Corrections of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e23" altimg="si8.svg"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>∕</mml:mo><mml:msubsup><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>)</mml…

We calculate the contributions of weak magnetism and proton recoil order O(Ee2∕mN2)∼10−5, i.e. to next-to-next-to-leading in large nucleon mass expansion, neutron lifetime correlation coefficients beta decay, where Ee mN are electron energy mass, respectively. analyze electron-energy angular distribution for decay with a polarized neutron, an unpolarized proton. Together Wilkinson’s corrections (Wilkinson, 1982; radiative O(αEe∕mN)∼10−5 Ivanov et al., 2019), calculated as next-to-leading expansion Sirlin’s O(α∕π) (Sirlin, 1967), O(Ee2∕mN2)∼10−5 provide improved level precision theoretical background Standard Model, experimental searches interactions beyond Model.