Emergent CPT violation from the splitting of Fermi points

In a fermionic quantum vacuum, the parameters k(mu) of a CPT-violating Chern-Simons-like action term induced by CPT-violating parameters of the fermionic sector depend on the universality class of the system. As a concrete example, we consider the Dirac Hamiltonian of a massive fermionic quasiparticle and add a particular term with purely-spacelike CPT-violating parameters b(mu) = (0, b). A quantum phase transition separates two phases, one with a fully-gapped fermion spectrum and the other with topologically-protected Fermi points (gap nodes). The emergent Chern-Simons "vector" k(mu) = (0, k) now consists of two parts. The regular part, k(reg), is an analytic function of vertical bar b vertical bar across the quantum phase transition and may be nonzero due to explicit CPT violation at the fundamental level. The anomalous (nonanalytic) part, k(anom), comes solely from the Fermi points and is proportional to their splitting. In the context of condensed-matter physics, the quantum phase transition may occur in the region of the BEC-BCS crossover for Cooper pairing in the p-wave channel. For elementary particle physics, the splitting of Fermi points may lead to neutrino oscillations, even if the total electromagnetic Chern-Simons-like term cancels out.