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Mitglied der Helmholtz- Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI) Beam Dynamics meets Diagnostics, Firenze, Italy

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Page 1: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Mit

glie

d d

er

Helm

holt

z-G

em

ein

sch

aft

Challenges of Electric Dipole Moment searches

using Storage Rings

November 4, 2015 Frank Rathmann (on behalf of JEDI)Beam Dynamics meets Diagnostics, Firenze, Italy

Page 2: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 2

Outline

[email protected]

• Introduction• Achievements• Technical challenges• Toward a first direct EDM measurement• Conclusion

Page 3: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

3

Physics: Observed Baryon Asymmetry

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings

Carina Nebula: Largest-seen star-birth regions in the galaxy

Observed WMAP+COBE (2003)

SM exp.

• Search for new physics beyond the standard model• Mystery of missing antimatter addresses the puzzle of our existence

Why this strange number? Why not zero?

Page 4: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 4

Physics: Baryogenesis

Ingredients for baryogenesis: 3 Sakharov conditions

[email protected]

(1967)

Page 5: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] 5Challenges of Electric Dipole Moment searches using Storage Rings

Permanent EDMs violate both and symmetry.

Assuming to hold, violated also.

Not Charge symmetric (aligned with spin)

EDMs: Discrete Symmetries

: MDM: EDM

EDM:

: :

Page 6: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 6

EDMs: Naive estimate of the nucleon EDM scale

• & conserving magnetic moment nuclear magneton

• A non-zero EDM requires • violation: the price to pay is , and• violation (from K-decays): the price to pay is

• In summary:

• In SM (without term):

[email protected]

Khriplovich & Lamoreux (1997); Nikolaev (2012)

Region to search for BSM physics :

|𝒅𝑵|≈𝟏𝟎−𝟕×𝟏𝟎−𝟑×𝝁𝑵≈𝟏𝟎−𝟐𝟒𝐞𝐜𝐦

|𝒅𝑵𝐒𝐌|≈𝟏𝟎−𝟕×𝟏𝟎−𝟐𝟒≈𝟏𝟎−𝟑𝟏𝐞𝐜𝐦

Page 7: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

EDM searches: Up to now only upper limits (in )

[email protected] 7Challenges of Electric Dipole Moment searches using Storage Rings

Particle/Atom Current EDM Limit Future Goal

Electron

Muon

Neutron

Proton

Deuteron ?

Physics: Present limits of EDMs

Large effort on worldwide scale to improve limits and to find EDMs

• No direct measurements of electron ( molecule) or proton () EDMs• No measurement at all of deuteron EDM

Page 8: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 8

Prospects of charged particle EDMs:

[email protected]

• No direct measurements of charged hadron EDMs

• Potentially higher sensitivity than neutrons• protons/deuterons are stable• more stored polarized protons/deuterons• larger electric fields

• Approach complimentary to neutron EDM

• EDM of a single particle not sufficient to identify source • access to

Charged particle EDM experiments potentially provide a higher sensitivity than, e.g., nEDM

?

Page 9: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] 9Challenges of Electric Dipole Moment searches using Storage Rings

For transverse electric and magnetic fields in a ring, theanomalous spin precession is described by Thomas-BMT equation:

Magic condition: Spin along momentum vector

1. For any sign of , in a combined electric and magnetic machine

, where and

2. For (protons) in an all electric ring

(magic)

Concept for srEDM: Frozen spin Method

Magic rings to measure EDMs of free charge particles

ΩMDM=𝑞𝑚 {𝐺 ∙ ��− 𝛾 𝐺𝛾+1

�� ( �� ∙𝐸 )−[𝐺− 1

𝛾 2−1 ] ��× ��𝑐 }(𝐺=𝑔−22 )

Page 10: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

• Place particles in a storage ring• Align spin along momentum („freeze“ horizontal spin precession)• Search for time development of vertical polarization

[email protected] 10Challenges of Electric Dipole Moment searches using Storage Rings

Concept: Rings for EDM searches

New Method to measure EDMs of charged particles:• Magic rings with spin frozen along momentum• Polarization buildup

