1. Towards a measurement of the muon electric dipole moment with a compact storage ring
Klaus Kirch
Nufact08, Valencia, 2008

2. Contents Lepton dipole moments Muon spin precession in B and E fields
Measurement of (g–2)µ and µEDM at storage rings
Motivations to go below 10–19 e cm
The “frozen spin” technique
Sensitivity estimate for low momentum
A schematic layout for PSI

3. Lepton dipole moments Hamiltonian:
Define g and h as dimension-less quantities describing magnetic and electric dipole moments, respectively:
For a Dirac particle (i.e. lepton): g = 2 (+ corrections) and h = 0 (+ super-tiny corrections from CP-violating interactions)
* convenient to define:

4. P T EDM and symmetries _ + _ + + _
A nonzero particle EDM violates P, T and, assuming
CPT conservation, also CP
Purcell and Ramsey, PR78(1950)807; Lee and Yang; Landau

5. Electric Dipole Moments
EDMs of elementary particles violate P and T symmetries, and violate CP if CPT is conserved.
Most beyond-SM-theories introduce additional CP violation.
Current efforts are mainly focused on neutral particles (neutron, atoms).
Lepton EDMs are theoretically much cleaner.
No contributions from QED and strong interactions, only higher-order electroweak!
See, e.g., M. Pospelov, A. Ritz: Electric dipole moments as probes of new physics, Annals of Physics 318 (2005) 119

6. Standard model lepton EDMs
F. Hoogeveen: The Standard Model Prediction for the Electric Dipole Moment of the Electron, Nucl. Phys. B 241 (1990) 322
Fourth order electroweak,
… + new physics?

7. Standard model lepton EDMs
F. Hoogeveen: The Standard Model Prediction for the Electric Dipole Moment of the Electron, Nucl. Phys. B 241 (1990) 322
Fourth order electroweak,
Completely negligible at any experimental sensitivity we can imagine today!
Much greater sensitivity to new, CP-violating physics!
… + new physics?

8. Muon spin precession in B and E field
Muon spin precession in the presence of B and E field, perpendicular to each other and to the muon momentum: wa we
Example: B-field pointing down, E-field radially outward:
wa: spin precession in orbital plane (“g–2” precession) E
m-spin
we: spin precession out of orbital plane
m-trajectory B
w = wa + we tilts the precession plane out of the orbital plane

9. Muon spin precession in B and E fieldwa we
Strategy for (recent) g–2 measurement at storage rings:
run at “magic g”, g = 29.3 (pm= 3.1 GeV) ⇒ no effect from electric fields, can use electric focusing (need for uniform B field precludes magnetic focusing)
assume h small for measurement of a ⇒ direct access to a if B is known
look for small vertical oscillation to put a limit on h.
All recent limits have been obtained in this way (CERN, Brookhaven)
Plagued by systematics: g–2 precession interferes strongly!

10. g–2 Measurement (E821@Brookhaven)
A 20-year effort to improve the precision on am from 7 ppm to 0.5 ppm:
am = (63)
G.W. Bennett et al.: Final report of the E821 muon anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006)

11. g–2: the most recent state of affairs
G.W. Bennett et al.: Final report of the E821 muon anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006)
am(exp) = (63)
(0.54 ppm)
am(SM) = (48)
E. de Rafael: Theory of the muon anomalous magnetic moment P and T violation at low energies, Heidelberg 2008
(0.41 ppm)
am(exp) – am(SM) = (29.7 ± 7.9) × 10–10
3.7s discrepancy!
For the (beautiful!) history of g–2, see:
New physics or not?
The deviation is consistent with LHC-accessible SUSY in the few 100 GeV range...
A follow-up of E821 could potentially reduce the experimental error by a factor 2-5.
Both, experiment and theory are not far from their limits.
F.J.M. Farley, Y.K. Semertzidis: The 47 years of muon g–2, Prog. Part. Nucl. Phys. 52 (2004) 1
J.P. Miller, E. de Rafael, B.L. Roberts: Muon (g–2): Experiment and Theory , arXiv:hep-ph/
E969:
B.L. Roberts: Muon (g–2): Past, present and future, Nucl. Phys. Proc. Suppl. 155 (2006) 372

