Download Search for permanent Electric Dipole Moments of light ions

Mitglied der Helmholtz-Gemeinschaft
Search for permanent Electric Dipole Moments of
light ions (𝑝, 𝑑, 3He) in Storage Rings
September 18, 2012
Frank Rathmann
(on behalf of the BNL-EDM and JEDI collaborations)
SPIN2012, JINR, Dubna, Russia
Topics




Introduction
Search for Electric Dipole Moments
Spin coherence time
First direct measurement
Resonance Method with RF E(B)-fields
 Conclusion
[email protected]
Search for permanent Electric Dipole Moments of light ions in Storage Rings
2
What caused the Baryon asymmetry?
Carina Nebula: Largest-seen star-birth regions in the galaxy
What happened to the antimatter?
(nB  nB ) / n
Observed
610-10
SM expectation
~10-18
WMAP+COBE (2003)
Sakharov (1967): Three conditions for baryogenesis
1. B number conservation violated sufficiently strongly
2. C and CP violated, B and anti-Bs with different rates
3. Evolution of universe outside thermal equilibrium
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
3
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!
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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History of neutron EDM limits
• Smith, Purcell, Ramsey
PR 108, 120 (1957)
• RAL-Sussex-ILL
(dn  2.9 10-26 ecm)
PRL 97,131801 (2006)
Adopted from K. Kirch
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Limits for Electric Dipole Moments
EDM searches - only upper limits, in 𝐞𝐜𝐦 (up to now):
 𝒅𝒏 equivalent
Particle/Atom
Current EDM Limit
Future Goal
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
𝟏𝟎−𝟐𝟗
Deuteron
?
𝟏𝟎−𝟐𝟗
𝟑 𝟏𝟎−𝟐𝟗 – 𝟓 × 𝟏𝟎−𝟑𝟏
Huge efforts underway to improve limits / find EDMs
Sensitivity to NEW PHYSICS beyond the Standard Model
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Why also EDMs of protons and deuterons?
Proton and deuteron EDM experiments may provide one order higher sensitivity.
In particular the deuteron may provide a much higher sensitivity than protons.
Consensus in the theoretical community:
Essential to perform EDM measurements on different targets (𝑝, 𝑑, 3He) with
similar sensitivity:
• unfold the underlying physics,
• explain the baryogenesis.
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
7
Search for Electric Dipole Moments
NEW: EDM search in time development of spin in a storage ring:

G  0
  
ds
 d E
dt
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“Freeze“ horizontal spin precession; watch
for development of a vertical component !
Search for permanent Electric Dipole Moments of light ions in Storage Rings
8
Search for Electric Dipole Moments
NEW: EDM search in time development of spin in a storage ring:

G  0
  
ds
 d E
dt
“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
[email protected]
One machine
with 𝒓 ~ 𝟑𝟎 m
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Two storage ring projects being pursued
BNL for protons all electric machine
Jülich, focus on deuterons,
or a combined machine
CW and CCW propagating beams
(from R. Talman)
[email protected]
(from A. Lehrach)
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Most recent:
Richard Talmans concept for a Jülich all-in-one machine
Iron-free, current-only, magnetic bending, eliminates hysteresis
B
A
B
A
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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BNL Proposal
2 beams simultaneously rotating in an all electric ring (cw, ccw)
Approved BNL-Proposal
Submitted to DOE
Goal for protons
 d  2.5 1029 e  cm (one year)
p
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 experiments
(demonstrators) at COSY
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
12
The frozen spin Method
   
For transverse electric and magnetic fields in a ring (   B    E  0 ),
anomalous spin precession is described by
 
2



m  E

q 
G   G  B  G    

m
p
c

  


x
g 2

G



2


Magic condition: Spin along momentum vector
1. For any sign of 𝐺, in a combined electric and magnetic machine
GBc 2
2
E

