Quenched Chiral Log and Light Quark Mass from Overlap Fermions Page: 1 of 3
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Quenched Chiral Log and Light Quark Mass from Overlap Fermions * t
Terrence Draper a, Shao-Jing Dong a, Ivan Horvath a, Frank Lee b c, Keh-Fei Liu a, Nilmani Mathur a,
and Jianbo Zhang d
aDepartment of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA
O bCenter for Nuclear Studies, Dept. of Physics, George Washington Univ., Washington, DC 20052, USA
Cpl CJefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA
dCSSM and Dept. of Physics and Math. Physics, Univ. of Adelaide, Adelaide, SA 5005, Australia
We study the quenched chiral behavior of the pion with mass as low as ~ 180 MeV. The calculation is done on
a quenched lattice of size 163 x 28 and a = 0.2 fm with 80 configurations using overlap fermions and an improved
Cl gauge action. Using an improved constrained curve fitting technique, we find that the ground state pseudoscalar
mass versus bare quark mass behavior is well controlled with small statistical errors; this permits a reliable fit of
the quenched chiral log effects, a determination of the chiral log parameter (b = 0.26(3)), and an estimate of therenormalized mass of the light quark (mIS(p = 2 GeV)
1. Simulation Details
Using a j3 2.264 renormalization-group-
improved Iwasaki [1] gauge action, we study the
chiral properties of hadrons on a 163 x 28 lattice
with the overlap fermion [2,3] and massive overlap
operator [4 6]D(mo)
m+ a
2m a'
2where E(H) H/ H , H ysD, and De is
the usual Wilson fermion operator, except with a
negative mass parameter -p 1/2n -4 in which
nc < n < 0.25; we take n 0.19 in our calculation
which corresponds to p 1.368.
We use the optimal partial fraction expan-
sion with a 14th-order Zolotarev approximation
of the matrix sign function [7]; the sign func-
tion approximated to better than 3 parts in 1010.
As the conjugate-gradient inverter accommodates
multi-mass [8] we obtain the quark propagator at
26 masses including 18 masses at or below the
strange quark mass with less than 10% overhead.
*Talk presented by T. Draper at Lattice 2002.
tThis work is supported in part by the U.S. Department
of Energy under grant numbers DE-FG05-84ER40154 and
DE-FG02-02ER,45967.3.7(3) MeV).
2. Pion Decay Constant and ZA
The renormalized pion decay constant is
f(/R)2 ZAf() 2f(m )
(mg./2m o)2m App
(mm/2mo)where mw is the unrenormalized quark mass,
fPU - 2m1App is the unrenormalized pseu-
doscalar decay constant, and ApP is the am-
plitude of the two-point local-local correlator,
GpP(t) - App(emrt+e-m(T-t)). Since f(R)
is free of quenched chiral logs, and since we de-
termine it quite precisely, we use f(R) to set the
scale and obtain a-i 0.978(5) GeV.
As a bonus, we obtain the axial-vector renor-
malization constant, ZA, via the axial Ward
identity ZA&pA 2ZmmoZpP and the rela-
tions Z Zp Zs protected by the chiral
symmetry of the overlap fermion. Thus ZA
Ao AP which is plotted in Fig. 1.
mr AAg4P
A covariant polynomial fit yields
ZA 1.85(1) - 0.60(12)moAQcDa2
+0.59(4)mwa2 ; AQCDa 0.25
so O(moAQcDa2) and O(mwa2) terms are small.C
0
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Draper, Terrence; Dong, Shao-Jing; Horvath, Ivan; Lee, Frank; Liu, Keh-Fei; Mathur, Nilmani et al. Quenched Chiral Log and Light Quark Mass from Overlap Fermions, article, June 1, 2002; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc738615/m1/1/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.