  Neutrinos are perhaps the most elusive known particles in the universe. We
know they have some nonzero mass, but unlike all other particles, the absolute
scale remains unknown. In addition, their fundamental nature is uncertain; they
can either be their own antiparticles or exist as distinct neutrinos and
antineutrinos. The observation of the hypothetical process of neutrinoless
double-beta ($0\nu\beta\beta$) decay would at once resolve both questions,
while providing a strong lead in understanding the abundance of matter over
antimatter in our universe. In the scenario of light-neutrino exchange, the
decay rate is governed by, and thereby linked to the effective mass of the
neutrino via, the theoretical nuclear matrix element (NME). In order to extract
the neutrino mass, if a discovery is made, or to assess the discovery potential
of next-generation searches, it is essential to obtain accurate NMEs for all
isotopes of experimental interest. However, two of the most important cases,
$^{130}$Te and $^{136}$Xe, lie in the heavy region and have only been
accessible to phenomenological nuclear models. In this work we utilize powerful
advances in ab initio nuclear theory to compute NMEs from the underlying
nuclear and weak forces driving this decay, including the recently discovered
short-range component. We find that ab initio NMEs are generally smaller than
those from nuclear models, challenging the expected reach of future ton-scale
searches as well as claims to probe the inverted hierarchy of neutrino masses.
With this step, ab initio calculations with theoretical uncertainties are now
feasible for all isotopes relevant for next-generation $0\nu\beta\beta$ decay
experiments.
