Abstract: After a short introduction on the delicate and crucial
treatment of chiral anomaly in axion physics we will discuss a current
controversy on the trace anomaly. The existence of CP violating terms in
the trace of the energy-momentum tensor (EMT) in chiral theories coupled
to gravity has no answer yet. Consequently, the neutrino could carry a
source of CP or unitarity violation in its trace anomaly within the
Standard Model. This black board talk will aim to clarify the situation
by presenting two exclusive non-perturbative computations of the trace
anomaly. The first method, more generic, proceeds from the EMT relying
only on symmetry arguments. The second method involves the path integral
measure to obtain directly the trace anomaly of a Weyl fermion à la
Fujikawa.
