We present a polarization resolved study of the low energy band structure in the optimally doped iron pnictide superconductor Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ (T$_c$=37K) using angle resolved photoemission spectroscopy. Polarization-contrasted measurements are used to identify and trace all three low energy hole-like bands predicted by local density approximation (LDA) calculations. The photoemitted electrons reveal an inconsistency with LDA-predicted symmetries along the $Gamma$-X high symmetry momentum axis, due to unexpectedly strong rotational anisotropy in electron kinetics. We evaluate many-body effects such as Mott-Hubbard interactions that are likely to underlie the anomaly, and discuss how the observed deviations from LDA band structure affect the energetics of iron pnictide Cooper pairing in the hole doped regime.
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