Froggatt-Nielsen Meets the SMEFT

We study the matching of Froggatt-Nielsen theories of flavour onto the Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy Beyond-the-Standard-Model (BSM) scalar `flavon' whose vacuum expectation value breaks an Abelian flavour symmetry at energies $\Lambda_\text{FN}$ well above the electroweak scale, $\Lambda_\text{FN} > \Lambda_\text{SM}$. We include matching contributions to the infrared $d_\text{SM}=6$ (Warsaw basis) SMEFT sourced from ultraviolet contact terms suppressed up to order $1 / \Lambda_\text{UV}^2$ in the Froggatt-Nielsen Lagrangian, where $\Lambda_\text{UV} > \Lambda_\text{FN}$ is an arbitrary deep-ultraviolet scale where further unspecified BSM particles are dynamical. This includes tree-level (one-loop) ultraviolet diagrams with $d_{\text{FN}}=6$ $(5)$ effective vertices. We first do so with a toy model, but then generalize our findings to arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial signature of Froggatt-Nielsen theories on the (otherwise) model-independent operators of the SMEFT, and we briefly speculate on extending our analysis to broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories. We thus take an important step towards determining how to use rapidly developing theoretical and experimental SMEFT technologies to gain unambiguous insight into the SM's longstanding fermion flavour puzzle.