  We consider large-R-charge Coulomb branch correlation functions in
$\mathcal{N} = 2$ superconformal QCD in D=4 dimensions, with gauge group
$SU(2)$ and $N_f = 4$ hypermultiplets in the fundamental representation. Using
information from supersymmetric recursion relations, S-duality, and matching of
EFT parameters with the double-scaling limit, we give an exact formula for the
massless Coulomb branch EFT contribution to the correlation function two-point
functions of the n.th power of the chiral ring generator,
$G_{2n}^{\text{(EFT)}} = \frac{2^{4n}}{Z_{S^4}[\tau]} \Gamma(2n + 5/2)
e^{A[\tau]n + B[\tau]}$ with $A[\tau]$ and $B[\tau]$ given as explicit
functions of the coupling constant $\tau$ in closed form. We note the precise
agreement of the EFT formula with supersymmetric localization even at low
values of $n$, and discuss aspects of the post-EFT remainder contributed by the
macroscopic virtual propagation of massive particles.
