Controlling excited-state contamination in nucleon matrix elements

Abstract

We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2 þ 1-flavor ensemble with lattices of size 32 3 × 64 generated using the rational hybrid Monte Carlo algorithm at a ¼ 0.081 fm and with M π ¼ 312 MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation t sep . We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of t sep needed to demonstrate convergence of the isovector charges of the nucleon to the t sep → ∞ estimates is presented.

Nucleon electromagnetic form factors in the continuum limit from ( 2+1+1 )-flavor lattice QCD

“…The new CODATA-2018 value [25] resolves the puzzle in favor of the muonic-hydrogen result. The magnetic radius of the proton extracted from experiments using electrons is [4,24] r p M = 0.776 (38) fm electrons .…”

Excited-state effects in nucleon structure on the lattice using hybrid interpolators

“…Variational approaches have been used to study nucleon structure in Refs. [5][6][7][8][9], which used bases of interpolators with different smearing widths and different site-local spin structures, and Ref. [10], which used the distillation method to enable the use of interpolators with a variety of local structures including covariant derivatives.…”

Controlling excited-state contributions with distillation in lattice QCD calculations of nucleon isovector charges gSu−d , gAu−Egerer1, Richards2, Winter3 2019Phys. Rev. DSelf Cite250330View full textAdd to dashboardCite

“…This smearing yields a tadpole-improved tree-level clover coefficient that is nearly identical to the corresponding non-perturbative determination. The reader is referred to [12,13] for a discussion regarding the gauge action used to generate this ensemble. Calculations were performed on a 32 3 × 64 lattice with periodic (spatial) and anti-periodic (temporal) boundary conditions and an inverse coupling of β = 6.3.…”

“…[12,13]) N (x) is smeared with 60 hits of Jacobi smearing, with width σ = 5.0. We refer the reader to [12,13] for an extensive analysis of the effect different Jacobi smearing parameters has on the determination of nucleon isovector charges. Herein we refer to the Jacobi smeared interpolator as "Jacobi-SS".…”