  A powerful aspect of effective field theories is connecting scales through
renormalisation group (RG) flow. The anomalous dimension matrix of the Standard
Model Effective Field Theory (SMEFT) encodes clues to where to find relics of
heavy new physics in data, but its unwieldy 2499-by-2499 size (at operator
dimension 6) makes it difficult to draw general conclusions. In this paper, we
study the flavour structure of the SMEFT one loop anomalous dimension matrix of
dimension 6 current-current operators, a 1460-by-1460 submatrix. We take an
on-shell approach, laying bare simple patterns by factorising the entries of
the matrix into their gauge, kinematic and flavour parts. We explore the
properties of different diagram topologies, and make explicit the connection
between the IR-finiteness of certain diagrams and their gauge and flavour
structure. Through a completely general flavour decomposition of the Wilson
coefficient matrices, we uncover new flavour selection rules, from which small
subsystems emerge which mix almost exclusively amongst themselves. We show
that, for example, if we neglect all Yukawa couplings except for that of the
top quark, the selection rules produce block diagonalisation within the
current-current operators in which the largest block is a 61-by-61 matrix. We
provide all the ingredients of the calculations in comprehensive appendices,
including SM and SMEFT helicity amplitudes, and explicit results for phase
space integrals and gauge contractions. This deconstruction of the matrix, and
its resulting block-diagonalisation, provides a first step to understanding the
IR-relevant directions in the SMEFT parameter space, hence closing in on
natural places for heavy new physics to make itself known.
