LAUSR

The ${S}_{E1}$ factor of radiative $\ensuremath{\alpha}$ capture on $^{12}\mathrm{C}$ is studied in effective field theory up to next-to-leading order (NLO), and a modification of the counting rules for the radiative capture amplitudes is discussed. I find that only two unfixed parameters remain in the amplitudes up to NLO, and those two parameters are fitted to the experimental ${S}_{E1}$ data. A value of the ${S}_{E1}$ factor is calculated at the Gamow-peak energy as ${S}_{E1}=59\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{4pt}{0ex}}\mathrm{keV}\phantom{\rule{0.16em}{0ex}}\mathrm{b}$, and the result is found to be about 30% smaller than the estimates reported recently. An uncertainty of the estimate in the present work is also discussed.