Radiative Neutron β-Decay in Effective Field Theory
We consider radiative β-decay of the neutron in heavy baryon chiral perturbation theory. Nucleon-structure effects not encoded in the weak coupling constants gA and gV are determined at next-to-leading order in the chiral expansion, and enter at the 0(0.5 %)-level, making a sensitive test of the Dirac structure of the weak currents possible.
Experimental studies of β-decay at low energies have played a crucial role in the rise of the Standard Model (SM) . 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 . One component of such, the “outer” radiative correction, is captured by electromagnetic interactions with the charged, final-state particles, in the limit in which their structure is neglected. In this, neutron radiative β-decay enters, and we consider 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, enter in muon radiative capture , and (ii) to test the Dirac structure of the weak current, through the determination of the circular polarization of the associated photon [4, 5]. Here we report on our recent work—please see Ref.  for all details.
In neutron radiative β-decay, bremsstrahlung from either charged particle can occur, and radiation can be emitted from the effective weak vertex. In the pioneering work of Ref.  only the bremsstrahlung terms are computed—this suffices only if all 0(1/M) terms are neglected. Here we describe a systematic analysis of neutron radiative β-decay in the framework of heavy baryon chiral perturbation theory (HBCHPT) [7, 8, 9] and in the small scale expansion (SSE) , including all terms in 0 (1/M), i.e., at next-to-leading order (NLO) in the small parameter ε . We note that ε collects all the small external momenta and quark (pion) masses, relative to the heavy baryon mass M, which appear when HBCHPT is utilized; in case of the SSE, such is supplemented by the Δ(1232)-nucleon mass splitting, relative to M, as well. These systematic approaches allow us to calculate the recoil-order corrections in a controlled way.