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We use the critical point large $N$ formalism to calculate the criticalexponents corresponding to the fermion mass operator and flavour non-singletfermion bilinear operator in the universality class of Quantum Electrodynamics(QED) coupled to the Gross-Neveu model for an $SU(N)$ flavour symmetry in$d$-dimensions. The $\epsilon$ expansion of the exponents in $d$ $=$ $4$ $-$$2\epsilon$ dimensions are in agreement with recent three and four loopperturbative evaluations of both renormalization group functions of theseoperators. Estimates of the value of the non-singlet operator exponent in threedimensions are provided.

Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class