1. Direct EDM search for charged hadrons at COSY
October 2, Frank Rathmann
(on behalf of the BNL-EDM and JEDI collaborations)
EDM searches in Storage rings, ECT*, Trento, Italy

2. Direct EDM search for charged hadrons at COSY
Topics
Introduction
Search for Electric Dipole Moments
Spin coherence time
First direct measurement
Resonance Method with RF E(B)-fields
Polarimetry
Conclusion
Direct EDM search for charged hadrons at COSY

3. What caused the Baryon asymmetry?
Carina Nebula: Largest-seen star-birth regions in the galaxy
What happened to the antimatter?
Observed
610-10
WMAP+COBE (2003)
SM expectation
~10-18
Sakharov (1967): Three conditions for baryogenesis
B number conservation violated sufficiently strongly
C and CP violated, B and anti-Bs with different rates
Evolution of universe outside thermal equilibrium
Direct EDM search for charged hadrons at COSY

4. Electric Dipole Moments (EDMs)
Permanent EDMs violate parity P and time reversal symmetry T
Assuming CPT to hold,
combined symmetry CP violated as well.
EDMs are candidates to solve mystery of matter-antimatter asymmetry
 may explain why we are here!
Direct EDM search for charged hadrons at COSY 4 4

5. History of neutron EDM limits
Smith, Purcell, Ramsey PR 108, 120 (1957)
RAL-Sussex-ILL (dn  2.9 10-26 ecm) PRL 97, (2006)
Adopted from K. Kirch
Direct EDM search for charged hadrons at COSY

6. Direct EDM search for charged hadrons at COSY
Limits for Electric Dipole Moments
EDM searches - only upper limits (in 𝐞𝐜𝐦)up to now:
Particle/Atom
Current EDM Limit
Future Goal
 𝒅𝒏 equivalent
Neutron
 𝟑  𝟏𝟎 −𝟐𝟔
 𝟏𝟎 −𝟐𝟖
𝟏𝟎 −𝟐𝟖
𝟏𝟗𝟗𝐇𝐠
 𝟑.𝟏× 𝟏𝟎 −𝟐𝟗
 𝟏𝟎 −𝟐𝟗
𝟏𝟎 −𝟐𝟔
𝟏𝟐𝟗𝐗𝐞
 𝟔× 𝟏𝟎 −𝟐𝟕
 𝟏𝟎 −𝟑𝟎 – 𝟏𝟎 −𝟑𝟑
 𝟏𝟎 −𝟐𝟔 – 𝟏𝟎 −𝟐𝟗
Proton
 𝟕.𝟗× 𝟏𝟎 −𝟐𝟓
𝟏𝟎 −𝟐𝟗
Deuteron ?
𝟑  𝟏𝟎 −𝟐𝟗 – 𝟓× 𝟏𝟎 −𝟑𝟏
Huge efforts underway to improve limits / find EDMs
Sensitivity to NEW PHYSICS beyond the Standard Model
Direct EDM search for charged hadrons at COSY 6 6

7. Direct EDM search for charged hadrons at COSY
Why also EDMs of protons and deuterons?
Proton and deuteron EDM experiments may provide higher sensitivity.
In particular deuterons may provide a much higher sensitivity than protons.
Consensus in the theoretical community:
Essential to perform EDM measurements on different targets (𝑛, 𝑝, 𝑑, 3He) with similar sensitivity:
unfold the underlying physics,
explain the baryogenesis.
Direct EDM search for charged hadrons at COSY

8. Search for Electric Dipole Moments
NEW: EDM search in time development of spin in a storage ring:
“Freeze“ horizontal spin precession; watch
for development of a vertical component !
Direct EDM search for charged hadrons at COSY 8 8

9. Direct EDM search for charged hadrons at COSY
Frozen spin Method
For transverse electric and magnetic fields in a ring ( ),
anomalous spin precession is described by x
Magic condition: Spin along momentum vector
For any sign of 𝐺, in a combined electric and magnetic machine
For 𝐺>0 (protons) in an all electric ring
𝐸=𝐸radial
𝐵=𝐵vertical
(magic)
Direct EDM search for charged hadrons at COSY

