Identify the linear combination X = a M + b S in Sp(2) with one flavour

Determine the coefficients a and b (up to normalization conventions) in the U(1)-neutral R-charge-2 generator X = a M + b S of the infinite-coupling Higgs-branch chiral ring of the five-dimensional N=1 Sp(2) gauge theory with N_f = 1, where X satisfies the relation X^3 + I\tilde{I} = 0.

Background

In the N_f=1 Sp(2) example at infinite coupling, the Hilbert series and plethystic logarithm indicate generators consisting of a neutral operator X at R-charge 2 and instanton operators I, \tilde{I} at R-charge 3. The only relation observed is X^3 + I\tilde{I} = 0.

The authors note that X is a linear combination of the meson M and the gaugino bilinear S, but the precise coefficients are not determined. They suggest, based on higher-flavour cases, that M^2 = S^2 and hence X may be related to S, but the exact coefficients a and b remain to be fixed.