# Classical improvement of lattice actions and quantum effects: a unified view

## TL;DR

This paper investigates how choosing specific lattice actions can reduce one-loop lattice artifacts in quantum models, especially focusing on the finite-volume mass gap in two-dimensional O(N) sigma models, introducing a 'tree perfect' action.

## Contribution

It introduces a 'tree perfect' Symanzik action that formally eliminates all one-loop lattice artifacts in the mass gap for 2D O(N) sigma models, providing a unified view of classical and quantum improvements.

## Key findings

- The finite-space-volume mass gap m(L) is an improved observable.
- The 'tree perfect' Symanzik action removes all one-loop lattice artifacts in m(L).
- On-shell improved actions do not eliminate these artifacts.

## Abstract

The possibility of removing the one-loop perturbative effects of lattice artifacts by a proper choice of the lattice action is explored, and found to depend crucially on the properties of the physical quantity considered. In this respect the finite-space-volume mass gap m(L) is an improved observable. We find an explicit momentum space representation of the one-loop contribution to m(L) for arbitrary lattice actions in the case of two-dimensional O(N) sigma models. We define a ``tree perfect'' Symanzik action and find that it formally removes all one-loop lattice artifacts in m(L). On-shell improved actions do not share this property.