  We present new RHESSI upper limits in the 3-200 keV energy range for solar
hard X-ray emission in the absence of flares and active regions, i.e. the quiet
Sun, using data obtained between July 2005 and April 2009. These new limits,
substantially deeper than any previous ones, constrain several physical
processes that could produce hard X-ray emission. These include cosmic-ray
effects and the generation of axions within the solar core. The data also limit
the properties of "nanoflares", a leading candidate to explain coronal heating.
We find it unlikely for nanoflares involving nonthermal effects to heat the
corona because such events would require a steep electron spectrum E^{-\delta}
with index \delta > 5 extending to very low energies (<1 keV), into the thermal
energy range. We also use the limits to constrain the parameter space of an
isothermal model and coronal thin-target emission models (powerlaw and kappa
distributions)
