Diagonalising the LEFT

TL;DR

This paper reorganizes four-fermion interactions in the low energy effective field theory into irreducible representations, enabling semi-analytical solutions for their renormalization group evolution and providing insights into flavor physics phenomenology.

Contribution

It introduces a novel grouping of operators into parity and flavor symmetry irreps, simplifying the RG analysis and revealing new phenomenological implications.

Findings

Semi-analytical solutions for RG evolution of operator subsets

Eigenvalues and eigenvectors of one- and two-loop running

Implications for $b\to s \tau \tau$ decays and flavor bounds

Abstract

We organise the four-fermion vector current interactions below the weak scale -- i.e., in the low energy effective field theory (LEFT) -- into irreps of definite parity and $SU(N)$ flavour symmetry. Their coefficients are thus arranged into small subsets with distinct phenomenology, which are significantly smaller than traditional groupings of operators by individual fermion number. As these small subsets only mix among themselves, we show that the renormalisation group evolution is soluble semi-analytically, and examine the resulting eigenvalues and eigenvectors of the one- and two-loop running. This offers phenomenological insights, for example into the radiative stability of lepton flavour non-universality. We use these to study model-independent implications for $b\to s \tau \tau$ decays, as well as setting indirect bounds on flavour changing four-quark interactions.