10. Search for Electric Dipole Moments
NEW: EDM search in time development of spin in a storage ring:
“Freeze“ horizontal spin precession; watch
for development of a vertical component !
A magic storage ring for protons (electrostatic), deuterons, …
particle
𝒑 (𝐆𝐞𝐕/𝐜)
𝑬 (𝐌𝐕/𝐦)
𝑩 (𝐓)
proton
𝟎.𝟕𝟎𝟏
𝟏𝟔.𝟕𝟖𝟗
𝟎.𝟎𝟎𝟎
deuteron
𝟏.𝟎𝟎𝟎
−𝟑.𝟗𝟖𝟑
𝟎.𝟏𝟔𝟎
𝟑𝐇𝐞
𝟏.𝟐𝟖𝟓
𝟏𝟕.𝟏𝟓𝟖
−𝟎.𝟎𝟓𝟏
One machine with 𝒓 ~ 𝟑𝟎 m
Direct EDM search for charged hadrons at COSY 10 10

11. Two storage ring projects being pursued
Jülich, focus on deuterons, or a combined machine
BNL for protons all electric machine
CW and CCW propagating beams
(from R. Talman)
(from A. Lehrach)
Direct EDM search for charged hadrons at COSY

12. Most recent: Richard Talmans concept for a Jülich all-in-one machine
Iron-free, current-only, magnetic bending, eliminates hysteresis A B A B
Direct EDM search for charged hadrons at COSY

13. Carry out proof of principle (demonstrator) experiments at COSY
BNL Proposal
2 beams simultaneously rotating in an all electric ring (cw, ccw)
Approved BNL-Proposal
Submitted to DOE 11/2012 Goal for protons
Circumference
~ 200 m
Technological challenges !
Spin coherence time (𝟏𝟎𝟎𝟎 𝐬)
Beam positioning (𝟏𝟎 𝐧𝐦)
Continuous polarimetry (<𝟏 𝐩𝐩𝐦)
E - field gradients (~ 𝟏𝟕 𝐌𝐕/𝐦 𝐚𝐭 𝟐 𝐜𝐦)
Carry out proof of principle (demonstrator) experiments at COSY
Direct EDM search for charged hadrons at COSY 13 13

14. Direct EDM search for charged hadrons at COSY
Parameters for Jülich all-in-one machine (R. Talmans concept )
Talman/Gebel give maximum achievable field of copper magnets of ~ 0.15 T.
𝒓=𝟏𝟎 𝐦
particle
𝒑 (𝐆𝐞𝐕/𝐜)
𝑻 (𝐆𝐞𝐕)
𝑬 (𝐌𝐕/𝐦)
𝑩 (𝐓)
proton
𝟖𝟓𝟓.𝟑
𝟑𝟑𝟏.𝟑
𝟔.𝟖
−𝟎.𝟎𝟎𝟓
deuteron
𝟑𝟖𝟏.𝟎
𝟑𝟖.𝟑
−𝟏.𝟑
−𝟎.𝟎𝟏𝟓
𝟑𝐇𝐞
𝟕𝟑𝟗.𝟖
𝟗𝟓.𝟖
𝟏𝟑.𝟐𝟒𝟎
−𝟎.𝟎𝟓𝟎
Fitting such a machine into the COSY building favors lower momenta.
Direct EDM search for charged hadrons at COSY

15. EDM at COSY – COoler SYnchrotron
Cooler and storage ring for (polarized) protons and deuterons
𝑝=0.3 –3.7 GeV/c
Phase space
cooled internal &
extracted beams
COSY
… the spin-physics machine
for hadron physics
Injector cyclotron
Direct EDM search for charged hadrons at COSY 15

16. EDM at COSY – COoler SYnchrotron
Cooler and storage ring for (polarized) protons and deuterons
𝑝=0.3 –3.7 GeV/c
Phase space
cooled internal &
extracted beams
COSY
… an ideal starting point
for a srEDM search
Injector cyclotron
Direct EDM search for charged hadrons at COSY 16

