Scenario 1

– LHC finds SUSY– (g-2), LFV help provide information on

important aspects of this new reality; for (g-2) → tan

• Scenario 2– LHC finds the Standard Model Higgs at a

reasonable mass, nothing else, (g-2) discrepancy and m might be the only indication of new physics

– virtual physics, e.g. (g-2), EDM, →e conversion would be even more important.

Stay tuned !

Thank you

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Extra slides

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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

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Tests of CVC (A. Höcker – ICHEP04)

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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

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The MECO ApparatusStraw Tracker

Crystal Calorimeter

Muon Stopping Target

Muon Beam Stop

Superconducting Production Solenoid

(5.0 T – 2.5 T)

Superconducting Detector Solenoid

(2.0 T – 1.0 T)

Superconducting Transport Solenoid

(2.5 T – 2.1 T)

Collimators

10-17 BR single event sensitivity

p beam

approved but not funded

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MEG @ PSI (10-13 BR sensitivity)

MEG will start running in 2006

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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

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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.

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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