12. µEDM at g–2 storage rings
Search for a vertical oscillation signal in g–2 data (vertical segmentation of some of the electron detectors)
Seriously limited by two effects:
g–2 rotation of spin strongly suppresses the effect of we
Trajectories of the decay electrons are very different at the two extremes of vertical oscillation, leading to large systematic effects.
Best current limit from Brookhaven E821:
Only preliminary, but soon to be published (L. Roberts).
Only modest improvement with respect to previous (CERN) experiment.
dm < 2.4 × 10–19 e cm
R. McNabb et al.: hep-ex/ , unpublished
dm < 2.0 × 10–19 e cm
Lee Roberts [BNL 2008]: private communication

13. History of µEDM measurements
D. Berley et al., Phys. Rev. Lett. 1 (1960) 144
D. Berley, G. Gidal, Phys. Rev. 118 (1960) 1086
G. Charpak et al., Nuovo Cim. 22 (1961) 1043
J. Bailey et al., J. Phys. G: Nucl. Phys. 4 (1978) 345
R. McNabb et al., hep-ex/ , unpublished
BNL [2008]
Stalling progress with conventional storage ring method...
… need new method, but first look at motivations

14. What is the motivation to go below 10–19 e cm?
BNL [2008]
What is the motivation to go below 10–19 e cm?
Various:
model independent …
model dependent …
forget models …

15.
Sensitivity about 5 x e cm for 1 year measurement time with single muon mode
Improvements possible if many muons can be injected (present muon beam provides times more muons)
PSI sensitivity with „one muon per time“ ?

16.
Sensitivity about 5 x e cm for 1 year measurement time with single muon mode
Improvements possible when many muons can be injected (present muon beam provides times more muons) but:
electron EDM limit (90% C.L.) at 1.6 x e cm (and improvements due) Is it worth the effort ?
PSI sensitivity with „one muon per time“ ?
electron EDM limit
scaled linearly by mm / me
B.C. Regan et al. Phys. Rev. Lett. 88 (2002)

17. mEDM@PSI Yes: EDM mass scaling not necessarily linear
BNL [2008]
The g-2 anomaly isn´t
EDM mass scaling not necessarily linear
viable models with muon EDM much larger than e cm
in connection with muon g-2 model independent arguments in favor of pushing in steps to below and e cm
g-2 anomaly and generic new physics dipole ?

18. The g –2 anomaly isn't? ! am(exp) – am(SM) = (29.7 ± 7.9) × 10–10
G.W. Bennett et al. Final report of the E821 muon anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006)
J.P. Miller, E. de Rafael, B.L. Roberts Muon (g–2): Experiment and Theory, Rept. Prog. Phys. 70, 795 (2007)
Recent update: E. de Rafael: Theory of the muon anomalous magnetic moment P and T violation at low energies, Heidelberg 2008
J. Feng, T.M. Matchev, Y. Shadmi The Measurement of the Muon's Anomalous Magnetic Moment Isn't, Phys. Lett. B 555 (2003) 89
See already: J. Bailey et al. New limits on the electric dipole moments of positive and negative muons, J. Phys. G: Nucl. Phys. 4 (1978) 345 !

19. Generic new-physics dipole moment
If one assumes that both non-SM MDM (amNP) and EDM (dµ) are manifestations of the same new-physics object: and with D a general dipole operator (W. Marciano), then the Brookhaven measurement can be interpreted as i.e. either dµ is of order 10–22 e cm, or the CP phase is strongly suppressed!
3.0
29.7 x
J.L. Feng, K.T. Matchev, Y. Shadmi Theoretical Expectations for the Muon's Electric Dipole Moment, Nucl. Phys. B 613 (2001) 366

20. Muon spin precession in B and E fieldwa we
New method for EDM measurement: the “frozen spin” technique!
Go to lower momentum, install a “magic E field” (radially), such that wa vanishes completely:
The spin remains parallel to the momentum along the orbit (“frozen spin”)
In the presence of an EDM (h≠0) the spin is slowly rotated out of the orbital plane.
Much superior sensitivity than with parasitic approach!
F. Farley et al.: New Method of Measuring Electric Dipole Moments in Storage Rings, Phys. Rev. Lett. 93 (2004)

21. J-PARC letter of intent
A. Silenko et al.: J-PARC Letter of Intent: Search for the Permanent Muon Electric Dipole Moment at the 10–24 e cm Level.
Semertzidis, Farley et al. in proposed an experiment exploiting the frozen spin technique at J-PARC (PRISM-II FFAG).
Design: 7-m radius ring, with B = 0.25 T, E = 2 MV/m and p = 500 MeV/c (gt = 11 µs).
Estimated sensitivity is around 10–24 e cm
So far a “virtual project”, realization not likely before 2015.
Can one do this with lower momentum muons?
Can one start at an existing beamline? … at PSI?

