An Ultraweak Focusing Storage Ring for Proton EDM Measurement - PowerPoint PPT Presentation

1 An Ultraweak Focusing Storage Ring for Proton EDM Measurement Richard Talman Laboratory for Elementary-Particle Physics Cornell University 4 October, 2017, Juelich

2 Outline Force Field Symmetries Why Measure EDM? Two experiments that “could not be done” Achievable precision (assuming *Stern-Gerlach polarimetry* and *Phase-locked “Penning-like” trap operation* ) Design requirements for proton EDM storage ring, e.g. at CERN Proposed ring design *Weak-weaker WW-AG-CF focusing* Parameter table The Brookhaven “AGS-Analogue” electrostatic ring Off-momentum closed orbits Potential energy Ultraweak focusing Total drift length condition for below-transition operation *Self-magnetometry* Lattice Functions Heading only—Analytic betatron oscillation description Heading only— *Virial theorem “absence” of decoherence* Heading only— *Stochastic cooling stabilization of IBS ?*

3 Force Field Symmetries: Vectors and Pseudovectors moving + charges + I I + + + EDM = MDM = current, I charge x separation current x area a vector a pseudo−vector a vector compass needle I looks like vector acts like pseudo−vector S N ◮ An electric dipole moment (EDM) points from plus charge toward minus charge—the “orientation” of a true vector . ◮ The axis of a magnetic dipole moment (MDM) is perpendicular to a current loop, whose direction gives a different “orientation”. The MDM is a pseudo-vector . ◮ Amp` ere: how does the compass needle know which way to turn?

4 Capsule history of force field symmetries ◮ Newton: Gravitational field, (inverse square law) central force ◮ Coulomb: By analogy, electric force is the same (i.e. central) ◮ Ampere: How can compass needle near a current figure out which way to turn? Magnetic field is pseudo-vector . A right hand rule is somehow built into E&M and into the compass needle. ◮ The upshot: by introducing pseudo-vector magnetic field, E&M respects reflection symmetry, ◮ but compound objects need not exhibit the symmetry. ◮ this was the first step toward the grand unification of all forces. ◮ Lee, Yang, etc: A particle with spin ( pseudo-vector ), say “up”, can decay more up than down ( vector ); ◮ i.e. the decay vector is parallel (not anti-parallel) to the spin pseudo-vector, ◮ viewed in a mirror, this statement is reversed. ◮ i.e. weak decay force violates reflection symmetry (P). ◮ Fitch, Cronin, etc: standard model violates both parity (P) and time reversal (T), so protons, etc. must have both MDM and EDM ◮ Current task: How to exploit the implied symmetry violation to measure the EDM of proton, electron, etc?

5 Why Measure EDM? ◮ Violations of parity (P) and time reversal (T) in the standard model are insufficient to account for excess of particles over anti-particles in the present day universe. ◮ Any non-zero EDM of electron or proton would represent a violation of both P and T, and therefore also CP. Comments: ◮ Beam direction reversal is possible in all-electric storage ring, with all parameters except injection direction held fixed. This is crucial for reducing systematic errors. ◮ “Frozen spin” operation in all-electric storage ring is only possible with electrons or protons—by chance their anomalous magnetic moment values are appropriate. The “magic” kinetic energies are 14.5 MeV for e, 233 MeV for p.

6 EDM Sensitive Configuration—modern day Amp` ere experiment Proton is "magic" with all three spin components "frozen" (relative to orbit) proton spin proton orbit (Large) central negative point charge E x d torque d m E Do proton spins tip up or down? EDM MDM And by how much? Two issues: ◮ Can the tipping angle be measurably large for plausibly large EDM, such as 10 − 30 e-cm? With modern, frequency domain, technology, yes ◮ Can the symmetry be adequately preserved when the idealized configuration above is approximated in the laboratory? This is the main issue

