Frozen-Spin Storage Rings as Torsion Sensors: A Sensitivity Calculation

Storage rings that hold a beam's spin frozen relative to its momentum — built to search for electric dipole moments — are, by construction, exquisitely sensitive to any additional spin precession, including the precession an axial torsion background would drive. This paper converts their design sensitivities into torsion bounds. A proton frozen-spin ring targeting a precession sensitivity of 1e-09 radians per second bounds an axial torsion background at 3.34e-18 per metre, equivalent to a spin energy of 6.58e-25 eV; a deuteron ring at an existing facility, at 1e-07 radians per second, bounds it at 3.34e-16 per metre. The proton-ring figure is the second-strongest background-torsion bound in the laboratory, behind only comagnetometers, and it is obtained with a completely different systematic profile: a circulating relativistic beam rather than a stationary vapour. The paper also computes the torsion the ring's own polarised beam sources for itself — 3.28e-54 per metre for 1e11 polarised protons in a bunch — thirty-six orders below the bound, so self-sourcing is no correction at any foreseeable sensitivity. Two caveats are stated plainly: a torsion precession in a single ring is degenerate with an electric dipole signal, and the bound applies to backgrounds and extensions, since the minimal Einstein-Cartan theory provides no torsion in the ring's vacuum. Computed from stated assumptions, not measured.