We report the first precision measurement of the parity-violating asymmetry in the direction of proton emission with respect to the neutron spin, in the reaction $^{3}mathrm{He}(mathrm{n},mathrm{p})^{3}mathrm{H}$, using the capture of polarized cold neutrons in an unpolarized active $^3rm{He}$ target. The asymmetry is a result of the weak interaction between nucleons, which remains one of the most poorly understood aspects of electro-weak theory. The measurement provides an important benchmark for modern effective field theory (EFT) calculations. Measurements like this are necessary to determine the spin-isospin structure of the hadronic weak interaction. Our asymmetry result is $A_{PV} = left( 1.58 pm 0.97 ~mathrm{(stat)} pm 0.24~mathrm{(sys)}right)times10^{-8}$, which has the smallest uncertainty of any parity-violating asymmetry measurement so far.
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