# Evidence for eta prime - pion splitting in unquenched lattice QCD

## TL;DR

This paper investigates the eta prime and pion mass difference in unquenched lattice QCD, showing results consistent with theoretical predictions and previous quenched estimates, highlighting flavor dependence and the U(1) anomaly.

## Contribution

It provides the first unquenched lattice QCD estimates of the eta prime mass splitting extrapolated from negative to positive flavor numbers.

## Key findings

- Eta' - pion splitting shows flavor dependence consistent with the Witten Veneziano formula.
- Quantitative splitting aligns with quenched approximation estimates.
- Results support the role of the U(1) anomaly in eta' mass generation.

## Abstract

We perform an extrapolation from negative to positive flavour numbers of full QCD lattice estimates of the $\eta'$ mass. The extrapolations are carried out by keeping $\rho$ and $\pi$ masses at fixed values. We find an $\eta'$ -- $\pi$ splitting which shows a flavour dependence consistent with the Witten Veneziano formula based on the $U(1)$ anomaly. The quantitative splitting is consistent with the estimates made in the quenched approximation.