17. Direct EDM search for charged hadrons at COSY
Spin closed orbit
one particle with
magnetic moment
“spin tune”
“spin closed orbit vector”
ring
makes one turn
stable polarization
if ║ A
Direct EDM search for charged hadrons at COSY

18. Spin coherence
We usually don‘t worry about coherence of spins along
Polarization not affected!
Crucial for srEDM searches is understanding and improving spin coherence times
At injection all
spin vectors aligned (coherent)
After some time, spin vectors get out of phase and fully populate the cone
Situation very different, when you deal with 
Longitudinal polarization vanishes!
At injection all spin vectors aligned
After some time, the spin vectors are all out of phase and in the horizontal plane
In an EDM machine with frozen spin, observation time is limited.
Direct EDM search for charged hadrons at COSY

19. Estimate of spin coherence times (Kolya Nikolaev)
One source of spin coherence are random variations of the spin tune
due to the momentum spread in the beam
𝛿𝜃=𝐺𝛿𝛾
and 𝛿𝛾
is randomized by e.g., phase space cooling
cos 𝜔𝑡→ cos 𝜔𝑡+𝛿𝜃
𝜏 𝑠𝑐 ≈ 1 𝑓 rev 𝐺 2 𝛿𝛾 2 ≈ 1 𝑓 rev 𝐺 2 𝛾 2 𝛽 𝛿𝑝 𝑝 2 −1
𝑇 kin =100 MeV
𝑓 rev =0.5 MHz
Estimate:
More details in
Kolya Nikolaev‘s talk
𝑮 𝒑 =𝟏.𝟕𝟗
𝑮 𝒅 =−𝟎.𝟏𝟒
𝝉 𝒔𝒄 (𝒑)≈𝟑∙ 𝟏𝟎 𝟑 𝐬
𝝉 𝒔𝒄 (𝒅)≈𝟓∙ 𝟏𝟎 𝟓 𝐬
Spin coherence time for deuterons may be 𝟏𝟎𝟎× larger than for protons
Direct EDM search for charged hadrons at COSY

20. 2011 Test measurements at COSY
First measurement of spin coherence time
2011 Test measurements at COSY
Polarimetry:
Spin coherence time:
5 s
25 s
5 s
decoherence
time
oscillation
capture
from Ed Stephenson
and Greta Guidoboni
Direct EDM search for charged hadrons at COSY

21. Direct EDM search for charged hadrons at COSY
Topics
Introduction
Search for Electric Dipole Moments
Spin coherence time
First direct measurement
Resonance Method with RF E(B)-fields
Polarimetry
Conclusion
Direct EDM search for charged hadrons at COSY

22. Resonance Method with „magic“ RF Wien filter
Avoids coherent betatron oscillations of beam.
Radial RF-E and vertical RF-B fields to observe spin rotation due to EDM
Approach pursued for a first direct measurement at COSY.
𝐸 ∗ =0  𝐸𝑅 =−𝐵𝑦 „Magic RF Wien Filter“ no Lorentz force
Indirect EDM effect
Polarimeter (dp elastic)
stored d
RF E(B)-field
In-plane polarization
Tilt of precession plane due to EDM
Observable:
Accumulation of vertical polarization during spin coherence time
Statistical sensitivity for 𝒅𝒅 in the range 𝟏𝟎 −𝟐𝟑 to 𝟏𝟎 −𝟐𝟒 𝐞𝐜𝐦 range possible.
Alignment and field stability of ring magnets
Imperfection of RF-E(B) flipper
Direct EDM search for charged hadrons at COSY

23. Operation of „magic“ RF Wien filter
Radial E and vertical B fields oscillate, e.g., with 𝑓 𝐻𝑉 = 𝐾+𝐺𝛾 ∙ 𝑓 rev =−54.151× Hz (here 𝐾=0).
beam energy
𝑇𝑑=50 MeV
Spin coherence time may depend on excitation and on chosen harmonics 𝐾.
see Kolya Nikolaev‘s talk
Direct EDM search for charged hadrons at COSY

