Theta vacuum effects on the pseudoscalar condensates and the eta^prime meson in 2-dimensional lattice QED

TL;DR

This paper investigates how the theta vacuum influences pseudoscalar condensates and eta' meson correlations in 2D lattice QED, revealing long-range effects and the importance of topological sector contributions.

Contribution

It demonstrates that pseudoscalar operators condense in fixed topological sectors and that eta' meson correlations are affected by all sectors, providing new insights into topological effects in lattice QED.

Findings

Pseudoscalar operators condense in fixed topological sectors.

Long-range eta' meson correlations originate from topological sector contributions.

Accurate measurement of reweighting factors is crucial for understanding topological effects.

Abstract

We study the chiral condensates and the eta^prime meson correlators of the massive Schwinger model in non-zero theta vacuum. Our data suggest that the pseudoscalar operator does condense in a fixed topological sector and gives long range correlations of the eta^prime meson. We find that this is well understood from the clustering decomposition and statistical picture. Our result also indicates that even in theta=0 case, the long range correlation of eta^prime meson receives non-zero contributions from all the topological sectors and that their cancellation is non-trivial and requires accurate measurement of the reweighting factors as well as the expectation values. It is then clear that the fluctuation of the disconnected diagram originates from the pseudoscalar condensates.