Efficient Hadronic Operators in Lattice Gauge Theory

TL;DR

This paper addresses efficient construction of hadronic operators in quenched lattice QCD by using non-local gauge-invariant operators built from fuzzed gluon flux tubes of length $R$ to optimize overlaps with the ground state versus the first excited state. They perform two-exponential fits to correlators $C(t,R)$ across multiple $R$ and extract the Bethe-Salpeter wave function, finding a node in the excited-state wave function around $R \approx 8$ (≈ $3\,\mathrm{GeV}^{-1}$). The key result is that tuning $R$ near the node reduces excited-state contamination and yields an earlier plateau in the effective mass $m_{eff}(t)$ for mesons and baryons with light quarks. The approach is computationally efficient, generalizes across hadrons, and aligns with the heavy-quark adiabatic picture, enabling more reliable ground-state matrix-element calculations in lattice QCD. Overall, the work provides a practical strategy for precise hadron spectroscopy in lattice simulations.

Abstract

We study operators to create hadronic states made of light quarks in quenched lattice gauge theory. We construct non-local gauge-invariant operators which provide information about the spatial extent of the ground state and excited states. The efficiency of the operators is shown by looking at the wave function of the first excited state, which has a node as a function of the spatial extent of the operator. This allows one to obtain an uncontaminated ground state for hadrons.

Figures (8)

• Figure 1: (a) The spatially extended source used for the fuzzed propagator. It consists of a sum of fuzzed links of length $R$ in the six spatial orientations used. (b) The operators for baryons consisting of one fuzzed link (LLF) and two fuzzed links (LFF) joining the quarks. A sum over the six spatial orientations of each fuzzed link is used.
• Figure 2: The effective mass for the $\pi$ meson (in lattice units) using the operators (LL,LL) corresponding to $R=0$ (+), and (LL,LF) with R=4 ($\times$), 8 ($\diamond$), 10 ($\ast$) and 12 ($\Box$) at $K=0.14144$.
• Figure 3: The effective mass as in Fig. \ref{['fig:pimass']}, but for the $\rho$ meson.
• Figure 4: The effective mass (in lattice units) for the nucleon at $K=0.14144$. Here we show, from top to bottom, the (LLL,LLL) results corresponding to $R=0$, (LLL,LLF) with $R$ = 4, 8, 10 and 12 and (LLL,LFF) likewise. In each case the plateau value of the curves at large $t$ is the same: the results have been displaced by a constant in the vertical direction for legibility.
• Figure 5: The wave function for the ground state ($\times$) and first excited state ($\diamond$) for (a) the $\pi$ meson and (b) the $\rho$ meson at $K=0.14144$.