  The $pp$-chain of nuclear reactions is the primary route for energy
production in the Sun. The first step in that reaction sequence converts two
protons to a deuterium nucleus with the emission of a positron and electron
neutrino. This reaction is extremely slow because it is a weak interaction, and
significantly, it involves quantum tunneling through the Coulomb barrier.
Though the reaction rate can be calculated with high confidence in the Standard
Model, it has not been measured at solar energies. If there exist interactions
that are engendered by non-standard mediators then the rate of this reaction in
the Sun could be altered. We probe such non-standard interactions between two
protons by performing self-consistent calculations of solar evolution to the
current solar system age and then comparing to measured properties of the Sun,
including solar neutrino results. We thereby obtain constraints on mediator
mass and couplings in these beyond-standard-model scenarios. Constraints on
these non-standard parameters could be extended further with better confidence
on the value of the metallicity of the Sun and the solar neutrino CNO flux.