GBc

1  G 2 2
𝐸 = 𝐸radial
𝐵 = 𝐵vertical
1. For 𝐺 > 0 (protons) in an all electric ring
2
m
m
MeV


G    0  p 
 700.74
G
c
 p
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(magic)
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Magic condition: Protons
Case 1: 𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 field only

r2 280 m3He 0.0
r2 250 md 0.48 G
Proton EDM
100
radius (m)
80
𝐸 = 17 MV/m
60
r1( E)
40
𝑟 = 24.665 m
20
0
5
10
15
20
25
30
35
E
E-field (MV/m)
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
14
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.
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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
Injector cyclotron
[email protected]
COSY
… the spin-physics machine
for hadron physics
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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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
Injector cyclotron
[email protected]
COSY
… an ideal starting point
for a srEDM search
Search for permanent Electric Dipole Moments of light ions in Storage Rings
17
Spin closed orbit
one particle with
magnetic moment
makes one turn
n̂CO “spin closed orbit vector”
“spin tune”

S A
2 s

SA
ring
A
[email protected]
stable
polarization

if S ║ n̂CO
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Spin coherence
We usually don‘t worry about coherence of spins along n̂CO
Polarization not affected!
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 S  n̂CO
n̂CO
Longitudinal polarization
vanishes!
At injection all spin vectors aligned
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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.
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Estimate of spin coherence times (N.N. Nikolaev)
One source of spin coherence are random variations of the spin tune
due to the momentum spread in the beam
𝛿𝜃 = 𝐺𝛿𝛾
𝛿𝛾
and
is randomized by e.g., electron cooling
cos 𝜔𝑡 → cos 𝜔𝑡 + 𝛿𝜃
𝜏𝑠𝑐 ≈
Estimate:
1
𝑓rev 𝐺 2 𝛿𝛾 2
1
𝛿𝑝2
≈
𝑓rev 𝐺 2 𝛾 2 𝛽 4 𝑝
𝑇kin = 100 MeV
𝑓rev = 0.5 MHz
𝐺𝑝 = 1.79
𝐺𝑑 = −0.14
𝜏𝑠𝑐 (𝑝) ≈ 3 ∙ 103 s
𝜏𝑠𝑐 (𝑑) ≈ 5 ∙ 105 s
−1
Spin coherence time for deuterons may be 𝟏𝟎𝟎 × larger than for protons
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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First measurement of spin coherence time
2011 Test measurements at COSY
Polarimetry:
Spin coherence time:
5s
25 s
5s
decoherence oscillation
time
capture
[email protected]
from Ed Stephenson
and Greta Guidoboni
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Topics




