B. Lee Roberts, HIFW04, Isola d’Elba, 6 June 2004 - p. 1/39

Future Muon Dipole Moment Measurements

at a high intensity muon source

B. Lee RobertsDepartment of Physics

Boston University

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

A Precision Path to the Frontier

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Outline• theory and motivation of dipole moments,

including the transition moment for μ→e conversion

• muon (g-2) present and future

• muon EDM

• summary and conclusions

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Magnetic moments, g-factors

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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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Lagrangian for MDM and EDM

where α, β run from 0 to 3, and dμ is the electric dipole

moment. We could also use the dipole operator D

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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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Unlike the EDM, there is a large SM value for the MDM

The Electron: to the level of the experimental error (4ppb),

Contribution of μ, (or anything heavier than the electron) is ≤4 ppb.

For the muon, the relative contribution of heavier particles

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Standard Model Value for (g-2)

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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

Can hadronic decay data be used? Eventually from the lattice?

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Hadronic light-by-light

• This contribution must be determined by calculation.

• While there have been issues with this contribution, things are settling down.

• a lattice calculation might improve things further, and give confidence in the models.

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

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aμ is sensitive to all virtual particles which couple to the muon, e.g. SUSY

a toy model with equal susy masses gives:

If SUSY is discovered at LHC, then (g-2) will give a 20% determination of tan β

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SUSY connection between Dμ , μ → e

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Unlike the EDM, aμ is well measured.

the combined value is

Comparing with e+e- - data shows a discrepancy with the standard model of 2.4σ

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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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Discrepancy with e+e- based theory

• What might this mean?• It all depends on your religion…

– if you believe in SUSY, then it is the predicted effect, and evidence for SUSY.

– if you are a non-believer then this discrepancy is interesting, or a fluctuation…

• Whatever you believe, muon (g-2) provides a wonderful test of the standard model.

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aμ implications for the muon EDM

This paper, published before our February 2001 announcement predicts a large muon EDM, and a corresponding SUSY contribution to aμ comparable to what we might be observing, with the e- EDM predicted to be 0.1 of the present limit.

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aμ implications for the muon EDM

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Basis of the experiments:

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Spin Precession Frequencies:

The EDM causes the spin to precess out of plane.

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

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muon (g-2) storage ring

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Technique for muon (g-2)

use the magic γ = 29.3 and electrostatic focusing.

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Detectors and vacuum chamber

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E821 will improve muon EDM• however, the EDM signal is sitting on top

of a large background from g-2.

• we need to eliminate this background.

use a radial E field to turn off g-2 precession

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EDM – up/down Asymmetry• run off the magic γ and use a radial E-field

to turn off (g-2) precession

• Place detectors above and below the vacuum chamber and look for an up/down asymmetry which builds up with time

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The EDM ring• run with both μ+ and μ-.• there must be regions of combined E+B along

with separate focusing elements.• There needs to be a scheme to inject CW and

CCW.

E B p R

2 MV/m 0.25T 0.5 GeV/c 5 11μs 7 m

Possible Muon EDM Ring Parameters

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the lattice

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Detectors above and below

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up / down asymmetry

time (μs)

asym

met

ry

put in up-down/up+down

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NP2

• the figure of merit is Nμ times the polarization.

• we need

to reach the 10-24 e-cm level.

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Future Plans: (g-2)• we are preparing a proposal to BNL to

improve on our error from 0.5 ppm to ≤ 0.25 ppm.– proposal ready late July– defend in late September

This will require upgrades and ~28 weeks of beam time.• Longer term, if theory can support it, we

believe that at a high-intensity μ source we could reach 0.06 ppm.

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Future Plans: Muon EDM• The muon EDM experiment needs a high

intensity source, along with a polarized D beam to test systematic errors. A letter of intent was submitted to JPARC.

• A separate proposal to search for a Deuteron EDM is being prepared

(J. Miller, E. Stephenson and Y. Semertzidis

spokespersons).

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Deuteron EDM in a Storage Ring• Radial E-field to Control the g-2 Precession• Intense Polarized Deuteron Beams• Long Spin Coherence Time: 10s• Polarimeters: High Analyzing Power• Clockwise and Counter-Clockwise Injection

• Systematic Error: 10-27 ecm

• Statistical Error: 10-27 ecm

• Proposal This Summer to BNL, DOE/NSF

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Conclusions• The measured value of a differs from the SM

value by ~2.4 to 3 σ, and aμ will remain an important quantity. If SUSY is found, → tan β

• We propose to improve the precision of aμ .

• The muon EDM experiment can only be done at a high intensity muon source.

• We believe that a precision of 10-24 – 10-25 e-cm could be reached at a high intensity muon source.

• EDMs are an excellent opportunity to search for non-standard-model CP violation.