  We present a new basis for the hadronic light-by-light (HLbL) tensor that is
optimized for the evaluation of narrow-resonance contributions to HLbL
scattering in the anomalous magnetic moment of the muon. As main advantage,
kinematic singularities are manifestly absent for pseudoscalar, scalar, and
axial-vector states, while the remaining singularities for tensor resonances
are minimized, even avoided for special cases, and simple crossing relations
among the scalar functions maintained. We scrutinize the properties of this new
basis for the scalar-QED pion box, demonstrating that the partial-wave
convergence even slightly improves compared to our previous work, and discuss
the physical sum rules that ensure basis independence of the HLbL contribution.
Finally, we provide explicit expressions for narrow (pseudo-)scalar,
axial-vector, and tensor intermediate states in terms of their respective
transition form factors.
