We study the pairing symmetry of a two orbital $J_1-J_2$ model for FeAs layers in oxypnictides. We vary the doping and the value of $J_1$ and $J_2$ to compare all possible pairing symmetries in a mean-field calculation. We show that the mixture of an intra-orbital unconventional $s_{ x^2y^2}\sim \cos(k_x)\cos(k_y)$ pairing symmetry and a $d_{ x^2-y^2}\sim \cos(k_x)-\cos(k_y)$ pairing symmetry is favored in a large part of $J_1-J_2$ phase diagram. A pure $ s_{ x^2y^2}$ pairing state is favored for $J_2>>J_1$. The signs of the $d_{ x^2-y^2}$ order parameters in two different orbitals are opposite. While a small $d_{ xy}\sim \sin(k_x)\sin(k_y)$ inter-orbital pairing order coexists in the above phases, the intra-orbital $d_{ xy}$ pairing symmetry is not favored even for large values of $J_2$.
Categories: cond-mat.supr-con cond-mat.str-el