  We study the structure of the d-wave orbital order in FeSe in light of recent
STM and ARPES data, which detect the shapes of hole and electron pockets in the
nematic phase. The geometry of the pockets indicates that the sign of the
orbital order $\Gamma = \langle d^{\dagger}_{xz} d_{xz}- d^{\dagger}_{yz}
d_{yz}\rangle$ is different between hole and electron pockets $(\Gamma_h$ and
$\Gamma_e$). We argue that this sign change cannot be reproduced if one solves
for the orbital order within mean-field approximation, as the mean-field
analysis yields either no orbital order, or order with the same sign of
$\Gamma_e$ and $\Gamma_h$. We argue that another solution with the opposite
signs of $\Gamma_e$ and $\Gamma_h$ emerges if we include the renormalizations
of the vertices in $d-$wave orbital channel. We show that the ratio
$|\Gamma_e/\Gamma_h|$ is of order one, independent on the strength of the
interaction. We also compute the temperature variation of the energy of
$d_{xz}$ and $d_{yz}$ orbitals at the center of electron pockets and compare
the results with ARPES data.
