Lattice QCD Method To Study Hadron Mass Is Not Correct

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.