Introduction
Search for Electric Dipole Moments
Spin coherence time
First direct measurement
Resonance Method with RF E(B)-fields
 Conclusion
[email protected]
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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
RF E(B)-field
stored d
Polarimeter (dp elastic)
Tilt of precession plane
due to EDM
In-plane
polarization
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
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
23
Operation of „magic“ RF Wien filter
𝑓𝐻𝑉
Radial E and vertical B fields oscillate, e.g., with
= 𝐾 + 𝐺𝛾 ∙ 𝑓rev = −54.151 × 103 Hz (here 𝐾 = 0).
beam energy
𝑇𝑑 = 50 MeV
Spin coherence time may depend on excitation and on chosen harmonics 𝐾.
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
24
Simulation of resonance Method
with „magic“ Wien filter for deuterons at COSY
Parameters:
beam energy
assumed EDM
E-field
𝑇𝑑 = 50 MeV
𝑑𝑑 = 10−24 ecm
30 kV/cm
𝐿RF = 1 m
Linear extrapolation of 𝑃𝑦 for a time period of 𝑠𝑐 = 1000 s = 3.7108 turns .
EDM effect accumulates in 𝑃𝑦.
𝑃𝑥
Preliminary, based on K. Nikolaevs derivation of the
combined rotation matrices of E/B flipper and ring
𝑃𝑧
𝑃𝑦
𝜔 = 2𝜋𝑓𝑟𝑒𝑣 𝐺𝛾 = −3.402 × 105 Hz
turn number
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
25
Simulation of resonance Method
with „magic“ Wien filter for deuterons at COSY
Parameters:
beam energy
assumed EDM
E-field
𝑇𝑑 = 50 MeV
𝑑𝑑 = 10−24 ecm
30 kV/cm
𝐿RF = 1 m
Linear extrapolation of 𝑃𝑦 for a time period of 𝑠𝑐 = 1000 s (= 3.7108 turns).
𝑃𝑃𝑦
𝑦
EDM effect accumulates in 𝑃𝑦
turn number
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
26
Simulation of resonance Method
with Magic Wien filter for deuterons at COSY
Parameters:
beam energy
assumed EDM
E-field
𝑇𝑑 = 50 MeV
𝑑𝑑 = 10−24 ecm
30 kV/cm
𝐿𝑅𝐹 = 1 m
Linear extrapolation of 𝑃𝑦 for a time period of 𝑠𝑐 = 100000 s (= 3.71010 turns).
𝑃𝑦
EDM effect accumulates in 𝑃𝑦
turn number
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
27
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”
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
28
Stepwise approach for all-in-one machine for JEDI
Step Aim / Scientific goal
1
2
Device / Tool
Storage ring
Spin coherence time studies
Horizontal RF-B spin flipper
COSY
Systematic error studies
Vertical RF-B spin flipper
COSY
COSY upgrade
Orbit control, magnets, …
COSY
First direct EDM
measurement at 𝟏𝟎−𝟐𝟒 𝐞𝐜𝐦
RF-E(B) spin flipper
Modified
COSY
3
Built dedicated all-in-one ring Common magneticfor p, d, 3He
electrostatic deflectors
Dedicated
ring
4
EDM measurement of p, d,
3He at 𝟏𝟎−𝟐𝟗 𝐞𝐜𝐦
Dedicated
ring
Time scale: Steps 1 and 2: < 5 years
Steps 3 and 4: > 5 years
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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srEDM cooperations
International srEDM Network
Institutional (MoU) and Personal (Spokespersons …) Cooperation, Coordination
srEDM Collaboration (BNL)
JEDI Collaboration (FZJ)
(spokesperson Yannis Semertzidis)
(spokespersons: A. Lehrach, J. Pretz, F.R.)
Common R&D
RHIC
Beam Position Monitors
(…)
EDM-at-COSY
Polarimetry
Spin Coherence Time
Cooling
Spin Tracking (…)
Study Group
DOE-Proposal (submitted)
CD0, 1, …
