I am having trouble reconciling two pieces of information.
Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, h and ˆh. The Kähler potential K is canonical, K=h†e2gqVh+ˆh†e−2gqVˆh, while the superpotential W is the simplest possible: W=mhˆh.
Renormalized mass and fields are related to bare/original ones by: m0=Zmmr,h0=Zh1/2hr,ˆh0=Zh1/2ˆhr.
The SUSY non-renormalization theorems say that W is not perturbatively renormalized, implying that ZmZh=1⇒δm=−δh,

If one explicitly computes the divergent part of the h self energy at one loop in dimensional regularization, one finds* that: iΣh(p2)|div=ig2q2(4π)22ϵ(−4m2).
i.e. the divergent part of the self-energy at one loop is proportional to just m2.
QUESTION: I was expecting a divergent part proportional to (p2+m2), which is what can be cancelled by the aforementioned counterterm. Is this reasoning correct? What might have gone wrong?
Diagrams
To make this question more accessible, here are the diagrams (usual Feynman diagrams, not supergraphs) which sum to give iΣh(p2)|div:
I am assuming there is something naïve in my approach. Perhaps some subtlety with the gauge diagrams, or Wess-Zumino gauge (I don't know any more at this point).
Dimensional regularization
At the outset there doesn't seem to be a problem with using dimensional regularization. The SUSY violation introduced by it should be proportional to ϵ (Martin's SUSY Primer, p. 61), thus only affecting finite terms.
Symmetries and missing terms
An R-symmetry under which both h and ˆh have charge +1 forbids adding gauge invariant terms like hˆh to the Kähler.
The discrete symmetry under which h↔ˆh and V→−V forbids adding a Fayet-Iliopoulos term.
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