I have a conceptual question about how to judge a given operator, \(\mathcal{O}\), in 4d \(\mathcal{N}=1\) theories is relevant or not.

In the literature, the criterion is given by \(R(\mathcal{O}) \leqslant 2\). i.e., the operator is relevant or marginal if \(R(\mathcal{O}) \leqslant 2\). However, as I understand, an acceptable operator deformation for the theory must have \(R(\mathcal{O}) = 2\) so that \(R\)-symmetry is not broken.

How to understand why the \(R\)-charge, not the dimension of the operator, tells us that the operator is relevant, marginal or irrelevant? Are there any relations when the theory is in UV? How to resolve the "contradiction" that the \(R\)-charge for the superpotential should always be such that \(R=2\)?