24. Direct EDM search for charged hadrons at COSY
Simulation of resonance Method
with „magic“ Wien filter for deuterons at COSY
Parameters: beam energy 𝑇𝑑=50 MeV 𝐿RF=1 m
assumed EDM 𝑑𝑑= 10 −24 ecm
E-field 30 kV/cm
Linear extrapolation of 𝑃𝑦 for a time period of 𝑠𝑐=1000 s =3.7108 turns .
Preliminary, based on Kolya Nikolaevs derivation of the combined rotation matrices of E/B flipper and ring
EDM effect accumulates in 𝑃𝑦. 𝑃𝑥 𝑃𝑧 𝑃𝑦
𝜔= 2𝜋𝑓 𝑟𝑒𝑣 𝐺𝛾=−3.402× Hz
turn number
Direct EDM search for charged hadrons at COSY

25. Direct EDM search for charged hadrons at COSY
Simulation of resonance Method
with „magic“ Wien filter for deuterons at COSY
Parameters: beam energy 𝑇𝑑=50 MeV 𝐿RF=1 m
assumed EDM 𝑑𝑑= 10 −24 ecm
E-field 30 kV/cm
Linear extrapolation of 𝑃𝑦 for a time period of 𝑠𝑐=1000 s (=3.7108 turns).
EDM effect accumulates in 𝑃𝑦 𝑃𝑦
turn number
EDM effect accumulates in 𝑃𝑦
Direct EDM search for charged hadrons at COSY

26. Direct EDM search for charged hadrons at COSY
Simulation of resonance Method
with Magic Wien filter for deuterons at COSY
Parameters: beam energy 𝑇𝑑=50 MeV 𝐿𝑅𝐹=1 m
assumed EDM 𝑑𝑑= 10 −24 ecm
E-field 30 kV/cm
Linear extrapolation of 𝑃𝑦 for a time period of 𝑠𝑐= s (=3.71010 turns). 𝑃𝑦
turn number
Direct EDM search for charged hadrons at COSY

27. Some polarimetry issues
pC and dC polarimetry is the currently favored approach for the pEDM experiment at BNL
srEDM experiments use frozen spin mode, i.e., beam mostly polarized along direction of motion,
most promising ring options use cw & ccw beams.
scattering on C destructive on beam and phase-space,
scattering on C determines polarization of mainly particles with large betatron amplitudes, and
is not capable to determine 𝑃 = 𝑃 𝑥 𝑃 𝑦 𝑃 𝑧 .
For elastic scattering longitudinal analyzing powers are tiny ( 𝐴 𝑧 violates parity).
Ideally, use a method that would determine 𝑃 (𝑡).
Direct EDM search for charged hadrons at COSY

28. Exploit observables that depend on beam and target polarization
𝑥 (sideways)
𝑦 (up)
𝑧 (along beam) 𝜑 𝜃
beam 1 𝑃 = 𝑃 𝑥 𝑃 𝑦 𝑃 𝑧
target (or beam 2) 𝑄 = 𝑄 𝑥 𝑄 𝑦 𝑄 𝑧
Spin-dependent differential cross section for →
𝜎 𝜎 0 =1+ 𝐴 𝑦 𝑃 𝑦 + 𝑄 𝑦 cos 𝜑 − 𝑃 𝑥 + 𝑄 𝑥 sin⁡𝜑 𝐴 𝑥𝑥 𝑃 𝑥 𝑄 𝑥 cos 2 𝜑+ 𝑃 𝑦 𝑄 𝑦 sin 2 𝜑+ 𝑃 𝑥 𝑄 𝑦 + 𝑃 𝑦 𝑄 𝑥 sin 𝜑 cos 𝜑 𝐴 𝑦𝑦 𝑃 𝑥 𝑄 𝑥 sin 2 𝜑+ 𝑃 𝑦 𝑄 𝑦 cos 2 𝜑− 𝑃 𝑥 𝑄 𝑦 + 𝑃 𝑦 𝑄 𝑥 sin 𝜑 cos 𝜑 𝐴 𝑥𝑧 𝑃 𝑥 𝑄 𝑧 + 𝑃 𝑧 𝑄 𝑥 cos 𝜑 + 𝑃 𝑦 𝑄 𝑧 + 𝑃 𝑧 𝑄 𝑦 sin⁡𝜑 𝐴 𝑧𝑧 𝑃 𝑧 𝑄 𝑧
Analyzing power 𝐴 𝑦 = 𝐴 𝑦 𝜃
Spin correlations 𝐴 𝑖𝑗 = 𝐴 𝑖𝑗 (𝜃)
In 𝑝𝑝 scattering, necessary observables are well-known in the range 50−2000 MeV (not so for 𝑝𝑑 or 𝑑𝑑).
(see David Chiladze‘s talk)
Direct EDM search for charged hadrons at COSY

