The $S_{E1}$ factor of radiative $alpha$ capture on $^{12}$C in effective field theory

The $S_{E1}$ factor of radiative $alpha$ capture on $^{12}$C is studied in effective field theory. We briefly discuss the strategy for the calculation of the reaction and report a first result of $S_{E1}$ at the Gamow-peak energy, $E_G=0.3$~MeV.