Dispersion relation analysis of the radiative corrections to gA in the neutron β-decay
Mikhail Gorchtein, Chien-Yeah Seng
Abstract
A bstract We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant g A in the neutron β -decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function g 1 , we determine the contribution from the γW -box diagram to a precision better than 10 − 4 . Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron β -decay are almost identical, i.e. the ratio λ = g A /g V is almost unrenormalized. With this result, we predict the bare axial coupling constant to be $$ {\overset{\circ }{g}}_A=-1.2754{(13)}_{\mathrm{exp}}{(2)}_{\mathrm{RC}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>g</mml:mi> <mml:mo>∘</mml:mo> </mml:mover> <mml:mi>A</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.2754</mml:mn> <mml:msub> <mml:mfenced> <mml:mn>13</mml:mn> </mml:mfenced> <mml:mi>exp</mml:mi> </mml:msub> <mml:msub> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mi>RC</mml:mi> </mml:msub> </mml:math> based on the PDG average λ = − 1 . 2756(13).