Two-deuteron radiative capture reaction is one of the deuterium-burning processes that the cross section is not well known at very low-energies. We develop the formalism based on pionless Effective Field Theory (EFT) for deuteron–deuteron (dd) scattering to derive the cross section of two-deuteron radiative capture. Within this formalism the two- and three-body forces, should also be included in the capture cross section calculations. The aim of the present work is to calculate the observables of the low-energy dd photonuclear reactions. The cross section and the astrophysical S-factor for the 2H(d,γ)4He reaction have been calculated. The 4He is studied as four-body bound states in the pionless EFT. The theoretical uncertainties for observables are estimated based on the variation of the cutoffs. The astrophysical S-factor is accurately determined to be 6.9×10−6 keV b (6.1×10−6 keV b) for two-body (two- and three-body) at zero energy. A satisfactory agreement between theory and experiment for dd radiative capture observables up to order of calculation has been found by insertion of three-body force.