pEDM Ring at BNL
[email protected]
First direct measurement
Ring Design
HGF Application(s)
JEDI
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Summary
• Measurements of EDMs are extremely difficult,
but the physics is fantastic!
• Two storage ring projects, at BNL and 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
• JEDI collaboration established
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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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”
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Spares
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Search for permanent Electric Dipole Moments of light ions in Storage
Rings
33
Magic condition: Protons
Case 2: 𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 and 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝑩 fields
𝐵>0
𝐵<0
magic energy
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𝐵>0
𝐵<0
magic energy
Search for permanent Electric Dipole Moments of light ions in Storage Rings
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Magic condition: Deuterons
𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 and 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝑩 fields
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
35
Magic condition: Helions
𝐫𝐚𝐝𝐢𝐚𝐥 𝑬 and 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝑩 fields
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
36
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
𝑃𝑥
• is not capable to determine 𝑃 = 𝑃𝑦 .
𝑃𝑧
• For elastic scattering longitudinal analyzing powers are tiny (𝐴𝑧 violates parity).
Ideally, use a method that would determine 𝑃(𝑡).
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
37
Exploit observables that depend on
beam and target polarization
𝑃𝑥
beam 1 𝑃 = 𝑃𝑦
𝑃𝑧
𝑄𝑥
target (or beam 2) 𝑄 = 𝑄𝑦
𝑄𝑧
Spin-dependent differential cross section for
1
2
𝑦 (up)
+
1
2
1
1
→2+2
𝜃
𝑥 (sideways)
𝜑
𝑧 (along beam)
𝜎
= 1 + 𝐴𝑦 𝑃𝑦 + 𝑄𝑦 cos 𝜑 − 𝑃𝑥 + 𝑄𝑥 sin 𝜑
𝜎0
+ 𝐴𝑥𝑥 𝑃𝑥 𝑄𝑥 cos2 𝜑 + 𝑃𝑦 𝑄𝑦 sin2 𝜑 + 𝑃𝑥 𝑄𝑦 + 𝑃𝑦 𝑄𝑥 sin 𝜑 cos 𝜑
+ 𝐴𝑦𝑦 𝑃𝑥 𝑄𝑥 sin2 𝜑 + 𝑃𝑦 𝑄𝑦 cos 2 𝜑 − 𝑃𝑥 𝑄𝑦 + 𝑃𝑦 𝑄𝑥 sin 𝜑 cos 𝜑
+ 𝐴𝑥𝑧 𝑃𝑥 𝑄𝑧 + 𝑃𝑧 𝑄𝑥 cos 𝜑 + 𝑃𝑦 𝑄𝑧 + 𝑃𝑧 𝑄𝑦 sin 𝜑
+ 𝐴𝑧𝑧 𝑃𝑧 𝑄𝑧
Analyzing power 𝐴𝑦 = 𝐴𝑦 𝜃
Spin correlations 𝐴𝑖𝑗 = 𝐴𝑖𝑗 (𝜃)
In 𝑝𝑝 scattering, necessary observables are well-known
in the range 50 − 2000 MeV (not so for 𝑝𝑑 or 𝑑𝑑).
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
38
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.
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Search for permanent Electric Dipole Moments of light ions in Storage Rings
39
How could one do that, determine 𝑷 ?
Suggestion 2: Use colliding beam from external source
𝑃𝑥
cw beam 𝑃 = 𝑃𝑦
𝑃𝑧
𝑄𝑥
0
0
𝑄𝑥
probing beam 𝑄 = 𝑄Detector
0 , 𝑄𝑦 , or 0
𝑦 =
𝑄𝑧
𝑄𝑧
0
0
𝜎
= 1 + 𝐴𝑦 𝑃𝑦 + 𝑸𝒚 cos 𝜑 − 𝑃𝑥 + 𝑸𝒙 sin 𝜑
𝜎0
+ 𝐴𝑥𝑥 𝑃𝑥 𝑸𝒙 cos2 𝜑 + 𝑃𝑦 𝑸𝒚 sin2 𝜑 + 𝑃𝑥 𝑸𝒚 + 𝑃𝑦 𝑸𝒙 sin 𝜑 cos 𝜑
Polarized ion source
2 𝜑 − 𝑃 𝑸 + 𝑃 𝑸 sin 𝜑 cos 𝜑
+ 𝐴𝑦𝑦 𝑃𝑥 𝑸𝒙 sin2 𝜑 + 𝑃𝑦 𝑸𝒚 cos(~10
MeV)
𝑥 𝒚
𝑦 𝒙
+ 𝐴𝑥𝑧 𝑃𝑥 𝑸𝒛 + 𝑃𝑧 𝑸𝒙 cos 𝜑 + 𝑃𝑦 𝑸𝒛 + 𝑃𝑧 𝑸𝒚 sin 𝜑
+ 𝐴𝑧𝑧 𝑃𝑧 𝑸𝒛
• Collide two external beams with cw and ccw stored beams.
• Energy could be tuned 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
