T-odd momentum correlation in radiative β decay

Abstract

We consider neutron radiative β decay, n → pe −ν e γ, and compute the T-odd momentum correlation in the decay rate characterized by the kinematical variable ξ = l ν · (l e × k) arising from electromagnetic final-state interactions in the Standard Model. Our expression for the corresponding T-odd asymmetry A SM ξ is exact in O(α) 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 recoilorder 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 SM ξ in allowed nuclear radiative β decays and hyperon radiative β decays as well.

Gauge properties of hadronic structure of nucleon in neutron radiative beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

“…5e and Fig. 5f goes beyond the previous analysis of the neutron radiative β − -decay [69][70][71][72] (see also [20,21,30,73]). The contribution of the Feynman diagrams in Fig.…”

“…5d, Fig 5e and Fig 5f describe the contribution of strong low-energy interactions, which is fully caused by mesonic parts of the charged axial-vector hadronic current, defined in the LσM in the phase of spontaneously broken chiral symmetry. It should be also noticed that such a contribution does not appear in previous calculations of the neutron radiative β − -decay [69][70][71][72] (see also [20,21,30,73]).…”

“…where λ = 1, 2 characterizes physical polarization states of the photon [20,21,30,[69][70][71][72][73].…”

“…(62) is invariant under a gauge transformation ε * λ (k) → ε * λ (k) + c k. The first two terms in Eq. (62) describe the amplitude of the neutron radiative β − -decay to leading order in the large proton mass expansion in the previous analysis of such a decay [69][70][71][72] (see also [20,21,30,73]), where strong low-energy interactions contribute only in terms of the axial couping constant g A . The contributions of the last four terms in Eq.…”

“…Such tadpole contributions are mutually cancelled from the first two terms in curly brackets in Eq. (71). For the scalar product k · Λ p (k p , k) we obtain the following expression…”