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Abstract We consider N $$ \mathcal{N} $$ = 2 conformal QCD in four dimensions and the one-point correlator of a class of chiral primaries with the circular 1 2 $$ \frac{1}{2} $$ -BPS Maldacena-Wilson loop. We analyze a recently introduced double scaling limit where the gauge coupling is weak while the R-charge of the chiral primary Φ is large. In particular, we consider the case Φ = (Trφ 2) n , where φ is the complex scalar in the vector multiplet. The correlator defines a non-trivial scaling function at fixed κ = ng YM 2 and large n that may be studied by localization. For any gauge group SU(N) we provide the analytic expression of the first correction ~ ζ(3)κ 2 and prove its universality. In the SU(2) and SU(3) theories we compute the scaling functions at order O $$ \mathcal{O} $$ (κ 6). Remarkably, in the SU(2) case the scaling – function is equal to an analogous quantity describing the chiral 2-point functions Φ Φ ¯ $$ \left\langle \Phi \overline{\Phi}\right\rangle $$ in the same large R-charge limit. We conjecture that this SU(2) scaling function is computed at all-orders by a N $$ \mathcal{N} $$ = 4 SYM expectation value of a matrix model object characterizing the one-loop contribution to the 4-sphere partition function. The conjecture provides an explicit series expansion for the scaling function and is checked at order O $$ \mathcal{O} $$ (κ 10) by showing agreement with the available data in the sector of chiral 2-point functions.