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it Fermilab
FERMILAB-Conf-01/322-T October 2001
1
Highly Improved Naive and Staggered Fermions
Howard D. Trottiera b, G. Peter Lepagea, Paul B. Mackenziec, Quentin Masona, and Matthew A. Nobesb
(HPQCD Collaboration)
aPhysics Department, Cornell University, Ithaca, NY, 14853, USA
bPhysics Department, Simon Fraser University, Burnaby, B. C., Canada, V5A 1S6, permanent address.
CFermilab, P. O. Box 500, Batavia, IL 60510, USA
We present a new action for highly improved staggered fermions. We show that perturbative calculations for the new action
are well-behaved where those of the conventional staggered action are badly behaved. We discuss the effects of the new terms
in controlling flavor mixing, and discuss the design of operators for the action.1. INTRODUCTION
Naive and staggered fermion actions (which
have very similar properties) have numerous advan-
tages over actions based on four-component Wilson
fermions. They have an exact chiral symmetry, al-
lowing a simpler approach to the light-quark limit.
They require only even dimension correction oper-
ators, simplifying the improvement program. Stag-
gered fermion propagators can be calculated much
more rapidly than Wilson fermion propagators.
They thus offer the possibility of performing much
higher accuracy calculations on current computers
than with other methods. However, they have his-
torically suffered some drawbacks which must be ad-
dressed before they can be used effectively. Glu-
ons of momentum It induce unphysical transitions
between different flavors of doubler quarks, leading
to large flavor symmetry breaking, especially in the
pion sector. The perturbation series, even using im-
proved perturbation theory, is often more poorly be-
haved than the series for Wilson fermions. With stag-
gered fermions, quarks of different spins live on dif-
ferent sites of the lattice, leading to large O(a2) errors
that are not present for Wilson fermions. Finally, the
doubling of the fermion spectrum requires the taking
of a root of the determinant in simulations, requiring
more care in understanding the locality of the theory.
This paper will show that the improvement pro-
gram provides an elegant solution to the first three of
these problems.2. IMPROVED STAGGERED FERMIONS
One significant problem with ordinary naive and
staggered fermions is the large flavor nondegeneracy.
This problem is worst in the pion sector. For the B me-
son, and other particles with a single light quark, there
is no flavor mixing at the valence level, because the
heavy quark would be driven far off-shell by a gluon
of momentum 7L. However, since Bs couple to virtual
pions, flavor mixing interactions can still be impor-
tant.
At tree level, they arise from transitions between
doubler quarks of different flavors induced by gluons
of momentum 7L [1,2]. In Ref. [3], it was shown how
to turn "fat-link" improvement[4], which suppresses
the coupling of quarks to these gluons, into a tree level
0(a2) improved action by proper tuning of the coeffi-
cients and the inclusion of an additional term.
The improved action for naive quarks is given by:x A 2
Simp = E W(x) C - A' - -6 A' -3 - m I x).
X(1)
(The connection between naive and staggered quarks
is the usual one [3]). V, is a smeared link variable,
identical to the ordinary link variable (up to errors of
0(a2)) for low gluon momentum, but vanishes when
a gluon of momentum It/a is extracted. The action
has an exact doubling symmetry
W(x) - Bj(x)W(x), *(x) -+ W(x)B(x), where
B (x) = f] (iy5yp) exp(ign - x/a) for one of fifteen
vectors ( with one or more non-zero components,
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al., Howard D. Trottier et. Highly improved naive and staggered fermions, article, October 23, 2001; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc716552/m1/1/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.