Radiative capture reaction \(d(\alpha ,\gamma )^{6}Li \) is the only process in the Big-Bang model that produces \({}^{6}Li \). We develop the formalism based on pionless Effective Field Theory (EFT) for deuteron-alpha scattering to derive the cross-section of deuteron-alpha radiative capture. Based on this model, nucleons and alpha particle interact through separable two-body forces. The alpha particle is assumed point particle and the astrophysical S-factor for the \(d(\alpha ,\gamma )^{6}Li \) reaction is calculated in the low-energies. The coulomb effects are also considered as a coulomb correction in the cross-section for two first electric multipole transitions, up to Next to Leading Order (NLO). The obtained results are shown a satisfactory agreement between theoretical and experimental results for the calculated observables
