A Torsion Potential for Neutrino Oscillations in Polarised Terrestrial Matter

Neutrino oscillations in matter are governed by potentials: the charged-current potential from electrons, responsible for the MSW effect, sets the scale at about 1e-13 eV in Earth's crust. Any additional spin-dependent potential would perturb oscillation patterns, and Einstein-Cartan torsion supplies one wherever matter is polarised. This paper computes the torsion potential for long-baseline neutrinos in two settings. In ordinary crust, the only polarisation is the fraction of electron spins aligned by the geomagnetic field, about 1.12e-07 at surface temperatures, and the resulting torsion potential is 7.25e-53 eV — a fraction 5.72e-40 of the standard matter potential of 1.27e-13 eV, and therefore irrelevant to oscillation physics at any precision. In a deliberately engineered setting, a beamline target of magnetised iron, the potential rises to 1.23e-46 eV, still 31.9 orders of magnitude below the roughly 1e-14 eV potential resolution of oscillation experiments. The conclusion is stated without hedging: torsion does not participate in terrestrial neutrino oscillations, the standard matter potential is the whole story, and oscillation experiments contribute no torsion bound of interest beyond excluding coupling enhancements above about 1e32 in this channel. The paper identifies the one circumstance that could change the verdict — propagation through astrophysically polarised matter — and shows it does not occur for any baseline available to observation. Computed from stated assumptions, not measured.