The radiative proton capture on $^{15}$N, i.e., $^{15}$N(p,γ)$^{16}$O, is the key process which triggers the NO cycle and initiates the other types of the CNO cycle. In the present thesis, we investigate this nuclear reaction process within effective field theory approach. We first construct the effective Lagrangian which is appropriate for this process at stellar energies and calculate the capture am- plitudes by using the approach from the cluster effective field theory. From the obtained capture amplitudes, we evaluate the total cross sections and the astro- physical S-factor in terms of the resonance energies and widths of intermediate resonance states for this reaction. We then perform numerical calculations and determine the model parameters by fitting our results to the empirical data for the S-factor at the range of 180 keV < $E_p$ < 1800 keV. The obtained values of the parameters such as the low-energy constants, resonance energies, and widths allow us to extrapolate the S-factor to the extremely low-energy region, i.e., S(E = 0). As a result, we obtain the value of S(E = 0) = 41.6 keV ⋅ b which is in good agreement with the empirical value, S(E = 0) = 39.6 ± 2.6 keV ⋅ b.
Supervisor: Prof. Yongseok Oh