The neutron storage ring under construction at Preliminary results from the Bonn neutron the University of Bonn. Its 1.2 m diameter storage ring. After some losses in the first few superconducting magnet gives a peak field of minutes, the level of neutrons begins to 3.5 T and enables neutrons to be stored for decrease simply as a resuit ofbeta decay, with a some 20 minutes at an energy of 2 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA x W~ 6 eV. half life of some 15 minutes. This will enable The ring is now in opération at the Institut Laue- the lifetime of the neutron to be measured Langevin research reactor, Grenoble. accurately. 7 Two experiments that “could not be done” (Photo Bonn) t time [s] taking its particles from the low energy 0 20 40 60 80 région of the Maxwellian distribution (a) of neutrons emerging from the reactor, a précise velocity sélection would [rad] reduce the number of neutrons to an 3.5 unacceptable level. The Bonn storage ring therefore has to work with a wide momentum spread ( A p/p of about 3), ∼ ϕ with the resuit that many 'stopbands' phase 3 and résonance effects have to be con- fronted. To stabilise the neutron orbits and minimise losses due to thèse effects, the periodic sextupole field is sup- 2.5 plemented by a non-linear decapole contribution, which makes the beta- tron frequency amplitude-dependent. (b) Particle oscillations, which occur with increasing amplitudes in thèse résonance régions, can be controlled. 0 Only one spin component of the ] -9 neutrons, with the spin parallel to the [10 magnetic field, can be confined, and care has to be taken in the design of the field to avoid spin flips so as to s -2 maintain the number of stored ν ∆ neutrons. Neutrons from the reactor are guided and injected into the ring by a system of bent nickel-coated glass -4 mirrors. Neutrons passing througH matter have an effective refractive in- 0 10 20 30 40 50 60 70 dex and, under the right conditions, n 6 total reflection may occur, as with number of particle turns [10 ] electromagnetic radiation. The injec- tion system can be moved out of the storage zone by a pneumatic mecha- nism which opérâtes fast enough to FIG. 3. (a): Phase ˜ ϕ as a function of turn number n for allow injection of a single turn. The stored neutrons are detected by mov- all 72 turn intervals of a single measurement cycle for ν fix = f ing helium-3 counters into the ring. s The whole apparatus, including the − 0 . 160975407 , together with a parabolic fit. (b): Deviation , superconducting magnet, was con- ∆ ν s of the spin tune from ν fix as a function of turn number in structed at Bonn and then moved to s ILL. Within three weeks neutrons were the cycle. At t ≈ 38 s, the interpolated spin tune amounts to successfully stored at the first attempt. . After some losses in the first few minu- ν s = ( − 16097540771 . 7 ± 9 . 7) × 10 − 11 . The error band shows tes of each storage, the remaining neu- tron intensity decreases simply as a re- the statistical error obtained from the parabolic fit, shown in suit of beta decay, which has a half-life of about fifteen minutes. Neutrons are panel (a). still détectable after twenty minutes. 366 Figure: COSY, Eversmann et al.: (Pseudo-)frozen spin deuterons, and Bonn, Paul et al.: neutron storage ring

8 Achievable precision (assuming perfect phase-lock) ◮ EDM in units of (nominal value) 10 − 29 e-cm ≡ ˜ d ◮ 2 x EDM(nominal)/MDM precession rate ratio: 2 η ( e ) = 0 . 92 × 10 − 15 ≈ 10 − 15 ◮ duration of each one of a pair of runs = T run ◮ smallest detectable fraction of a cycle = η fringe = 0 . 001 N FF = EDM induced fractional fringe shift per pair of runs d 10 − 15 · 10 · 10 7 · 10 3 =(2 η ( e ) )˜ � e . g . d � ≈ ˜ = 0 . 1˜ h r f 0 T run d , 10 − 3 η fringe Assumed roll rate reversal error : ± η rev . e . g . = 10 − 10 σ rev . FF = roll reversal error measured in fractional fringes ≈ ± 10 2 · 10 − 10 · 10 3 � e . g . = ± f roll η rev . T run = 10 − 2 � . 10 − 3 η fringe

9 Anticipated precision limit Space domain, EDM-induced vertical polarization, p-Carbon polarimetry error after 10 4 particle | d elec | current upper limit pairs of runs e-cm e-cm 3 × 10 − 26 neutron 8 × 10 − 25 ± 10 − 29 proton 10 − 28 ± 10 − 29 electron Frequency domain, EDM-induced spin tune shift, phase-locked Stern-Gerlach polarimetry error after 10 4 particle | d elec | current excess fractional roll reversal upper limit cycles per pair pairs of runs error e-cm of 1000 s runs e-cm e-cm 3 × 10 − 26 neutron 8 × 10 − 25 ± 8 × 10 3 ± 10 − 30 ± 10 − 30 proton 10 − 28 ± 10 − 30 ± 10 − 30 electron ± 1