Abstract
We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant gA in the neutron β-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function g1, 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 = gA/gV 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}} based on the PDG average λ = −1.2756(13).
Highlights
Where the uncertainty in the numerator arises from the Standard Model (SM) theory input
We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant gA in the neutron β-decay
This parameter is renormalized by electroweak radiative corrections (RCs), and these latter are the primary focus of this article
Summary
We start by defining the hadronic currents relevant to the β-decay of the free neutron: Jeμm. Taking into account recoil corrections ∼ ∆/M, me/M on top of the overall αem/π factor would bring us to accounting for effects in the 10−6 range that exceed the precision goal by two or three orders of magnitude This defines the level of the detalization that is needed in our analysis. This approximation leads to the neglect of the pion pole due to the partiallyconserved axial current (PCAC) hypothesis: the pion pole contribution, when contracted with the lepton tensor, results in lepton mass terms which, as stated are neglected This precision level is supported by the fact that the lowest hadronic state is separated by the pion mass ∼ 140 MeV which is about hundred times larger than ∆.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call