Radiative Neutron β-Decay in Effective Field Theory

Experimental studies of β-decay at low energies have played a crucial role in the rise of the Standard Model (SM) [1]. In recent years, continuing, precision studies of neutron β-decay have been performed, to better both the determination of the neutron lifetime and of the correlation coefficients. To realize a SM test to a precision of ≈1 % or better requires the application of radiative corrections [2]. One component of such, the “outer ” radiative correction, is captured by electro-magnetic interactions with the charged, final-state par-ticles, in the limit in which their structure is neglected. In this, neutron radiative β-decay enters, and we con-sider it explicitly. We do so in part (i) to study the hadron matrix elements in O(1/M), as the same matrix elements, albeit at different momentum transfers, ente