skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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+1 flavor ensemble with lattices of size $$32^3 \times 64$$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $$M_\pi=312$$~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 two-state fit to data at multiple values of the source-sink separation $$t_{\rm sep}$$. 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 $$t_{\rm sep}$$ needed to demonstrate convergence of the isovector charges of the nucleon to the $$t_{\rm sep} \to \infty $$ estimates is presented.

Authors:
; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Contributing Org.:
Nucleon Matrix Elements (NME) Collaboration
OSTI Identifier:
1329018
Report Number(s):
JLAB-THY-16-2285; DOE/OR/23177-3842; arXiv:1602.07737
Journal ID: ISSN 2470-0010; PRVDAQ
DOE Contract Number:
AC05-00OR22725; KA-1401020; AC05-06OR23177; SC0011090; FG02-96ER40965
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review D; Journal Volume: 93; Journal Issue: 11
Country of Publication:
United States
Language:
English

Citation Formats

Yoon, Boram, Gupta, Rajan, Bhattacharya, Tanmoy, Engelhardt, Michael, Green, Jeremy, Joó, Bálint, Lin, Huey-Wen, Negele, John, Orginos, Kostas, Pochinsky, Andrew, Richards, David, Syritsyn, Sergey, and Winter, Frank. Controlling excited-state contamination in nucleon matrix elements. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.93.114506.
Yoon, Boram, Gupta, Rajan, Bhattacharya, Tanmoy, Engelhardt, Michael, Green, Jeremy, Joó, Bálint, Lin, Huey-Wen, Negele, John, Orginos, Kostas, Pochinsky, Andrew, Richards, David, Syritsyn, Sergey, & Winter, Frank. Controlling excited-state contamination in nucleon matrix elements. United States. doi:10.1103/PhysRevD.93.114506.
Yoon, Boram, Gupta, Rajan, Bhattacharya, Tanmoy, Engelhardt, Michael, Green, Jeremy, Joó, Bálint, Lin, Huey-Wen, Negele, John, Orginos, Kostas, Pochinsky, Andrew, Richards, David, Syritsyn, Sergey, and Winter, Frank. Wed . "Controlling excited-state contamination in nucleon matrix elements". United States. doi:10.1103/PhysRevD.93.114506. https://www.osti.gov/servlets/purl/1329018.
@article{osti_1329018,
title = {Controlling excited-state contamination in nucleon matrix elements},
author = {Yoon, Boram and Gupta, Rajan and Bhattacharya, Tanmoy and Engelhardt, Michael and Green, Jeremy and Joó, Bálint and Lin, Huey-Wen and Negele, John and Orginos, Kostas and Pochinsky, Andrew and Richards, David and Syritsyn, Sergey and Winter, Frank},
abstractNote = {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+1 flavor ensemble with lattices of size $32^3 \times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_\pi=312$~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 two-state fit to data at multiple values of the source-sink separation $t_{\rm sep}$. 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 $t_{\rm sep}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\rm sep} \to \infty $ estimates is presented.},
doi = {10.1103/PhysRevD.93.114506},
journal = {Physical Review D},
number = 11,
volume = 93,
place = {United States},
year = {Wed Jun 01 00:00:00 EDT 2016},
month = {Wed Jun 01 00:00:00 EDT 2016}
}
  • Cited by 8
  • 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+1-flavor ensemble with lattices of size 32 3 × 64 generated using the rational hybrid Monte Carlo algorithm at a = 0.081 fm and with M π = 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 separationmore » t sep. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. As a result, 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.« less
  • We present a dedicated precision analysis of the influence of excited states on the calculation of several nucleon matrix elements. This calculation is performed at fixed values of the lattice spacing, volume and pion mass that are typical of contemporary lattice computations. We focus on the nucleon axial charge, g{sub A}, for which we use 7,500 measurements, and on the average momentum of the unpolarized isovector parton distribution, x{sub u-d}, for which we use 23,000 measurements. All computations are done employing N{sub f}=2+1+1 maximally-twisted-mass Wilson fermions and non-perturbatively calculated renormalization factors. We find that excited state effects are negligible formore » g{sub A} and lead to a O(10%) downward shift for x{sub u-d}.« less
  • Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (H{sub ab}) for electron transfer reactions using {ital ab initio} electronic structure theory. The first is based on the generalized Mulliken{endash}Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn{sub 2}OH{sub 2}{sup +} and (b) the low-lying states of the benzene{endash}Cl atom complex andmore » its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn{sub 2}OH{sub 2}{sup +}. Both methods also yield a natural definition of the effective distance (r{sub DA}) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of r{sub DA}, generally based on molecular structure data. {copyright} {ital 1997 American Institute of Physics.}« less