Speaker
Description
The pseudoscalar $\eta$ and $\eta'$ mesons play a special role in the context of chiral dynamics as their physics properties are intimately linked to the chiral anomaly. While the $\eta$ meson would be a massless state in a $SU(3)$ flavor symmetric world like the other pseudoscalar octet mesons, the $\eta'$ remains massive even in the chiral limit due to the anomalous breaking of the axial $U(1)$ symmetry. Still, corrections due to $SU(3)$ flavor symmetry breaking are known to be large in the physical world, giving rise to a peculiar mixing pattern between flavor octet and singlet states.
Lattice calculations involving $\eta$ and $\eta'$ mesons are notoriously difficult due to large contributions of quark-disconnected diagrams and the resulting signal-to-noise problem particularly for the $\eta'$ state. However, there has been tremendous progress in recent years towards obtaining physical results with controlled systematics. Therefore, it has become feasible to reproduce the physical masses and mixing of $\eta$ and $\eta'$ mesons from first principles using lattice QCD. Beyond masses and mixing, $\eta$ and $\eta'$ mesons contribute in various processes of phenomenological interest such as e.g. $\eta,\eta'\rightarrow \gamma\gamma$ that can studied using lattice QCD. In this talk I review the current status and results for lattice calculations of $\eta$ and $\eta'$ mesons.
