SMEFTs living on the edge: determining the UV theories from positivity and extremality

Understand

We study the "inverse problem" in the context of the Standard Model Effective Field Theory (SMEFT): how and to what extend can one reconstruct the UV theory, given the measured values of the operator coefficients in the IR? The main obstacle of this problem is the degeneracies in the space of coefficients: a given SMEFT truncated at a finite dimension can be mapped to infinitely many UV theories.

• We discuss these degeneracies at the dimension-8 level, and show that positivity bounds play a crucial role in the inverse problem.
• In particular, the degeneracies either vanish or become significantly limited for SMEFTs that live on or close to the positivity bounds.
• The UV particles of these SMEFTs, and their properties such as spin, charge, other quantum numbers, and interactions with the SM particles, can often be uniquely determined, assuming dimension-8 coefficients are measured.