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Title: Excited State Effects in Nucleon Matrix Element Calculations

Abstract

We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge g{sub A} and for the first moment of the isovector unpolarized parton distribution x{sub u-d}. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using N{sub f} = 2+1+1 maximally twisted mass Wilson fermions.

Authors:
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1043047
Report Number(s):
JLAB-THY-12-1410; DOE/OR/23177-1945; arXiv:1112.2931
TRN: US1202997
DOE Contract Number:
AC05-06OR23177
Resource Type:
Conference
Resource Relation:
Journal Name: PoS(LATTICE2011); Conference: Lattice 2011 - The 29th International Symposium on Lattice Field Theory, July 11-16, 2011, Lake Tahoe, CA
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCURACY; DISTRIBUTION; EIGENVALUES; EXCITED STATES; FERMIONS; ISOVECTORS; LATTICE FIELD THEORY; MATRIX ELEMENTS; NUCLEONS

Citation Formats

Constantia Alexandrou, Martha Constantinou, Simon Dinter, Vincent Drach, Karl Jansen, Theodoros Leontiou, Dru B Renner. Excited State Effects in Nucleon Matrix Element Calculations. United States: N. p., 2011. Web.
Constantia Alexandrou, Martha Constantinou, Simon Dinter, Vincent Drach, Karl Jansen, Theodoros Leontiou, Dru B Renner. Excited State Effects in Nucleon Matrix Element Calculations. United States.
Constantia Alexandrou, Martha Constantinou, Simon Dinter, Vincent Drach, Karl Jansen, Theodoros Leontiou, Dru B Renner. 2011. "Excited State Effects in Nucleon Matrix Element Calculations". United States. doi:. https://www.osti.gov/servlets/purl/1043047.
@article{osti_1043047,
title = {Excited State Effects in Nucleon Matrix Element Calculations},
author = {Constantia Alexandrou, Martha Constantinou, Simon Dinter, Vincent Drach, Karl Jansen, Theodoros Leontiou, Dru B Renner},
abstractNote = {We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge g{sub A} and for the first moment of the isovector unpolarized parton distribution x{sub u-d}. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using N{sub f} = 2+1+1 maximally twisted mass Wilson fermions.},
doi = {},
journal = {PoS(LATTICE2011)},
number = ,
volume = ,
place = {United States},
year = 2011,
month =
}

Conference:
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  • 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
  • The energies of the excited states of the Nucleon, Delta and Omega are computed in lattice QCD, using two light quarks and one strange quark on anisotropic lattices. The calculations are performed at three values of the pion mass: 392(4), 438(3) and 521(3) MeV. We employ the variational method with a basis of about ten interpolating operators enabling six energies to be distinguished clearly in each irreducible representation of the octahedral group. We compare our calculations of nucleon excited states with the low-lying experimental spectrum. There is reasonable agreement for the pattern of states.
  • Cited by 5
  • 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 sizemore » $$32^3 \times 64$$ 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.« less