Double Gamow Teller transition and its relation to neutrinoless double beta decay matrix element

The double Gamow-Teller (DGT) resonance is of particular interest 
not only as an exotic collective excitation, but also in relevance to
the neutrinoless double-beta (0nbb) decay. In this contribution, we will present our
theoretical studies of the DGT transition and its relevance to 0nbb-decay
nuclear matrix element (NME) based on shell-model calculations. 
The shell-model study reveals that the centroid energy and
the width of the DGT strength distribution of 48Ca
are sensitive to the isovector and isoscalar pairing interactions, respectively.
We also found a simple relation between the centroid energy of the 48Ca
DGT giant resonance and the 0nbb-decay NME.
More generally, we observe a very good linear correlation between
the DGT transition to the ground state of the final nucleus and the 0nbb-decay NME.
It indicates that heavy-ion double charge exchange experiments 
would be a useful tool to obtain the information on the 0nbb-decay NME.