Radiative neutron capture on a proton at big-bang nucleosynthesis energies

Abstract

The total cross section for radiative neutron capture on a proton, $\mathit{np}\ensuremath{\rightarrow}d\ensuremath{\gamma}$, is evaluated at big-bang nucleosynthesis (BBN) energies. The electromagnetic transition amplitudes are calculated up to next-to-leading-order within the framework of pionless effective field theory with dibaryon fields. We also calculate the $d\ensuremath{\gamma}\ensuremath{\rightarrow}\mathit{np}$ cross section and the photon analyzing power for the $d\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\rightarrow}\mathit{np}$ process from the amplitudes. The values of low-energy constants that appear in the amplitudes are estimated by a Markov Chain Monte Carlo analysis using the relevant low-energy experimental data. Our result agrees well with those of other theoretical calculations except for the $\mathit{np}\ensuremath{\rightarrow}d\ensuremath{\gamma}$ cross section at some energies estimated by an $R$-matrix analysis. We also study the uncertainties in our estimation of the $\mathit{np}\ensuremath{\rightarrow}d\ensuremath{\gamma}$ cross section at relevant BBN energies and find that the estimated cross section is reliable to within $~1$% error.