
The discovery of a neutrinoless doubleβ decay of a nucleus would provide unambiguous
evidence of leptonnumber violation in nature, and have important implications for the
nature of neutrino mass. The search for such decays is a high priority of the nuclear
physics community in the US, as was highlighted in the 2015 Long Range Plan for Nuclear
Science. Theoretical predictions of the rates of such decays depend not only on the
underlying shortdistance mechanism, but also on strong interaction effects and the complexity
of nuclei. The new physics producing leptonnumber violation may manifest itself
over a large range of lengths scales  from light Majorana neutrino masses to sixfermion
effective operators arising from dynamics far beyond the reach of the LHC  and
their effects must be calculated in a moderately large nucleus. Even if the underlying operator
structure is known, calculating the resulting nuclear lifetimes has significant uncertainties.
This can influence the experimental design and budget, and further limits the
physical insight that could be gained from an observation of neutrinoless doubleβ decay.
Our ability to calculate nonperturbative properties of multinucleon systems through the
method of Lattice Quantum Chromodynamics (LQCD) has increased dramatically both in
complexity and in precision in recent years, and suggests that more challenging problems
in the realm of nuclear physics are not far from being amenable to this method. While it
is only recently that LQCD has been applied to multinucleon systems, significant
progress has already been made. Light nuclei and hypernuclei have been shown to naturally
emerge from the QCD degrees of freedom, and some of their structure properties
have been studied directly from QCD at unphysical quark masses. Fast progress toward
the physical point is anticipated in upcoming years with the deployment of Exascale
computing capabilities. Determination of electroweak reactions in light nuclei from
LQCD has recently become a reality, an achievement that opens up the door to further
LQCD studies of nuclear environments when probed by external currents.
This twoday workshop, focused on LQCD input for neutrinoless doubleβ decay, was
held during the secondtolast week of the sixweek INT program on Neutrinoless Doubleβ Decay.
In a nutshell, the purpose was to facilitate the exchange of ideas and nearterm
foci between LQCD experts with interests in this area and the larger efforts in the
nuclear physics community. The workshop was attended by about 25 scientists  from
senior researchers to graduate students. As the goals of the meeting were to foster the
exchange of ideas, to encourage collaboration, and to put bridges in place to facilitate
quantitative connections between QCD and nuclei, the presentations were targeted to address
specific points designed to spark discussions. This was met with success and the
discussion sessions turned out to be very enlightening.
The scientific output of the workshop can be summarized as follows:

First LQCD results on both local sixfermion operator matrix elements and on bilocal
secondorder weak interactions in the lightest nuclei were presented. Their connection
(and usefulness) to phenomenology was discussed and possible avenues for future
work were explored.

There has been continued progress by many LQCD groups in reducing the uncertainties
in calculations of gA which is an important ingredient in doubleβ decay calculations.
It is desirable to further reduce the uncertainty in gA down to, or below, 0.3%  the precision
at which radiative effects are expected to contribute. Also, related to this, is the
need for calculations of the axial form factors (FF) for momentum transfers below
about 1 GeV, and determinations of the axial radii. Such calculations are already in
process, but neutrinoless doubleβ decay and the long baseline neutrino program both
need more precise QCD input on these quantities.

With regard to related nuclear manybody calculations, it would be interesting to have
some simplified doubleβ decay benchmark calculations, for instance those with the
axial FF replaced with gA (i.e. ignoring the momentum dependence of the FF), and
have some understanding of the sensitivity of calculations to the different phenomenological
forms of the axial FF.

One point of interest that emerged from the discussions on gA, but was agreed to be
broadly applicable, is the growing need for blind analyses in LQCD calculations. This
is particularly important in the verification phase of LQCD, and as one moves forward
to make reliable predictions for unknown quantities, such as those relevant for the doubleβ decay program. Nuclear manybody experts in the workshop commented on a
similar trend in their program  noting the consensus in evaluating and comparing neutrinoless
doubleβ decay matrix elements in several light isotopes that do not undergo
the decay in nature, but can be evaluated more straightforwardly with various manybody
methods.

There was related discussion focused on the needs of matrixelement calculations for
both Standard Model (SM) backgrounds and Beyond the SM (BSM) signals, particularly
the pseudoscalar FF. It was commented that there is a need to satisfy the partial conservation
of the axial current (PCAC) as part of the verification and validation process
in LQCD calculations of such quantities. Some current calculations do not correctly
implement this important constraint.

Finally, there was extended discussion on the matching of LQCD calculations to nuclear
manybody systems. This is, at the least, essentially a twostep process; with the
matching to the few nucleon systems, and then matching to the few nucleon systems
embedded in truncated Hilbert spaces. A classic example of this is matching to multinucleon
forces at the chiral symmetry breaking scale, and then determining their evolution
as the nuclear modelspace cutoff is reduced. This becomes even more challenging
for the multibody forces coupling to electroweak currents or higherdimension operators
inducing neutrinoless doubleβ decay. It was suggested that having multibody
operators RGevolved down to below a momentum of 50 MeV would be helpful. This
lowenergy matching requires care in order to maintain rigorous connection to the underlying
QCD calculations.
In summary, in the end of the twoday workshop it was agreed that closer collaboration
between the LQCD and the nuclear structure communities will be necessary to reach the
desired goal of refining the calculations of the nuclear matrix elements relevant for neutrinoless
doubleβ decay. The meeting highlighted the challenges and the ensuing discussions
led to new directions of inquiry that may allow the communities to begin to make
rigorous predictions for doubleβ decay rates in nuclei used in experiments. The efforts
to identify priorities, target precisions and conditions for future calculations appeared
helpful, but only time can tell.
