Difference of measured proton and He3 EDMs: a reduced systematics test of T-reversal invariance

The upper limit on (time reversal symmetry T-violating) permanent hadron electric dipole moments (EDMs) is the PSI neutron EDM value; $d_n = (0.0\pm1.1_{\rm stat}\pm0.2_{\rm sys}\times10^{-26})\,e$\,cm. This paper describes an experiment to be performed at a BNL-proposed CLIP project which is to be capable of producing intense polarized beams of protons, $p$, helions (He${}^3$ nuclei), h, and other isotopes. The EDM prototype ring PTR (proposed at COSY Lab, Juelich) is expected to measure individual particle EDMs (for example ${\rm EDM\_p}$ for the proton) using simultaneous counter-rotating polarized proton beams, with statistical error $\pm10^{-30}$e.cm after one year running time, four orders of magnitude less than the PSI neutron EDM upper limit, and with comparable systematic error. A composite particle, the helion faces T-symmetry constraints more challenging than the proton. Any measurably large value of $$\Delta={\rm EDM}_h-{\rm EDM}_p,$$ the difference of helion and proton EDMs, would represent BSM physics. The plan is to replicate PTR at BNL. The dominant systematic error would be canceled two ways, both made possible by phase-locking "doubly-magic" 38.6\,MeV proton and 39.2\,MeV helion spin tunes. This stabilizes their MDM-induced in-plane precessions, without affecting their EDM-induced out-of-plane precessions. The dominant systematic error would therefore cancel in the meaurement of $\Delta$ in a fixed field configuration. Another systematic error cancellation will come from averaging runs for which both magnetic field and beam circulation directions are reversed. Precise magnetic field reversal is made possible by the reproducible absolute frequency phase-locking over long runs to eliminate the need for (impractically precise) magnetic field measurement. Risk of EDM measurement failure is discussed in a final appendix.