22. Sensitivity estimate dµ < 5 × 10–23 e cm dµ < 10–24 e cm
F. Farley et al.: New Method of Measuring Electric Dipole Moments in Storage Rings, Phys. Rev. Lett. 93 (2004)
Uncertainty on h from a simple asymmetry counting experiment with N decays:
A : electron asymmetry, assume A = 0.3 P : polarization of muons
J-PARC proposal: gt = 11 µs, b = 0.978, P = 50%, B = T
→ sh = 4 × 10–3/√N ; N = 4 × 1016 ⇒ sh = 2 × 10-11
dµ < 10–24 e cm
PSI: gt = 3.4 µs, b = 0.76, P = 90%, B = 1.0 T
→ sh = 2.4 × 10–3/√N ; N = 4 × 1012 ⇒ sh = 10–9
dµ < 5 × 10–23 e cm
Muon statistics is the dominant factor!

23. A µEDM experiment at PSI?

24. Muons at PSI

25. Muons at PSI
µE1 area

26. pion decay channel (8 m, 4–5 T)
µE1 beamline and area
pp = 220 MeV/c
pion decay channel (8 m, 4–5 T)
50.63 MHz (19.75 ns)
Existing infrastructure
Muon “beam”:
~400 p mm mrad emittance
~108 µ+ / s
Bunch width 3.9 ns FWHM
pµ = 125 MeV/c p sµ nµ
For comparison: my car
I.C. Barnett et al. : Nucl. Instr. and Meth. A 455 (2000) 329; also:

27. Concept for an experiment at PSI
Apply frozen spin technique at lower momentum than JPARC:
PSI µE1: pμ=125 MeV/c (b = 0.76, = 1.55), Pμ = 92%
Choose B = 1 T (conventional magnet, straightforward change of polarity)
→ 42 cm orbit radius, radial E-field 0.64 MV/m (64kV/10cm gap).
Trade off high intensity of muon beam for beam quality, selecting the muons to be injected into the ring:
Reduce from 100 MHz to ~200 kHz
One muon at a time! Average measurement time  gtµ = 3.4 µs.
Assume run-time of 2 × 107 s, times 200 kHz gives × 1012 electron decays (per year)
Clockwise and counter-clockwise operation (systematics)
Positively and negatively charged muons can be injected (systematics)

28. µE1 beamline and area
A ~1-m-diameter storage ring with support fits in comfortably
For comparison: my car

29. Artist's impression (A. Streun)

30. Main challenges Injection Injection trigger
Conventional kicker too slow, very short revolution time (11.6 ns)
Possible solution: resonance injection at half-integer tune using a non-linear field perturbator (inflector)
Injection trigger
Minimal latency between detection of “good muon” and ramp-up of inflector
E, B-field setup, alignment and control
Detector
Timing, position resolution, E, B-field, limited space, systematics
Data processing / storage
O(1012) muon decays, almost all of them carry interesting information

31. Injection study for µEDM project
Andreas Adelmann, using TRACY program
20 turns ramp of non-linear perturbator
Acceptance ±7 mm / ±11 mrad, average latency for acceptable μ: ~1.2 μs
Average measurement time gtm= 3.4 μs
~200 kHz repetition rate for perturbator
Challenging, in particular for “random” ramp-up
Can we trigger the perturbator in time to catch the “good” muon?
Injection phase space diagram (TRACY)
Acceptance
Injection turns
stable orbits