��𝐺=0

𝑑 ��𝑑𝑡

=��× ��

Page 11: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

A magic storage ring for protons (electrostatic), deuterons, …

[email protected] 11Challenges of Electric Dipole Moment searches using Storage Rings

particleproton

Concepts: Magic Storage ring

Possible to measure , , using one machine with m

B

deuteron

280.0

��𝐺=0𝑑 ��𝑑𝑡

=��× ��

Page 12: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 12

Goal: provide to the same level

𝝈𝐬𝐭𝐚𝐭 ≈𝟏

√𝑵 ∙ 𝒇 ∙𝝉 ∙𝑷 ∙ 𝑨𝒚 ∙𝑬⇒𝝈𝐬𝐭𝐚𝐭 (𝟏𝐲𝐞𝐚𝐫 )=𝟏𝟎−𝟐𝟗𝐞 ∙𝐜𝐦

• High precision, primarily electric storage ring• alignment, stability, field homogeneity, and shielding from

perturbing magnetic fields• High beam intensity ()• Stored polarized hadrons ()• Large electric fields ()• Long spin coherence time ()• Efficient polarimetry ()

[email protected]

Concept: Experimental requirements

Page 13: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 13

Magnetic fields:• Radial field mimics EDM effect when • With in a field of ,

• Solution: Use two beams simultanously, clockwise (CW) and counter-clockwise (CCW), the vertical separation of the beam orbits is sensitive to .

[email protected]

Challenges: Systematic errors

Use CW and CCW beams to tackle systematics

Page 14: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 14

• Splitting of beam orbits: • denotes the vertical betatron tune• Modulate with • Splitting corresponds to • In one year of measurement: fills of each

per fill

[email protected]

Concept: Systematics, Orbit splitting (Dave Kawall)

Required sensitivity , achievable with state-of-the-art SQUID magnetometers.

Page 15: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

A

AS

one particle with magnetic moment

“spin tune”

“spin closed orbit vector”COn

s2AS

ring

makes one turn

stable polarizationS

if ║ COn

[email protected] 15Challenges of Electric Dipole Moment searches using Storage Rings

Insert: Spin closed orbit and spin tune

Spin closed orbit

¿2𝜋𝛾𝐺

The number of spin precessions per turn is called spin tune

Page 16: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenge: Spin coherence time (SCT)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings 16

We usually don‘t worry about coherence of spins along

At injection all spin vectors aligned (coherent)

After some time, spin vectors get out of phase and fully populate the cone

Polarization along not affected!

Situation very different, when you deal with machines with frozen spin.

At injection all spin vectors aligned Later, spin vectors are out of phase in the horizontal plane

Longitudinal polarization vanishes!

COn

In a machine with frozen spins the buildup time

to observe a polarization is limited by .

Page 17: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

EDM at COSY: COoler SYnchrotron

Cooler and storage ring for (polarized) protons and deuterons

Phase space cooled internal & extracted beams

Injector cyclotron

COSY

… the spin-physics machinefor hadron physics

[email protected] 17Challenges of Electric Dipole Moment searches using Storage Rings

… an ideal starting pointfor EDM search

Page 18: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 18

Outline

[email protected]

• Introduction• Achievements

• Spin coherence time• Spin tune measurement

• Technical challenges• Toward a first direct EDM measurement• Conclusion

Page 19: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings [email protected]

Polarimeter: Determination of SCT

Observed experimental decay of the asymmetry as function of time, .

𝝉𝐒𝐂𝐓≈𝟐𝟎𝐬

Page 20: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings [email protected]

Polarimeter: Optimization of SCTUsing sextupole magnets in the machine, higher order effects can be corrected, and the SCT is substantially increased

𝝉𝐒𝐂𝐓≈𝟒𝟎𝟎𝐬

More details by Volker Hejny on Thursday

Good progress toward

Page 21: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 21

SCT: Chromaticity studies

[email protected]

Maximal horizontal polarization lifetimes from scans with a horizontally wide or a long beam

agree well with the lines of .

Chromaticity defines the betatron tune change with respect to the momentum deviation

• Strong connection between and observed.

• COSY Infinity predicts negative natural chromaticities and .

• Measured natural chromaticity: and .

Crucial for achieving a large is careful adjustment of .

