The Self Energy of Massive Lattice Fermions
Bartholomeus P.G. Mertens, Aida X. ElKhadra, and
Andreas
S. Kronfeld
BLM
scales for the rest mass
General Information
The information posted here is a companion to the article of the same name,
available electronically as
heplat/9712024,
FERMILABPUB97/412T.
SPIRES entry.
The article has been published in Phys. Rev. D58 (1998)
034505.
One of the authors of this website (BPGM) received a Ph. D. in physics
from the University of Chicago for this research, and we thank Prof. Jon
Rosner for his supervisory role.
Numerical Results
As described in the article, we evaluated the oneloop correction to the
rest
mass,
kinetic mass, and
wavefunction
renormalization factor, for massive lattice fermions described by the
SheikholeslamiWohlert action. The treelevel mass was chosen to facilitate
Chebyshev interpolation. For definitions and notation, please consult the
article.
The remainder of this page gives hypertext links to tables containing
our results for values of the functions and for Chebyshev coefficients.
Each table of values contains five columns:

the treelevel rest mass,

the gluon mass (always zero),

the result,

the uncertainty estimate (from VEGAS),

the chi^2 (from VEGAS).
Each table of coefficients contains two columns:

the coefficient index j,

the coefficient.
(Uncertainties in the coefficients are a few to several parts per million.
They are not given because they are highly correlated.)
The Rest Mass
We tabulate the quantity defined in Eq. (6.3) of the article, with color
factor 4/3.
Values
Chebyshev coefficients
The Kinetic Mass
We tabulate the quantity defined in Eq. (4.6) of the article, with color
factor 4/3.
Values
Chebyshev coefficients
The Wavefunction Renormalization Factor
We tabulate the quantity defined in Eq. (5.9) of the article, with color
factor 4/3.
Values
Chebyshev coefficients
Numerical
Results for BLM scales
Calculations for the BLM scale of the
rest
mass are finished, and for
kinetic mass in progress. We give
results with c_{SW}=0 (Wilson action) and c_{SW}=1 (SW
action). As above, the treelevel rest mass is used to label the
columns. For now we provide only the functions; Chebyshev coefficients
will appear later.
The remainder of this page gives hypertext links to tables containing
our results for values of the functions and for Chebyshev coefficients.
Each table of values now contains four columns:

the treelevel rest mass,

the result for log(q^{*}a),

the uncertainty estimate (from VEGAS),

the chi^2 (from VEGAS).
The gluon mass is always zero and, thus, not tabulated. Errors for
log(q^{*}a), which is a ratio, are propagated from
underlying VEGAS integrals.
The Rest Mass
We tabulate log(q^{*}a) for M_{1}.
In normal perturbation theory (PT), let
log(q^{*}a)^{2} =
^{*}M_{1}/M_{1}
Then, with tadpole improvement it becomes
log(q^{*}a)^{2} =
(^{*}M_{1}
+ ^{*}u_{0}R)/(M_{1}
+ u_{0}R)
where R = M_{0}/(1+M_{0}), u_{0}
= C_{F}/16, and ^{*}u_{0} =  C_{F}0.153036.
The numerator ^{*}M_{1} can be obtained from the
table for log(q^{*}a) and the table for M_{1}
above.
Values
The Kinetic Mass
We will not tabulate ^{*}M_{2} until it is thoroughly
checked.
29 May 1998  Andreas Kronfeld
ask@fnal.gov
updated 30 June 2000