Reconstructing Effective Lagrangians Embedding Residual Family Symmetries

TL;DR

This paper develops a method to reconstruct effective Lagrangians with residual family symmetries, linking UV BSM physics to low-energy flavor phenomenology and guiding model building.

Contribution

It introduces an algorithmic approach to derive effective Lagrangians from residual family symmetries, connecting bottom-up phenomenology with top-down model construction.

Findings

Reconstruction of effective Lagrangians from residual family symmetries.

Application to models controlling CKM and PMNS mixing patterns.

Extension to scenarios with flavorful leptoquark couplings.

Abstract

We consider effective Lagrangians which, after electroweak- and family-symmetry breaking, yield fermionic mass matrices and/or other flavoured couplings exhibiting residual family symmetries (RFS). Thinking from the bottom up, these RFS intimately link ultraviolet (UV) Beyond-the-Standard Model (BSM) physics to infrared flavour phenomenology without direct reference to any (potentially unfalsifiable) UV dynamics. While this discussion is typically performed at the level of RFS group generators and the UV flavour groups they can close, we now also focus on the RFS-implied shape of the low-energy mass/coupling matrices. We then show how this information can be used to algorithmically guide the reconstruction of an effective Lagrangian, thereby forming top-down models realizing the typical bottom-up phenomenological conclusions. As a first application we take results from scans of finite groups capable of controlling (through their RFS) CKM or PMNS mixing within the SM alone. We then extend this to recently studied scenarios where RFS also control special patterns of leptoquark couplings, thus providing proof-in-principle completions for such `Simplified Models of Flavourful Leptoquarks.'