# Quenched Chiral Logs, the $\eta'$ Mass, and the Hairpin Diagram

## TL;DR

This paper investigates the suppression of quenched chiral logs in Wilson fermions, linking it to the hairpin diagram's behavior, and provides a direct calculation of the $ ext{η'}$ mass from topological susceptibility data.

## Contribution

It demonstrates that small quenched chiral logs result from hairpin diagram suppression and directly estimates the $ ext{η'}$ mass using topological susceptibility data.

## Key findings

- Chiral logs are suppressed due to hairpin diagram behavior.
- The $ ext{η'}$ mass is approximately 1 GeV from topological susceptibility.
- Hairpin diagram contributions are smaller than the physical $ ext{η'}$ mass.

## Abstract

Limits on the size of quenched chiral logs in the pion mass for Wilson fermions are investigated. The smallness of chiral logs is shown to be a result of the suppression of the hairpin diagram for small $p^2$, such that the value of the hairpin on the pion mass shell is much smaller than the physical $m_{\eta'}^2$. A direct calculation of the topological susceptibility from the same data gives $m_{\eta'}\approx 1$ GeV.