29. How could one do that, determine 𝑷 ?
Suggestion 1: Use a polarized H storage cell target
Detector CW
CCW
cell
Detector determines 𝑃 of cw & ccw beams separately, based on kinematics.
Alignment of target polarization 𝑄 along 𝑥, 𝑦, 𝑧 axes by magnetic fields. Leads to unwanted MDM rotations  absolute no-go in EDM experiments.
Direct EDM search for charged hadrons at COSY

30. How could one do that, determine 𝑷 ?
Suggestion 2: Use colliding beam from external source
cw beam 𝑃 = 𝑃 𝑥 𝑃 𝑦 𝑃 𝑧
probing beam 𝑄 = 𝑄 𝑥 𝑄 𝑦 𝑄 𝑧 = 𝑄 𝑥 , 0 𝑄 𝑦 0 , or 𝑄 𝑧
Detector
Polarized ion source (~10 MeV)
𝜎 𝜎 0 =1+ 𝐴 𝑦 𝑃 𝑦 + 𝑸 𝒚 cos 𝜑 − 𝑃 𝑥 + 𝑸 𝒙 sin⁡𝜑 𝐴 𝑥𝑥 𝑃 𝑥 𝑸 𝒙 cos 2 𝜑+ 𝑃 𝑦 𝑸 𝒚 sin 2 𝜑+ 𝑃 𝑥 𝑸 𝒚 + 𝑃 𝑦 𝑸 𝒙 sin 𝜑 cos 𝜑 𝐴 𝑦𝑦 𝑃 𝑥 𝑸 𝒙 sin 2 𝜑+ 𝑃 𝑦 𝑸 𝒚 cos 2 𝜑− 𝑃 𝑥 𝑸 𝒚 + 𝑃 𝑦 𝑸 𝒙 sin 𝜑 cos 𝜑 𝐴 𝑥𝑧 𝑃 𝑥 𝑸 𝒛 + 𝑃 𝑧 𝑸 𝒙 cos 𝜑 + 𝑃 𝑦 𝑸 𝒛 + 𝑃 𝑧 𝑸 𝒚 sin⁡𝜑 𝐴 𝑧𝑧 𝑃 𝑧 𝑸 𝒛
Collide two external beams with cw and ccw stored beams.
Energy tunable to match detector acceptance.
Polarization components of probing low-energy beam can be made large, would be selected by spin rotators in the transmission lines.
Luminosity estimates necessary.
Direct EDM search for charged hadrons at COSY

