Nuclear matrix element (NME) for neutrinoless $\beta \beta$ decay (DBD) is required for studying neutrino physics beyond the standard model by using DBD. Experimental information on nuclear excitation and decay associated with DBD is crucial for theoretical calculations of the DBD-NME. The spin-dipole (SD) NME for DBD via the intermediate SD state is one of the major components of the DBD-NME. The experimental SD giant-resonance energy and the SD strength in the intermediate nucleus are shown for the first time to be closely related to the DBD-NME and are used for studying the spin-isospin correlation and the quenching of the axial-vector coupling, which are involved in the NME. So they are used to help the theoretical model calculation of the DBD-NME. Impact of the SD giant resonance and the SD strength on the DBD study is discussed.

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• Charge-exchange reactions
• Collective levels
• Electroweak interactions in nuclear physics
• Neutrinoless double beta decay
• Nucleus-neutrino interactions
• 90 ≤ A ≤ 149