  We compute the R\'enyi mutual information of two disjoint spheres in free
massless scalar theory in even dimensions higher than two. The spherical twist
operator in a conformal field theory can be expanded into the sum of local
primary operators and their descendants. We analyze the primary operators in
the replicated scalar theory and find the ones of the fewest dimensions and
spins. We study the one-point function of these operators in the conical
geometry and obtain their expansion coefficients in the OPE of spherical twist
operators. We show that the R\'enyi mutual information can be expressed in
terms of the conformal partial waves. We compute explicitly the R\'enyi mutual
information up to order $z^d$, where $z$ is the cross ratio and $d$ is the
spacetime dimension.