31. How could one do that, determine 𝑷 ?
Suggestion 3: Use directly reactions from colliding beams
Detector CW
CCW
cw beam 𝑃 = 𝑃 𝑥 𝑃 𝑦 𝑃 𝑧
ccw beam 𝑄 = 𝑄 𝑥 𝑄 𝑦 𝑄 𝑧
𝜎 𝜎 0 =1+ 𝐴 𝑦 𝑃 𝑦 + 𝑄 𝑦 cos 𝜑 − 𝑃 𝑥 + 𝑄 𝑥 sin⁡𝜑 𝐴 𝑥𝑥 𝑃 𝑥 𝑄 𝑥 cos 2 𝜑+ 𝑃 𝑦 𝑄 𝑦 sin 2 𝜑+ 𝑃 𝑥 𝑄 𝑦 + 𝑃 𝑦 𝑄 𝑥 sin 𝜑 cos 𝜑 𝐴 𝑦𝑦 𝑃 𝑥 𝑄 𝑥 sin 2 𝜑+ 𝑃 𝑦 𝑄 𝑦 cos 2 𝜑− 𝑃 𝑥 𝑄 𝑦 + 𝑃 𝑦 𝑄 𝑥 sin 𝜑 cos 𝜑 𝐴 𝑥𝑧 𝑷 𝒙 𝑸 𝒛 + 𝑷 𝒛 𝑸 𝒙 cos 𝜑 + 𝑷 𝒚 𝑸 𝒛 + 𝑷 𝒛 𝑸 𝒚 sin⁡𝜑 𝐴 𝑧𝑧 𝑷 𝒛 𝑸 𝒛
Requires luminosity, 𝛽-functions at IPs should be rather small.
Advantage over suggestion 2.: 𝑓rev supports luminosity.
Disadvantage: Sensitivity mainly from terms with 𝐴𝑥𝑧 and 𝐴𝑧𝑧.
Detailed estimates necessary.
Direct EDM search for charged hadrons at COSY

32. Luminosity estimate for the collider option
kinetic energy (MeV)
Luminosity
𝛽=10 m
𝛽=1 m
𝛽=0.1 m
Tmagic=232.8 MeV
𝜎(𝛽)= 𝜖∙𝛽
𝐿(𝑇,𝛽)= 𝑁 1 𝑁 2 𝑓 rev (𝑇) 𝑛 𝑏 4𝜋 𝜎(𝛽) 2
Conditions:
=1 m
𝑁1=𝑁2=1011
𝑛𝑏=4 (, , , )
𝛃 (𝐦)
𝛔 (𝐦𝐦) 10
3.2 1
0.1
0.32
Even under these optimistic assumptions, event rate might be sufficient.
𝐑𝐚𝐭𝐞=𝑳×𝒑𝒑
=3.1∙ [cm −2 s −1 ]× 10 −27 [ cm 2 mb −1 ]×15[mb] ≈𝟒𝟔𝟔 𝐬 −𝟏
4 polarimeters allow one to collect interactions from all bunch combinations.
(see David Chiladze‘s talk)
Direct EDM search for charged hadrons at COSY

33. Stepwise approach for all-in-one machine for JEDI
Aim / Scientific goal
Device / Tool
Storage ring 1
Spin coherence time studies
Horizontal RF-B spin flipper
COSY
Systematic error studies
Vertical RF-B spin flipper 2
COSY upgrade
Orbit control, magnets, …
First direct EDM measurement at 𝟏𝟎 −𝟐𝟒 𝐞𝐜𝐦
RF-E(B) spin flipper
Modified COSY 3
Built dedicated all-in-one ring for p, d, 3He
Common magnetic-electrostatic deflectors
Dedicated ring 4
EDM measurement of p, d, 3He at 𝟏𝟎 −𝟐𝟗 𝐞𝐜𝐦
Time scale: Steps 1 and 2: < 5 years
Steps 3 and 4: > 5 years
Direct EDM search for charged hadrons at COSY

34. Direct EDM search for charged hadrons at COSY
Summary
Measurements of EDMs are extremely difficult, but the physics is fantastic!
Two storage ring projects, at BNL and Jülich
Jülich all-in-one machine with copper-only magnets
Pursue spin coherence time measurements at COSY
First direct EDM measurement at COSY
Resonance Method with RF E(B) -fields
Optimize beam-beam polarimeter concept
JEDI collaboration established
Direct EDM search for charged hadrons at COSY

35. Georg Christoph Lichtenberg (1742-1799)
“Man muß etwas Neues machen, um etwas Neues zu sehen.”
“You have to make (create) something new,
if you want to see something new”
Direct EDM search for charged hadrons at COSY

