Anomalous dimensions from the $\mathcal{N}=4$ SYM hexagon

We consider the correlator $⟨\mathcal{L}\mathcal{K}\tilde{\mathcal{K}}⟩$ of the Lagrange operator of $\mathcal{N}=4$ super Yang-Mills theory and two conjugate two-excitation operators in an $su(2)$ sector. We recover the planar one-loop anomalous dimension of the renormalised operators from this hexagon computation.