# Second moment of the pion distribution amplitude with the momentum smearing technique

## TL;DR

This paper demonstrates that the momentum smearing technique significantly reduces statistical errors in lattice QCD calculations of the pion distribution amplitude's second moment, improving efficiency over traditional methods.

## Contribution

It introduces and tests the momentum smearing technique for lattice calculations, showing its advantages over traditional smearing methods in reducing errors.

## Key findings

- Momentum smearing reduces statistical errors compared to Wuppertal smearing.
- The technique is effective across different lattice volumes and pion masses.
- It enables more precise lattice calculations of hadronic matrix elements.

## Abstract

Using the second moment of the pion distribution amplitude as an example, we investigate whether lattice calculations of matrix elements of local operators involving covariant derivatives may benefit from the recently proposed momentum smearing technique for hadronic interpolators. Comparing the momentum smearing technique to the traditional Wuppertal smearing we find - at equal computational cost - a considerable reduction of the statistical errors. The present investigation was carried out using $N_f=2+1$ dynamical non-perturbatively order $a$ improved Wilson fermions on lattices of different volumes and pion masses down to 220 MeV.