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The weak proton-proton fusion into a deuteron ($^2$H) is the driving reactionin the energy production in the Sun, as well as similar main sequence stars.Its reaction rate in the solar interior is determined only theoretically. Here,we provide a new determination of the rate of this reaction in solar conditions$S^{11}(0)$, and analyze theoretical and experimental sources foruncertainties, using effective field theory of quantum chromo-dynamics withoutexplicit pions at next-to-leading order. We find an enhancement of $S^{11}$ by$1-4\%$ over the previously recommended value. This change reduces thecalculated fluxes of neutrinos originating in $^8$B and $^7$Be nuclearreactions in the Sun, thus favoring higher abundances for metallic photosphericelements, in the tension between different composition determination, known asthe ``Solar Composition Problem''.

Theoretical evaluation of solar proton-proton fusion reaction rate and its uncertainties