Page 22: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings [email protected]

Spin tune: D

Spin tune determined to in 2 s time interval, and in a cycle at to (PRL 115, 094801 (2015)

Monitor phase of asymmetry with fixed in a 100 s cycle.

see talk by Volker Hejny

Page 23: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 23

New precision tool: Spin tune determination

[email protected]

• Study long term stability of an accelerator• Develop feedback systems to minimize variations• Phase-locking the spin precession to RF devices possible

Observed behavior of subsequent cycles

Page 24: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 24

Outline

[email protected]

• Introduction• Achievements• Technical challenges

• Magnetic shielding• Beam position monitors• Electrostatic deflectors

• Toward a first direct EDM measurement• Conclusion

Page 25: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings

Charged particle EDM searches require the development of a new class of high-precision machines with mainly electric fields for bending and focussing.

Topics:• Magnetic shielding of machine

• Beam position monitoring • Electric field gradients at plate distance • Spin coherence time • Continuous polarimetry • Spin tracking

Topics must be addressed experimentally at existing facilities

Technical challenges: Overview

Page 26: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 26

Recent Progress: Magnetic shielding

Next generation nEDM experiment under development at TUM (FRM II):• Goal: Improve present nEDM limit by factor .• Experiment shall use multi-layer shield.• Applied magnetic field: .

[email protected]

J. Appl. Phys. 117 (2015)

At mHz frequencies, damping of achieved

Page 27: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings [email protected]

EDM experiments use bunched beams:• Rogowski coil system well-suited.• Small size allows for flexible installation ( Stripline RF Wien filter)

Quadrant signals of Rogowski coil sensitive to beam position.

• Integral signal measures beam current• Quadrant signals sensitive to position

Challenge BPMs: Rogowski coil

𝑥=¿¿ ¿¿¿ ¿

𝑦=up−downup+downleft right

down

up

Dynamic range• particles• Maximum deviation from axis • Resolution:

Page 28: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings

Challenge: Niobium electrodes

Large-grain Nb at plate separation of a few cm yields ~20 MV/m

Show one slide on JLAB data HV devicesDPP stainless steel fine-grain Nb

large-grain Nblarge-grain Nb single-crystal Nb

Page 29: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings [email protected]

Challenge: Electric deflectors for magic rings

Electrostatic separators at Tevatron were used to avoid unwanted interactions - electrodes made from stainless steel

Routine operation at at

L~2.5 m

Need to develop new electrode materials and surface treatments

May 2014: Transfer of separator unit plus equipment from FNAL to Jülich

Page 30: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 30

Outline

[email protected]

• Introduction• Achievements• Technical challenges• Toward a first direct EDM measurement• Conclusion

Page 31: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings

Use COSY for a first direct and EDM measurement

Use an RF technique:

• RF device operates on some harmonic of the spin precession frequency

• accumulate EDM signal with time

Proof-of-principle: A storage ring EDM measurement

Page 32: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings 32

Direct EDM measurement : 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.

„Magic RF Wien Filter“ no Lorentz force Indirect EDM effect

Observable:Accumulation of vertical polarization during spin coherence time

Polarimeter (dp elastic)

stored d

RF E(B)-fieldIn-plane

polarization

Statistical sensitivity for in the range to range possible.• Alignment and field stability of ring magnets• Imperfection of RF-E(B) flipper

Page 33: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings 33

First direct EDM measurement: Resonance Method for deuteronsParameters: beam energy

assumed EDME-field

𝐭𝐮𝐫𝐧𝐧𝐮𝐦𝐛𝐞𝐫

𝑷 𝒙 𝑷 𝒛 𝑷 𝒚

EDM effect accumulates in (see Phys. Rev. ST AB 16, 114001 (2013))

Page 34: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings 34

Parameters: beam energy assumed EDME-field

EDM effect accumulates in

𝑃 𝑦

𝐭𝐮𝐫𝐧𝐧𝐮𝐦𝐛𝐞𝐫

𝑷 𝒚

Linear extrapolation of for a time period of yields a sizeable .

First direct Edm measurement: Resonance Method for deuterons

Systematics of EDM polarization buildup with RF Wien filter dominated by machine imperfection fields, closed-orbit distortions etc.

see talk by Marcel Rosenthals today

Page 35: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 35

Next: RF Wien filter: Strip line design

[email protected]

Strip line design provides

Strip-line RF Wien filter (in cooperation with RWTH).Available 2nd half of 2015.

