Polarized Neutron $\beta$-decay: the Proton Asymmetry and Recoil-Order Currents

We present an analytic calculation of the proton asymmetry from polarized neutron $\beta$-decay, including recoil-order effects. The differential decay rate in terms of electron energy and proton direction follows, parametrized in terms of the most general Lorentz-invariant hadron current coupled to a left-handed lepton current. Implications for experimental efforts to measure recoil-order currents are discussed.