Spectral function and excited states in lattice QCD with maximum entropy method

TL;DR

This paper uses the maximum entropy method to extract spectral functions from lattice QCD data, identifying ground and excited meson states and unphysical doubler states, providing new insights into lattice artifacts.

Contribution

It applies the maximum entropy method to lattice QCD correlators to determine excited state spectra and identify unphysical doubler states for the first time.

Findings

Determined masses of first excited pseudoscalar and vector mesons.

Identified unphysical states as bound states of Wilson quark doublers.

Provided continuum limit estimates for excited state masses.

Abstract

We apply the maximum entropy method to extract the spectral functions for pseudoscalar and vector mesons from hadron correlators previously calculated at four different lattice spacings in quenched QCD with the Wilson quark action. We determine masses and decay constants for the ground and excited states of the pseudoscalar and vector channels from position and area of peaks in the spectral functions. We obtain the results, $m_{\pi_1} = 660(590)$ MeV and $m_{\rho_1} = 1540(570)$ MeV for the masses of the first excited state masses, in the continuum limit of quenched QCD. We also find unphysical states which have infinite mass in the continuum limit, and argue that they are bound states of two doublers of the Wilson quark action. If the interpretation is correct, this is the first time that the state of doublers is identified in lattice QCD numerical simulations.