Uncovering the Root of LEFT in SMEFT

At energies below the electroweak scale, baryon number $B$ and lepton number $L$ violating processes are of significant importance in identifying the nature of UV extensions of the Standard Model. The imprint of UV theories on low-energy measurements can be calculated to a high accuracy using the theoretical framework of the Low Energy Effective Theory (LEFT). Using $B,\; L$ and the operators' dimensions as classifying characteristics, we construct a network connecting operator classes of the LEFT with the Standard Model Effective Theory (SMEFT). Following the links of this network, the contact interactions described by the effective operators of LEFT can be unambiguously embedded into those of SMEFT, which enables us to constrain the possible realisations of UV theories. In turn, this can help to prioritise low energy measurements with the aim of comprehensively testing all classes of LEFT and SMEFT operators.