32. Muon EDM beam schematicsp
(2 mA, 590 MeV)
(220 MeV/c)
(125 MeV/c) E B
µE1 beam line
inflector
design orbit (r = 42 cm)
~20 turns injection
radial capacitor
(1 T)
(6.4 kV/cm)
trigger
Target E
F.J.M. Farley et al.
New method of Measuring Electric Dipole
Moments in Storage Rings
Phys. Rev. Lett. 93, (2004)
A. Adelmann, K. Kirch
Search for the muon electric dipole
moment using a compact storage ring
arXiv:hep-ex/
A. Adelmann, K. Kirch, C.J.G. Onderwater,
T. Schietinger, A. Streun
to be published

33. Various systematics issues...
Vertical E field component: E⊥ < 10–4 Erad.
Rotational misalignments and residual g–2 precession
Instabilities of E, B fields, detector,...
...but many ways to control them:
Injection of μ+ and μ–
Factor 3 less statistics for μ–
Clockwise and counter-clockwise orbit
g–2 precession for calibration
Spin rotation?
F. Farley et al.: New Method of Measuring Electric Dipole Moments in Storage Rings, Phys. Rev. Lett. 93 (2004)

34. Muon EDM summary Present limit around 2-3 × 10–19e cm
At PSI improve orders of magnitude in sensitivity to this fundamental particle property (limit or discovery)
Sensitivity of 5×10–23e cm with single muon mode
Important model independent test of g-2 anomaly
Rule out (or confirm) EDM explanation for g-2 anomaly
Rule out (or confirm) naïve relation for new physics MDM and EDM
Experiment possible long before J-PARC (or anyone else) can get there
Proof of principle for new technique at relatively low cost and could possibly be upgraded.

35. Thanks … for your attention !
to my collaborators from PSI and Groningen: Andreas Adelmann, Gerco Onderwater, Thomas Schietinger, Andreas Streun
to Thomas Schietinger who created many of the transparencies; for a longer talk by him, see:
for various input and fruitful discussions with Francis Farley, Klaus Jungmann, Peter Kammel, Jim Miller, Lee Roberts, Stefan Ritt, Yannis Semertzidis, …

38. A new slow m+ beam?
D. Taqqu proposed a new technique for the production of a high-quality slow m+ beam, PRL 97, (2006).
the most intense available m+ beam as input, would yield a 106/s muons at (10±0.5) eV in 1 cm2 with 10 ns timing.
Reaccelerated muons of 10 keV could be focused into less than 100mm diameter beam spot.
This m+ beam could be used for surface mSR and a muon microscope. Its phase space density is more than a billion times higher than presently available! It would also be a unique tool for fundamental physics.
There is nothing in principle against even higher intensities and higher momenta.

39. D. Taqqu, PRL 97, (2006)

40. The “frozen spin” technique
Turn off the g–2 precession with a radial E field
Up-down detectors measure decay electrons
Emission of electrons strongly correlated with spin direction, in particular for high- energy electrons
Look for an up-down asymmetry, building up linearly with time
Detectors on the inside and outside to measure g –2 precession (cross check)
A. Silenko et al.: J-PARC Letter of Intent: Search for the Permanent Muon Electric Dipole Moment at the 10–24 e cm Level.

41. Detection cos(q) cos(q)1
Detection
cos(q)
Identify direction of decay e± (at least up/down)
Energy resolution helps (at least low energy cutoff)
Full reconstruction nice (at least some segmentation in q, f, z)
Timing below 1 ns desirable (at least 10 ns)
Limited space and E,B-field challenging
RooFit toy Monte Carlo study in progress
Full GEANT4 simulation in preparation
pe [MeV/c] -1
145 1
cos(q) -1

42. Resonance injection method
T. Takayama et al.: Resonance injection method for the compact superconducting SR-ring, Nucl. Instr. and Meth. A 24/25 (1987) 420
Developed for injection into commercial tabletop synchrotron light-sources
AURORA series (50 cm orbit radius), MIRRORCLE (15.6 cm!) by photon production laboratories, Ltd.
Perturbator excites half-integer betatron resonance (e.g. 3/2), decay to stable orbit over several turns
H. Yamada: Commissioning of aurora: The smallest synchrotron light source, J. Vac. Sci. Tehnol. B 8 (1990) 1628
H. Yamada: Novel X-ray source based on a tabletop synchrotron and its unique features, Nucl. Instr. and Meth. B 199 (2003) 509
H. Yamada et al.: Development of the hard X-ray source based on a tabletop electron storage ring, Nucl. Instr. and Meth. A 467/468 (2001) 122