## Papers in the Biological Sciences

# Radiative Neutron β-Decay in Effective Field Theory

#### Abstract

We consider radiative *β*-decay of the neutron in heavy baryon chiral perturbation theory. Nucleon-structure effects not encoded in the weak coupling constants g_{A} and g_{V} 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.

1. Framework

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 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 [3], 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. [6] 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. [4] 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) [10], including all terms in *0* (1/*M*), i.e., at next-to-leading order (NLO) in the small parameter *ε* [6]. 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.

*This paper has been withdrawn.*