  The weak proton-proton fusion into a deuteron ($^2$H) is the driving reaction
in 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 for
uncertainties, using effective field theory of quantum chromo-dynamics without
explicit pions at next-to-leading order. We find an enhancement of $S^{11}$ by
$1-4\%$ over the previously recommended value. This change reduces the
calculated fluxes of neutrinos originating in $^8$B and $^7$Be nuclear
reactions in the Sun, thus favoring higher abundances for metallic photospheric
elements, in the tension between different composition determination, known as
the ``Solar Composition Problem''.
