Excited-state uncertainties in lattice-QCD calculations of hadron masses and scattering phase shifts

TL;DR

This paper introduces new Lanczos methods for lattice QCD that provide more accurate two-sided bounds on hadron masses and scattering phase shifts, reducing uncertainties in these calculations.

Contribution

The paper presents novel Lanczos algorithms that yield less assumption-dependent two-sided bounds in lattice QCD calculations of hadron properties.

Findings

Sub-percent constraints on nucleon mass

Meaningful bounds on nucleon-nucleon scattering phase shifts

Reduced uncertainties in excited-state energy estimates

Abstract

Lattice QCD has historically produced energy results interpretable as either estimates relying on implicit assumptions about asymptotic behavior or one-sided upper bounds. New Lanczos methods providing two-sided bounds with less-restrictive assumptions are introduced and quantified in a high-statistics calculation with unphysical quark masses. Two-sided bounds without spectral assumptions provide sub-percent constraints on the nucleon mass. Other bounds, which assume all states in a given energy window are resolved, provide meaningful two-sided constraints on nucleon-nucleon scattering phase shifts.