36. Direct EDM search for charged hadrons at COSY
Spares
Direct EDM search for charged hadrons at COSY

37. Direct EDM search for charged hadrons at COSY
Technically driven timeline for all-electric pEDM at BNL 12 13 14 15 16 17 18 19 20 21
Two years R&D/preparation One year final ring design Two years ring/beam-line construction Two years installation One year “string test”
Direct EDM search for charged hadrons at COSY

38. International srEDM Network (spokesperson Yannis Semertzidis)
srEDM cooperations
International srEDM Network
Institutional (MoU) and Personal (Spokespersons …) Cooperation, Coordination
srEDM Collaboration (BNL)
(spokesperson Yannis Semertzidis)
JEDI Collaboration (FZJ) (spokespersons: A. Lehrach, J. Pretz, F.R.)
Common R&D
RHIC EDM-at-COSY
Beam Position Monitors Polarimetry
(…) Spin Coherence Time
Cooling
Spin Tracking (…)
Study Group
First direct measurement
Ring Design
DOE-Proposal (submitted)
CD0, 1, …
HGF Application(s)
pEDM Ring at BNL
JEDI
Direct EDM search for charged hadrons at COSY

39. Resonance Method with RF E-fields
spin precession governed by:
(* rest frame)
Two situations:
𝐵 ∗ =0  𝐵𝑦 = 𝐸𝑅 (=70 G for 𝐸𝑅=30 kV/cm) EDM effect
𝐸 ∗ =0  𝐸𝑅 = −𝐵𝑦 no EDM effect
Polarimeter (dp elastic)
stored d
RF E-field
vertical polarization
This way, the EDM signal is accumulated during the cycle.
Statistical improvement over single turn effect is about:
Brings us in the 10 −24 ecm range for 𝑑𝑑.
But: Flipping fields will lead to coherent betatron oscillations, with hard to handle systematics.
Direct EDM search for charged hadrons at COSY

40. Direct EDM search for charged hadrons at COSY
Simulation of resonance Method with RF E-fields for deuterons at COSY
Parameters: beam energy 𝑇𝑑=50 MeV 𝐿RF=1 m
assumed EDM 𝑑𝑑= 10 −20 ecm
E-field 10 kV/cm
E-field reversed every −/(𝐺)≈21 turns
Constant E-field
Number of turns
Number of turns
Direct EDM search for charged hadrons at COSY

41. Direct EDM search for charged hadrons at COSY
Simulation of resonance Method with RF E-fields for deuterons at COSY
Parameters: beam energy 𝑇𝑑=50 MeV
assumed EDM 𝑑𝑑= 10 −20 ecm
E-field 10 kV/cm
Linear extrapolation of for a time period of 𝑠𝑐=1000 s (=3.7108 turns)
Number of turns
EDM effect accumulates
Polarimeter determines
𝑃𝑥, 𝑃𝑦 and 𝑃𝑧
Direct EDM search for charged hadrons at COSY

42. Direct EDM search for charged hadrons at COSY
Symmetries
Physical laws are invariant under certain transformations.
𝑷: 𝒙 𝒚 𝒛 → −𝒙 −𝒚 −𝒛
Parity:
T-Symmetry:
𝑻: 𝒕 → −𝒕
C-parity (or Charge parity):
Changes sign of all quantized charges
electrical charge,
baryon number,
lepton number,
flavor charges,
Isospin (3rd-component)
Direct EDM search for charged hadrons at COSY

43. Direct EDM search for charged hadrons at COSY
Magic condition: Protons
Case 1: 𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 field only
𝐸=17 MV/m
𝑟= m
Direct EDM search for charged hadrons at COSY

44. Direct EDM search for charged hadrons at COSY
Magic condition: Protons
Case 2: 𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 and 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝑩 fields
magic energy
𝐵>0
𝐵<0
magic energy
𝐵>0
𝐵<0
Direct EDM search for charged hadrons at COSY

45. Direct EDM search for charged hadrons at COSY
Magic condition: Deuterons
𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 and 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝑩 fields
Direct EDM search for charged hadrons at COSY

46. Direct EDM search for charged hadrons at COSY
Magic condition: Helions
𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 and 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝑩 fields
Direct EDM search for charged hadrons at COSY