Excited State Effects in Nucleon Matrix Element Calculations Page: 2 of 7
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Excited state Effects in Nucleon Matrix Element Calculations
1. Introduction
Quantities related to nucleon structure are among the most challenging that can be computed
within lattice QCD. During the past few years, there has been significant progress in these cal-
culations: quark masses used nowadays are close to the physical ones, lattice spacings are small
enough to allow for a controlled extrapolation to the continuum limit and volumes are sufficiently
large to suppress finite volume effects. But still even for some simple observables like the nucleon
axial charge gA or the average momentum of the unpolarized isovector parton distribution (x),-d
the values obtained from lattice calculations differ from their corresponding experimental values.
In Fig. 1 we show the relative deviation of lattice results for < x >ud from the value obtained in
Ref. [1] (ABMK). We also show the deviation of results from different phenomenological extrac-
tions from deep inelastic scattering experiments as compared to that of ABMK. The deviations of
the phenomenologically determined values for < x >ud between the different groups might be in-
terpreted as a systematic error related to different data sets and different analysis/fitting strategies.
However, as can be seen, the spread in the phenomenological number is much less than the relative
deviation between lattice data and phenomenology. One possible reason for the discrepancy can be
ABMK X-
JR
MSTW ' V-I
0.8
0.6
A
V 0.4
0.2 ETMC Nf =2 TMF f--4--
ETMC Nf=2+1+1 TMF 1--i
LHPC Nf =2+1 ASQTAD/DWF
QCDSF Nf =2 CF ---
0 - RBC/UKQCD Nf =2+1 DWF r
0 0.05 0.1 0.15 0.2 0.25 0.3
mj[GeV2]
Figure 1: With the filled symbols we show the deviation of the values of < x >ud obtained from lattice
calculations using twisted mass fermions (TMF) [2, 3] (ETMC), a hybrid action of domain wall fermions
(DWF) on a stagerred sea [4] (LHPC), Clover fermions [5, 6] (QCDSF) and DWF [7] (RBC/UKQCD). The
open symbols show the deviation of the phenomenological results [8] (JR) and [9] (MSTW) as compared to
ABMK [1].
systematic effects that enter in the lattice calculations. Therefore the latter have to be thoroughly
studied, which is a current important activity of many lattice collaborations. In these proceedings
we focus on one potential systematic effect, namely excited state contributions. Furthermore we
restrict ourselves to the two observables mentioned before, gA and (X)Ud, that are extracted from
the matrix element at zero momentum transfer. These quantities are calculated in lattice QCD by
studying the asymptotic behavior of suitable ratios of 3-point and 2-point correlation functions for
large Euclidean time separations.2
Simon Dinter
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Constantia Alexandrou, Martha Constantinou, Simon Dinter, Vincent Drach, Karl Jansen, Theodoros Leontiou, Dru B Renner. Excited State Effects in Nucleon Matrix Element Calculations, article, December 1, 2011; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc833503/m1/2/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.