A T-odd Momentum Correlation in Radiative \beta-Decay

Abstract

We consider neutron radiative \beta-decay, n\to p e^- \bar{\nu}_e\gamma, and compute the T-odd momentum correlation in the decay rate characterized by the kinematical variable \xi = {\bf l}_\nu \cdot ({\bf l}_e\times{\bf k}) arising from electromagnetic final-state interactions in the Standard Model. Our expression for the corresponding T-odd asymmetry A_\xi^{SM} is exact in O(\alpha) up to terms of recoil order, and we evaluate it numerically under various kinematic conditions. Noting the universality of the V-A law in the absence of recoil order terms, we retain the parametric dependence on masses and coupling constants throughout, so that our results serve as a template for the computation of A_\xi^{SM} in allowed nuclear radiative \beta-decays and hyperon radiative \beta-decays as well. We consider the pattern of A_\xi^{SM} which appears in nuclear decays and show that A_\xi^{SM} can be suppressed in particular cases, facilitating searches for new sources of CP-violation in such processes.