Precision theoretical analysis of neutron radiative beta decay

In the Standard Model of electroweak interactions and in the tree approximation we calculate the rate and branching ratio of the neutron radiative ${\beta }^{-}$ decay with one real photon emission by taking into account the contributions of the weak magnetism and proton recoil to order $1/m_p$ of the large proton mass $m_p$ expansion. We find that the obtained contributions of the weak magnetism and proton recoil increase the rate and branching ratio of the neutron radiative ${\beta }^{-}$ decay by about 0.70%. This is large compared with the contribution of the weak magnetism and proton recoil of about 0.16% to the rate of the neutron ${\beta }^{-}$ decay, calculated in Phys. Rev. D 88, 073002 (2013).

Figure 1

Feynman diagrams, defining the amplitude of the neutron radiative ${\beta }^{-}$ decay in the tree approximation.