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Benchmark comparisons between many-body methods are performed to assess theingredients necessary for an accurate calculation of neutrinoless double betadecay matrix elements. Shell model and variational Monte Carlo (VMC)calculations are carried out for $A=10$ and $12$ nuclei. Different variationalwavefunctions are used to evaluate the uncertainties in the {\it ab initio}calculations, finding fairly small differences between the VMC double betadecay matrix elements. For shell model calculations, the role of model spacetruncation, radial wavefunction choices, and short-range correlation areinvestigated and all found to be important. Based on the detailed comparisonsbetween the VMC and shell model approaches, we conclude that accuratedescriptions of neutrinoless double beta decay matrix elements require a propertreatment of both long-range and short-range correlations.

Comparison between Variational Monte Carlo and Shell Model Calculations of Neutrinoless Double Beta Decay Matrix Elements in Light Nuclei