Can double Gamow-Teller transitions calibrate the matrix elements?
In plain words
A related measurable process, the double Gamow-Teller transition (flipping the spin and charge of two nucleons), correlates strongly with the neutrinoless matrix element in calculations. If the correlation holds in all models, measuring it would calibrate the matrix elements.
Precise statement
Shell-model calculations show a near-linear correlation between the ground-state double Gamow-Teller matrix element $M^{\mathrm{DGT}}$ and $M^{0\nu}$ (Shimizu, Menendez and Yako, PRL 120, 142502, 2018). Determine whether the correlation holds across many-body methods and with two-body currents, and extract M^{DGT} from heavy-ion double-charge-exchange reactions (NUMEN at LNS Catania, RCNP Osaka). Answer: yes or no for model independence, with calibration slope and uncertainty.
What would settle it
Ab initio and QRPA calculations of $M^{\mathrm{DGT}}$ and $M^{0\nu}$ across ten or more nuclei, plus a reaction-theory-controlled extraction of $M^{\mathrm{DGT}}$ from double-charge-exchange data.