Spectral analysis for nucleon-pion and nucleon-pion-pion states in both parity sectors using distillation with domain-wall fermions

TL;DR

This paper employs the distillation method with domain-wall fermions to analyze nucleon and multi-hadronic states across different parity sectors, pion masses, and lattice parameters, demonstrating its effectiveness for baryonic spectral studies.

Contribution

It introduces an automated contraction algorithm for multi-pion correlation functions and applies the distillation method to baryonic spectra with multiple pions across various ensembles.

Findings

Successful extrapolation of nucleon mass to the physical point.

Validation of distillation method for multi-hadronic baryonic states.

Development of an automated contraction algorithm for complex correlation functions.

Abstract

We present a study using the distillation method to analyze the spectra of nucleon, nucleon-pion, and nucleon-pion-pion states in the positive-parity sector, as well as nucleon and nucleon-pion states in the negative-parity sector. The study uses seven domain-wall fermion ensembles with varying pion masses ($m_\pi = 139 - 279~\text{MeV}$), lattice spacings ($a^{-1} = 1.730~\text{GeV}$ and $a^{-1}=2.359~\text{GeV}$) and volumes ($m_\pi L = 3.8 - 7.5$). To address the large number of contractions in this project, we implemented an algorithm to automate the contraction of nucleon-pion correlation functions that contain an arbitrary number of pions. In the positive parity sector, we extrapolate the nucleon mass to the physical point. This study demonstrates the effectiveness of the distillation method for baryonic quantities with a focus on multi-hadronic states and establishes a foundation for future work.