Enhanced $S$-factor for the $^{14}$N$(p,\gamma)^{15}$O reaction and its impact on the solar composition problem

The solar composition problem has puzzled astrophysicists for more than 20 years. Recent measurements of carbon-nitrogen-oxygen (CNO) neutrinos by the Borexino experiment show a $\sim2\sigma$ tension with the "low-metallicity" determinations. $^{14}$N$(p,\gamma)^{15}$O, the slowest reaction in the CNO cycle, plays a crucial role in the standard solar model (SSM) calculations of CNO neutrino fluxes. Here we report a direct measurement of the $^{14}$N$(p,\gamma)^{15}$O reaction, in which $S$-factors for all transitions were simultaneously determined in the energy range of $E_p=110-260$ keV for the first time. Our results resolve previous discrepancies in the ground-state transition, yielding a zero-energy $S$-factor $S_{114}(0) = 1.92\pm0.08$ keV b which is 14% higher than the $1.68\pm0.14$ keV b recommended in Solar Fusion III (SF-III). With our $S_{114}$ values, the SSM B23-GS98, and the latest global analysis of solar neutrino measurements, the C and N photospheric abundance determined by the Borexino experiment is updated to $N_{\mathrm{CN}}=({4.45}^{+0.69}_{-0.61})\times10^{-4}$. This new $N_{\mathrm{CN}}$ value agrees well with latest "high-metallicity" composition, however, is also consistent with the "low-metallicity" determination within $\sim 1\sigma$ C.L., indicating that the solar metallicity problem remains an open question. In addition, the significant reduction in the uncertainty of $S_{114}$ paves the way for the precise determination of the CN abundance in future large-volume solar neutrino measurements.