  Quantitative theoretical techniques for understanding the substructure of
jets at the LHC enable new insights into the dynamics of QCD, and novel
approaches to search for new physics. Recently, there has been a program to
reformulate jet substructure in terms of correlation functions, $\langle
\mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \cdots \mathcal{E}(\vec n_k)
\rangle$, of light-ray operators, $\mathcal{E}(\vec n)$, allowing the
application of techniques developed in the study of Conformal Field Theories
(CFTs). In this paper we further develop these techniques in the particular
context of the three-point correlator $\langle \mathcal{E}(\vec n_1)
\mathcal{E}(\vec n_2) \mathcal{E}(\vec n_3) \rangle$, using recently computed
perturbative data in both QCD and $\mathcal{N}=4$ sYM. We derive the celestial
blocks appearing in the light-ray operator product expansion (OPE) of the
three-point correlator, and use the Lorentzian inversion formula to extract the
spectrum of light-ray operators appearing in the expansion, showing, in
particular, that the OPE data is analytic in transverse spin. Throughout our
presentation, we highlight the relation between the OPE approach, and more
standard splitting function based approaches of perturbative QCD, emphasizing
the utility of the OPE approach for incorporating symmetries in jet
substructure calculations. We hope that our presentation introduces a number of
new techniques to the jet substructure community, and also illustrates the
phenomenological relevance of the study of light-ray operators in the OPE limit
to the CFT community.

High Energy Physics - Phenomenology;High Energy Physics - Theory