  We study the momentum-space 4-point correlation function of identical scalar
operators in conformal field theory. Working specifically with null momenta, we
show that its imaginary part admits an expansion in conformal blocks. The
blocks are polynomials in the cosine of the scattering angle, with degree
$\ell$ corresponding to the spin of the intermediate operator. The coefficients
of these polynomials are obtained in a closed-form expression for arbitrary
spacetime dimension $d > 2$. If the scaling dimension of the intermediate
operator is large, the conformal block reduces to a Gegenbauer polynomial
$\mathcal{C}_\ell^{(d-2)/2}$. If on the contrary the scaling dimension
saturates the unitarity bound, the block is different Gegenbauer polynomial
$\mathcal{C}_\ell^{(d-3)/2}$. These results are then used as an inversion
formula to compute OPE coefficients in a free theory example.
