  We study the transverse spin structure of the squeezed limit of the
three-point energy correlator, $\langle \mathcal{E}(\vec n_1) \mathcal{E}(\vec
n_2) \mathcal{E}(\vec n_3) \rangle$. To describe its all orders perturbative
behavior, we develop the light-ray operator product expansion (OPE) in QCD. At
leading twist the iterated OPE of $\mathcal{E}(\vec n_i)$ operators closes onto
light-ray operators $\mathbb{O}^{[J]}(\vec n)$ with spin $J$, and transverse
spin $j=0,2$. We compute the $\mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2)$,
$\mathcal{E}(\vec n_1) \mathbb{O}^{[J]}(\vec n_2) $ and
$\mathbb{O}^{[J_1]}(\vec n_1) \mathbb{O}^{[J_2]}(\vec n_2) $ OPEs as analytic
functions of $J$, which allows for the description of arbitrary squeezed limits
of $N$-point correlators in QCD. We use these results with $J=3$ to reproduce
the perturbative expansion in the squeezed limit of the three-point correlator,
as well as to resum the leading twist singular structure for both quark and
gluon jets, including transverse spin contributions, as required for
phenomenological applications. Finally, we briefly comment on the transverse
spin structure at higher twists, and show that to all orders in the twist
expansion the highest transverse spin contributions are universal between quark
and gluon jets, and are descendants of the leading twist transverse spin-2
operator, allowing their resummation into a simple two-dimensional Euclidean
conformal block. Due to the general applicability of our results to arbitrary
correlation functions of energy flow operators, we anticipate that they can be
widely applied to improving our understanding of jet substructure at the LHC.
