Two searches for discrete-symmetry violation use precision comparisons
PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model
Symmetry and Flavour, Ch Parity, charge conjugation and time reversal as operators, and the CPT theorem
Problem
Two searches for discrete-symmetry violation use precision comparisons. Reversing an external electric field E while a spin precesses shifts its precession frequency by Δω=4dE/ℏ, where d is a permanent electric dipole moment and E=∣E∣.
((a)) The JILA (2023) limit on the electron electric dipole moment is ∣de∣<4.1×10−30ecm. In the molecular ion used, the bound electron feels an effective internal field of E=2.3×1010Vcm−1, far beyond any laboratory field. Using ℏ=6.582×10−16eVs, find the largest precession-frequency shift, in rads−1, that this limit on de still allows.
((b)) The BASE collaboration (2022) found the proton and antiproton charge-to-mass ratios equal to 1.6×10−11 (16 parts per trillion). Because electric charge is exactly conserved and quantised, the proton and antiproton charge magnitudes agree to far better than this precision, so the result also bounds the fractional mass difference, ∣mp−mpˉ∣/mp<1.6×10−11. Using mpc2=938.272MeV, convert this into an absolute upper bound on ∣mp−mpˉ∣, in eV, and state what the CPT theorem predicts this difference should be.