The CNO cycle is the main energy source in massive stars during their hydrogen burning phase, and, for our sun, it contributes at the $\ensuremath{\approx}1%$ level. As the $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$ reaction is the slowest in the cycle, it determines the CNO energy production rate and thus the CNO contribution to the solar neutrino flux. These CNO neutrinos are produced primarily from the $\ensuremath{\beta}$ decay of $^{15}\mathrm{O}$ and, to a lesser extent, from the decay of $^{13}\mathrm{N}$. Solar CNO neutrinos are challenging to detect, but they can provide independent new information on the metallicity of the solar core. Recently, CNO neutrinos from $^{15}\mathrm{O}$ have been identified for the first time with the Borexino neutrino detector at the INFN Gran Sasso underground laboratory. There are, however, still some considerable uncertainties in the $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$ reaction rate under solar temperature conditions. The low energy reaction data presented here, measured at the CASPAR underground accelerator, aim at connecting existing measurements at higher energies and attempts to shed light on the discrepancies between the various data sets, while moving towards a better understanding of the $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$ reaction cross section. The present measurements span proton energies between 0.27 and 1.07 MeV, closing a critical gap in the existing data. A multichannel $R$-matrix analysis was performed with the entire new and existing data sets and is used to extrapolate the astrophysical $S$ factors of the ground state and the 6.79 MeV transition to low energies. The extrapolations are found to be in agreement with previous work, but find that the discrepancies between measured data and $R$-matrix fits, both past and present, still exist. We examine the possible reasons for these discrepancies and thereby provide recommendations for future studies.
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