Our ability to constrain nonperturbative properties of multi-nucleon systems through the method of Lattice Quantum Chromodynamics (LQCD) has increased by orders of magnitude compared with the past, both in complexity and in precision, and suggest that more challenging problems in realm of nuclear physics are not far from being amenable to the method of LQCD. While it is only recently that LQCD has been applied to multi-nucleon 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. Electroweak nuclear reactions from LQCD have recently become a reality in light nuclei, an achievement that opens up the door to further LQCD studies of nuclear environments when probed by external currents.

Studying the nuclear-physics contribution to the rate of the important neutrinoless double-β decay process is a problem where LQCD physicists aim to make significant contributions to, in particular by providing few-nucleon constraints for many-body methods. Extensive consideration has been given to this problem in recent years and a few preliminary calculations are underway. Some exciting first results in matching the QCD matrix elements to nucleonic matrix elements will appear in the upcoming year, with challenges to be overcome, and a roadmap to be built to relate the LQCD matrix elements in light nuclei to those relevant for planned experiments. This INT workshop, which is purposefully embedded in a larger program on the topic with the involvement of nuclear effective field theorists and nuclear many-body physicists, aims to introduce and specify the LQCD input to this program. Among the questions to be addressed in this focused two-day meeting are:

1. What are the relevant matrix elements to be calculated with LQCD, within various new-physics scenarios that incorporate the lepton-number violation? Are there common features in terms of LQCD techniques and formalism for each of these matrix elements, in particular within short-range and long-range scenarios?

2. Is there any value in a direct evaluation of the simplest (neutrinoless) double-β decay amplitude that can be studied with LQCD, namely nn → ppee, beyond providing constraints on two-nucleon effective field theory couplings to the external currents? What are the smallest nuclear systems where independent LQCD and many-body calculations of the relevant matrix elements will enable a diagnostic of many-body assumptions and limitations?

3. Are there other nuclear quantities that once constrained directly with LQCD, could help constraining indirectly the matrix elements relevant to the (neutrinoless) double-β decay in realistic nuclei? Are there alternative methods to the direct matrix element evaluation, such as the successfully tested background field techniques, that by demanding less computational resources, could expedite the matching program in the few-nucleon sector?

4. What formulation of the nuclear effective field theories is superior in providing the framework to match QCD results to the nuclear matrix elements, given the energy scales involved in a (neutrinoless) double-β decay in heavy nuclei, and given the limitations of the current nuclear many-body techniques?

We encourage all the interested scientists in the LQCD, effective field theory and nuclear many-body subfields to apply. This is a new program with fewer ideas and more challenges at present, and new perspectives on this problem are extremely welcome.

There will be a $15 registration fee to attend the workshop. The registration fee includes participation in the workshop, lectures, and coffee breaks.