Dispersive Evaluation of the Inner Radiative Correction in Neutron and Nuclear $\beta$-decay

Understand

We propose a novel dispersive treatment of the so-called inner radiative correction to the neutron and nuclear $\beta$-decay.

• We show that it requires knowledge of the parity-violating structure function $F_3^{(0)}$ that arises from the interference of the axial vector charged current and the isoscalar part of the electromagnetic current.
• By isospin symmetry, we relate this structure function to the charged current inelastic scattering of neutrinos and antineutrinos.
• Applying this new data-driven analysis we obtain a new, more precise evaluation for the universal radiative correction $\Delta_{R}^{V,\,new}=0.02467(22)$ that supersedes the previous estimate by Marciano and Sirlin, $\Delta_R^V=0.02361(38)$.