Bayesian analysis of capture reactions \(\varvec{^3}\hbox {He}\varvec{(\alpha ,\gamma )^7}\hbox {Be}\) and \(\varvec{^3}\hbox {H}\varvec{(\alpha ,\gamma )^7}\hbox {Li}\)

Bayesian analysis of the radiative capture reactions $$^3\mathrm {He}(\alpha ,\gamma )^7\mathrm {Be}$$ and $$^3\mathrm {H}(\alpha ,\gamma )^7\mathrm {Li}$$ are performed to draw inferences about the cross sections at threshold. We do a model comparison of two competing effective field theory power countings for the capture reactions. The two power countings differ in the contribution of two-body electromagnetic currents. In one power counting, two-body currents contribute at leading order, and in the other they contribute at higher orders. The former is favored for $$^3\mathrm {He}(\alpha ,\gamma )^7\mathrm {Be}$$ if elastic scattering data in the incoming channel is considered in the analysis. Without constraints from elastic scattering data, both the power countings are equally favored. For $$^3\mathrm {H}(\alpha ,\gamma )^7\mathrm {Li}$$, the first power counting with two-body current contributions at leading order is favored with or without constraints from elastic scattering data.