∫−𝐿

𝐿

𝐵𝑦𝑑𝑧=0.02371Tmm

𝐹𝐿=12𝐿∫

−𝐿

𝐿

𝐹𝐿𝑑𝑧=1.8 ∙10− 4 eVm

Device will be installed in PAX low- section

BPM(Rogowski coil)

Ferrit cage

Copperelectrodes

Mechanical

support

RF feedthrough

Device rotatable by in situ

Page 36: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Step Aim / Scientific goal Device / Tool Storage ring

1Spin coherence time studies Horizontal RF-B spin flipper COSY

Systematic error studies Vertical RF-B spin flipper COSY

2COSY upgrade Orbit control, magnets, … COSY

First direct EDM measurement at

RF Wien filterModified COSY

3Built dedicated all-in-one ring for , ,

Common magnetic-electrostatic deflectors

Dedicated ring

4EDM measurement of , , at Dedicated

ring

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings 36

Timeline: Stepwise approach towards all-in-one machine

Time scale: Steps 1 and 2: years

Steps 3 and 4: years

Page 37: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 37

JEDI Collaboration

• JEDI = Jülich Electric Dipole Moment Investigations

• ~100 members (Aachen, Dubna, Ferrara, Indiana, Ithaka, Jülich, Krakow, Michigan, Minsk, Novosibirsk, St Petersburg, Stockholm, Tbilisi, … http://collaborations.fz-juelich.de/ikp/jedi/)

• ~ 10 PhD students

[email protected]

May the force be with us!

Page 38: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

• EDMs offer new window to disentangle sources of violation, and to explain matter-antimatter asymmetry of the universe.

• First direct EDM measurements () at COSY using stripline RF Wien filter

• Development of a dedicated EDM storage ring • Conceptual design report

• Spin tune: A new precision tool for accelerator studies

• Development of:• Feedback systems to minimize spin tune variations, phase-locking

the spin precession to RF devices• high-precision spin tracking tools, incl. RF structures.• electrostatic deflectors (also ).• beam position monitors • magnetic shielding

[email protected] Challenges of Electric Dipole Moment searches using Storage Rings 38

Conclusion

Very challenging …, but the physics is fantastic.

Page 39: Mitglied der Helmholtz-Gemeinschaft Challenges of Electric Dipole Moment searches using Storage Rings November 4, 2015 Frank Rathmann (on behalf of JEDI)

Challenges of Electric Dipole Moment searches using Storage Rings 39

Publications

Experiment:

1. A. Lehrach, B. Lorentz, W. Morse, N.N. Nikolaev, F. Rathmann, Precursor Experiments to Search for Permanent Electric Dipole Moments (EDMs) of Protons and Deuterons at COSY, e-Print: arXiv:1201.5773 (2012).

2. N.P.M. Brantjes et al., Correcting systematic errors in high-sensitivity deuteron polarization measurements, Nucl. Instrum. Meth. A664, 49 (2012), DOI: 10.1016/j.nima.2011.09.055

3. P. Benati et al., Synchrotron oscillation effects on an rf-solenoid spin resonance, Phys. Rev. ST Accel. Beams 15 (2012) 124202, DOI: 10.1103/PhysRevSTAB.15.124202.

4. F. Rathmann, A. Saleev, N.N. Nikolaev [JEDI and srEDM Collaborations], The search for electric dipole moments of light ions in storage rings, J. Phys. Conf. Ser. 447 (2013) 012011, DOI: 10.1088/1742-6596/447/1/012011.

5. Z. Bagdasarian et al., Measuring the Polarization of a Rapidly Precessing Deuteron Beam, Phys. Rev. ST Accel. Beams 17 (2014) 052803, DOI: 10.1103/PhysRevSTAB.17.052803.

6. F. Rathmann et al. [JEDI and srEDM Collaborations], Search for electric dipole moments of light ions in storage rings, Phys. Part. Nucl. 45 (2014) 229, DOI: 10.1134/S1063779614010869.

7. D. Eversmann et al. [JEDI Collaboration], New method for a continuous determination of the spin tune in storage rings and implications for precision experiments, Phys. Rev. Lett. 115, 094801 (2015), DOI: 10.1103/PhysRevLett.115.094801

[email protected]

Theory:

J. Bsaisou, J. de Vries, C. Hanhart, S. Liebig, Ulf-G. Meißner, D. Minossi, A. Nogga, A. Wirzba, Nuclear Electric Dipole Moments in Chiral Effective Field Theory, Journal of High Energy Physics 3, 104 (2015), DOI:10.1007/JHEP03(2015)104