Nonperturbative estimates of the Standard Model parameters Page: 4 of 7
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example of the former shortcoming is that the masses of the six types of quarks (up,
down, strange, charm, bottom and top) are not predictions of the theory, but rather
parameters extracted from experiment. One unanswered question is why, in the SM,
particles appear to come in "families" (up+down+electron, strange+charm+muon,
bottom+top+tau) that are repetitions of one another. To establish the SM it must be
subjected to as many quantitative tests as possible. The goals are to determine precise
values for the unknown parameters as well as look for deviations from the SM that will
yield clues to the structure of a new theory.
A serious limitation to obtaining accurate values for these parameters is the large
correction due to the strong interactions (described by quantum chromodynamics-QCD),
so it is very difficult to deduce quantitative predictions of the full SM using analytical
techniques. Thus an enormous body of experimental information cannot be used
effectively. One example is the weak decay amplitudes of mesons containing bottom
quarks. The rate of the decay B -> pev will be measured in the next few years. This
should allow one to extract a fundamental parameter of the SM, namely the Cabibbo-
Kobayashi-Maskawa (CKM) matrix element V,.
Without the knowledge of the strong interaction corrections, encapsulated in the so called
semi-leptonic form factors, however, this extraction is not possible.
Solving QCD will enhance our understanding of the fundamental forces of nature
and allow us to test the Standard Model of particle interactions. In the last few years there
has been a significant development in numerical methods such that a number of
phenomenologically interesting questions can be answered with an accuracy far exceeding
that obtainable from approximate analytical methods. We believe that over the next five
years systematic errors can be made smaller than 5%. Furthermore, for some quantities
analytic results can be used to roughly correct for these errors. The one area which is still
in an exploratory stage, both in terms of algorithms and in terms of the computer power
available, is including the effects of quark loops, i.e., the theory with dynamical fermions.
The approximate theory that neglects the effect of quark loops (called quenched QCD) is
simpler to simulate by a factor of 1000-10000. Since the effects of this approximation are
expected to be at the level of 10% for a number of observables, and as the results described
below show, it has been opportune to carry out a statistics study of these quantities using a
large statistical sample.
To simulate Lattice QCD we use stochastic methods based on Monte Carlo
integration that include Metropolis, overrelaxed and cluster update algorithms as well as
Molecular Dynamics and Langevin evolution. The most computer intensive part of the QCD
calculation is a matrix inversion necessary to calculate the quark propagator. We solve the
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Gupta, R.; Bhattacharya, T.; Tamayo, P.; Grandy, T.; Kilcup, G. & Sharpe, S. Nonperturbative estimates of the Standard Model parameters, report, August 1, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc694443/m1/4/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.