Novel Fat-Link Fermion Actions Page: 3 of 5
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J.M. Zanotti et al. /Nuclear Physics B (Proc. Supply ) 109A (2002) 101-105
Table 1
The value of the mean link for different numbers
of smearing sweeps, n.
n u (uo )4
0 0.88894473 0.62445197
4 0.99658530 0.98641100
12 0.99927343 0.99709689This corresponds to - 2.5 times the smearing
used in Refs. [6,9]. Further investigation reveals
that improved gauge fields with a small lattice
spacing (a = 0.125 fm) are smooth after only
4 sweeps. Hence, we perform calculations with
4 sweeps of smearing at a = 0.7 and consider
n = 12 as a second reference. Table 1 lists the
values of uoL for n = 0, 4 and 12 smearing sweeps.
A fixed boundary condition is used for the
fermions by settingUt(i, nt) = 0 and UFL(x, nt) = 0
V x (5)
Csw is expected to be adequate'. In addition,
actions with many irrelevant operators (e.g. the
D234 action) can now be handled with confidence
as tree-level knowledge of the improvement coeffi-
cients should be sufficient. Another advantage is
that one can now use highly improved definitions
of F., (involving terms up to uo2), which give
impressive near-integer results for the topological
charge [13].
In particular, we employ an 0(a4) improved
definition of Fp, [13] in which the standard clover-
sum of four 1 x 1 Wilson loops lying in the p, v'
plane is combined with 2 x 2 and 3 x 3 Wilson
loop clovers.
Work by DeForcrand et al. [14] suggests that
7 cooling sweeps are required to approach topo-
logical charge within 1% of integer value. This
is approximately 16 APE smearing sweeps at
a = 0.7 [15]. However, achieving integer topo-
logical charge is not necessary for the purposes
of studying hadron masses, as has been well es-
tablished. To reach integer topological charge,
even with improved definitions of the topologi-
cal charge operator, requires significant smooth-
ing and associated loss of short-distance informa-
tion. Instead, we regard this as an upper limit on
the number of smearing sweeps.
Using unimproved gauge fields and an unim-
proved topological charge operator, Bonnet et
al. [7] found that the topological charge settles
down after about 10 sweeps of APE smearing at
a = 0.7. Consequently, we create fat links with
APE smearing parameters n = 12 and a = 0.7.
'Our experience with topological charge operators sug-
gests that it is advantageous to include uo factors, even as
they approach 1.in the hopping terms of the fermion action. The
fermion source is centered at the space-time lo-
cation (x, y, z, t) = (1, 1, 1, 3), which allows for
two steps backward in time without loss of sig-
nal. Gauge-invariant gaussian smearing [16] in
the spatial dimensions is applied at the source to
increase the overlap of the interpolating operators
with the ground states.
4. RESULTS
Hadron masses are extracted from the Eu-
clidean time dependence of the calculated two-
point correlation functions. The effective masses
are given byM(t + 1/2) = log[G(t)] - log[G(t + 1)] .
(6)
The critical value of K, ie, is determined by lin-
early extrapolating m2 as a function of me to
zero. We used five values of quark mass and the
strange quark mass was taken to be the second
heaviest quark mass.
Effective masses (6) are calculated as a func-
tion of time and various time-fitting intervals
are tested with a covariance matrix to obtain
X2/NDF. Good values of X2/NDF are obtained
for many different time-fitting intervals as long as
one fits after time slice 8. All fits for this action
are therefore performed on time slices 9 through
14. For the Wilson action and the FLIC action
with n = 12 ("FLIC12") the fitting regimes used
are 9-13 and 9-14, respectively.
The behavior of the p, nucleon and A masses as
a function of squared pion mass is shown in Fig. 1
for the various actions. The first feature to note is
the excellent agreement between the FLIC4 and103
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Zanotti, J. M.; Bilson-Thompson, S.; Bonnet, F. D. R.; Coddington, P. D.; Leinweber, D. B.; Williams, A. G. et al. Novel Fat-Link Fermion Actions, article, July 1, 2001; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc715618/m1/3/: accessed April 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.