  Using random-phase approximation spin-fluctuation theory, we study the
influence of the hybridization between iron $d$-orbitals and pnictide
$p$-orbitals on the superconducting pairing state in iron-based
superconductors. The calculations are performed for a 16-orbital Hubbard-Hund
tight-binding model of BaFe$_2$As$_2$ that includes the As-$p$ orbital degrees
of freedom in addition to the Fe-$d$ orbitals and compared to calculations for
a 10-orbital Fe-$d$ only model. In both models we find a leading $s^\pm$
pairing state and a subleading $d_ {x^2-y^2}$-wave state in the parent
compound. Upon doping, we find that the $s^\pm$ state remains the leading state
in the 16-orbital model up to a doping level of 0.475 electrons per unit cell,
at which the hole Fermi surface pockets at the zone center start to disappear.
This is in contrast to the 10-orbital model, where the $d$-wave state becomes
the leading state at a doping of less than 0.2 electrons. This improved
stability of $s^\pm$ pairing is found to arise from a decrease of $d_{xy}$
orbital weight on the electron pockets due to hybridization with the As-$p$
orbitals and the resulting reduction of near $(\pi,\pi)$ spin-fluctuation
scattering which favors the competing $d$-wave state. These results show that
the orbital dependent hybridization of Fermi surface Bloch states with the
usually neglected $p$-orbital states is an important ingredient in an improved
itinerant pairing theory.