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40
How could one do that, determine 𝑷 ?
Suggestion 3: Use directly reactions from colliding beams
𝑃𝑥
cw beam 𝑃 = 𝑃𝑦
𝑃𝑧
𝑄𝑥
ccw beam 𝑄 = 𝑄𝑦
𝑄𝑧
CW
Detector
CCW
𝜎
= 1 + 𝐴𝑦 𝑃𝑦 + 𝑄𝑦 cos 𝜑 − 𝑃𝑥 + 𝑄𝑥 sin 𝜑
𝜎0
+ 𝐴𝑥𝑥 𝑃𝑥 𝑄𝑥 cos2 𝜑 + 𝑃𝑦 𝑄𝑦 sin2 𝜑 + 𝑃𝑥 𝑄𝑦 + 𝑃𝑦 𝑄𝑥 sin 𝜑 cos 𝜑
+ 𝐴𝑦𝑦 𝑃𝑥 𝑄𝑥 sin2 𝜑 + 𝑃𝑦 𝑄𝑦 cos2 𝜑 − 𝑃𝑥 𝑄𝑦 + 𝑃𝑦 𝑄𝑥 sin 𝜑 cos 𝜑
+ 𝐴𝑥𝑧 𝑷𝒙 𝑸𝒛 + 𝑷𝒛 𝑸𝒙 cos 𝜑 + 𝑷𝒚 𝑸𝒛 + 𝑷𝒛 𝑸𝒚 sin 𝜑
+ 𝐴𝑧𝑧 𝑷𝒛 𝑸𝒛
Requires luminosity, 𝛽-functions at IP should be rather small.
• Advantage over suggestion 2. is that 𝑓rev supports luminosity.
• Disadvantage is that sensitivity comes mainly from terms with 𝐴𝑥𝑧 and 𝐴𝑧𝑧.
• Detailed estimates necessary.
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41
Luminosity estimate for the collider option
Tmagic = 232.8 MeV
𝜎(𝛽) =
𝜖∙𝛽
𝑁1 𝑁2 𝑓rev (𝑇)𝑛𝑏
𝐿(𝑇, 𝛽) =
4𝜋𝜎(𝛽)2
Luminosity
𝛽 = 0.1 m
Conditions:
 = 1 m
𝑁1 = 𝑁2 = 1011
𝑛𝑏 = 4
𝛃 (𝐦)
𝛔 (𝐦𝐦)
10
3.2
1
1
0.1
0.32
𝛽 =1m
𝛽 = 10 m
kinetic energy (MeV)
Even under these very optimistic assumptions, event rate will be rather low.
𝐑𝐚𝐭𝐞 = 𝑳 × 𝒑𝒑
= 3.1 ∙ 1028 [cm−2 s−1 ] × 10−27 [cm2 mb−1 ] × 15[mb] ≈ 𝟒𝟔𝟔 𝐬 −𝟏
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42
Resonance Method with RF E-fields
spin precession governed by:
(* rest frame)
Two situations:
1. 𝐵∗ = 0  𝐵𝑦 = 𝐸𝑅 (= 70 G for 𝐸𝑅 = 30 kV/cm)
2. 𝐸 ∗ = 0  𝐸𝑅 = −𝐵𝑦
RF E-field
EDM effect
no EDM effect
vertical
polarization
stored d
Polarimeter (dp elastic)
This way, the EDM signal is accumulated during the cycle.
• Statistical improvement over single turn effect is about: 1000s / 1s  105 .
• 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.
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43
Simulation of resonance Method with RF E-fields for
deuterons at COSY
Parameters:
beam energy
assumed EDM
E-field
Constant E-field
Number of turns
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𝑇𝑑 = 50 MeV
𝑑𝑑 = 10−20 ecm
10 kV/cm
𝐿RF = 1 m
E-field reversed every
−/(𝐺) ≈ 21 turns
Number of turns
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44
Simulation of resonance Method with RF E-fields for
deuterons at COSY
Parameters:
beam energy
assumed EDM
E-field
Linear extrapolation of P 
𝑇𝑑 = 50 MeV
𝑑𝑑 = 10−20 ecm
10 kV/cm
Px2  Pz2 for a time period of 𝑠𝑐 = 1000 s (= 3.7108 turns)
EDM effect accumulates
Polarimeter determines
𝑃𝑥, 𝑃𝑦 and 𝑃𝑧
Number of turns
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45
Symmetries
Physical laws are invariant under certain transformations.
Parity:
𝑷:
𝒙
−𝒙
𝒚 → −𝒚
𝒛
−𝒛
T-Symmetry:
𝑻:
𝒕 → −𝒕
C-parity (or Charge parity):
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Changes sign of all quantized charges
• electrical charge,
• baryon number,
• lepton number,
• flavor charges,
• Isospin (3rd-component)
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46
EDM Workshop at ECT* (Trento)
October 1-5, 2012
http://www.ectstar.eu/
Organizing committee
 Jülich
Hans Ströher [email protected]
Frank Rathmann [email protected]
Andreas Wirzba [email protected]
 Brookhaven
Mei Bai [email protected]
William Marciano [email protected]
Yannis Semertzidis [email protected]
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47