  Building on arXiv:1911.05827, we uncover new properties of type-B conformal
anomalies for Coulomb-branch operators in continuous families of 4D
$\mathcal{N}=2$ SCFTs. We study a large class of such anomalies on the Higgs
branch, where conformal symmetry is spontaneously broken, and compare them with
their counterpart in the CFT phase. In Lagrangian theories, the
non-perturbative matching of the anomalies can be determined with a weak
coupling Feynman diagram computation involving massive multi-loop banana
integrals. We extract the part corresponding to the anomalies of interest. Our
calculations support the general conjecture that the Coulomb-branch type-B
conformal anomalies always match on the Higgs branch when the IR Coulomb-branch
chiral ring is empty. In the opposite case, there are anomalies that do not
match. An intriguing implication of the mismatch is the existence of a second
covariantly constant metric on the conformal manifold (other than the
Zamolodchikov metric), which imposes previously unknown restrictions on its
holonomy group.
