Lattice QCD Method To Study Hadron Mass Is Not Correct

TL;DR

The paper argues that the standard lattice QCD approach to calculating hadron masses is fundamentally flawed because it incorrectly assumes the QCD Hamiltonian's eigenstates correspond to physical hadron states, due to confinement effects.

Contribution

It demonstrates that the common assumption $H_{QCD}|n>=E_n|n>$ is invalid because the QCD Hamiltonian is unphysical, challenging the validity of existing lattice QCD hadron mass calculations.

Findings

QCD Hamiltonian does not have physical hadron eigenstates.

Energy flux in QCD affects the relation between $H_{QCD}$ and hadron energies.

Lattice QCD method for hadron mass calculation is fundamentally incorrect.

Abstract

Since the numerical path integration in the lattice QCD involves quark and gluon fields (not hadron fields) the lattice QCD cannot calculate any hadronic observable. Because of this reason the hadronic properties are extracted in the lattice QCD method by inserting complete set of hadron states $\sum_n |n><n|=1$ in between the partonic operators by assuming $H_{\rm QCD}|n>=E_n|n>$ where $E_n$ is the energy of the hadron. However, in this paper we find $H_{\rm QCD}|n>\neq E_n|n>$ because the QCD hamiltonian $H_{QCD}$ is unphysical but the $E_n$ and $|n>$ of the hadron are physical. We show that this is consistent with $E_{\rm QCD}(t)=<n|H_{QCD}|n>\neq E_n$ due to non-zero energy flux $E_{\rm flux}(t)$ in QCD because of confinement involving non-perturbative QCD. Hence we find that the lattice QCD method to study hadron mass is not correct.