Construction of general $N$-body lattice operators with arbitrary momenta

TL;DR

This paper introduces a systematic method and an open-source tool for constructing lattice QCD operators for multi-particle systems with arbitrary momenta, spins, and quantum numbers, facilitating complex hadronic studies.

Contribution

It provides explicit constructions for multi-hadron operators covering all symmetry representations, implemented in an accessible open-source package for future lattice QCD research.

Findings

Constructed operators for up to four hadrons in all symmetry representations

Developed an open-source package 7OpTion7 for operator construction

Enabling more complex and precise lattice QCD calculations

Abstract

We present a systematic method for constructing lattice QCD operators for systems of an arbitrary number of particles with arbitrary momentum, spin, and internal quantum numbers. Explicit constructions are provided for one-, two-, three-, and four-hadron operators, covering all irreducible representations of the relevant lattice symmetry groups in both rest and moving frames. The construction procedure has been implemented in the open-source package \texttt{OpTion} (Operator construcTion), available at https://github.com/wittscien/OpTion. The paper and the package are designed to serve as a practical and extensible dictionary for future lattice QCD studies, as lattice calculations advance towards increasingly complex hadronic systems.