The Self Energy of Massive Lattice Fermions

Bartholomeus P.G. Mertens, Aida X. El-Khadra, 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 hep-lat/9712024, FERMILAB-PUB-97/412-T. 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 one-loop correction to the rest mass, kinetic mass, and wave-function renormalization factor, for massive lattice fermions described by the Sheikholeslami-Wohlert action. The tree-level 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:

  1. the tree-level rest mass,
  2. the gluon mass (always zero),
  3. the result,
  4. the uncertainty estimate (from VEGAS),
  5. the chi^2 (from VEGAS).
Each table of coefficients contains two columns:
  1. the coefficient index j,
  2. 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 Wave-function 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 cSW=0 (Wilson action) and cSW=1 (SW action).  As above, the tree-level 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:

  1. the tree-level rest mass,
  2. the result for log(q*a),
  3. the uncertainty estimate (from VEGAS),
  4. 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 M1.  In normal perturbation theory (PT), let
log(q*a)2 = *M1/M1
Then, with tadpole improvement it becomes
log(q*a)2 = (*M1 + *u0R)/(M1 + u0R)
where R = M0/(1+M0), u0 = -CF/16, and *u0 = - CF0.153036.  The numerator *M1 can be obtained from the table for log(q*a) and the table for M1 above.

Values

The Kinetic Mass

We will not tabulate *M2 until it is thoroughly checked. 
29 May 1998 --- Andreas Kronfeld ask@fnal.gov
updated 30 June 2000