Double Gamow-Teller transitions and the matrix elements of neutrinoless double-beta decay

Neutrinoless double-beta decay (0nbb) is a decay of an atomic nucleus where only two electrons are emitted. Since two matter particles (leptons) are emitted without the balance of antimatter, this is a unique process to explore physics beyond the Standard Model of particle physics, establish the Majorana the nature of neutrinos, and gain insights on the dominance of matter in the Universe. Being the decay of an atomic nucleus, its lifetime depends on the square of a nuclear matrix element (NME) that needs to be calculated with nuclear many-body methods. However, different state-of-the art calculations typically disagree in the NME predictions, leading to an uncertainty of the physics reach of current 0nbb searches, and potentially limiting the extraction of the relevant physics once the decay is detected experimentally. In this contribution I will discuss the potential of double Gamow-Teller transitions, a process mediated by the strong interaction, to provide insights on the 0nbb NMEs. In particular, I will discuss theoretical studies performed with different many-body methods (the nuclear shell model, the quasiparticle random-phase approximation and the valence-space in-medium similarity renormalization group) relating theoretical double Gamow-Teller transitions and 0nbb NMEs of the same nucleus. Finally, I will discuss the origin of the correlation between the two processes.