2,306 research outputs found
A Prediction for the 4-Loop \beta Function
We predict that the four-loop contribution \beta_3 to the QCD \beta function
in the MS-bar prescription is given by
\beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where
N_f is the number of flavours and the coefficient of N_f^3 is an exact result
from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we
estimate \beta_3 = (7.6 \pm 0.1) x 10^3. We discuss our estimates of the errors
in these QCD predictions, basing them on the demonstrated accuracy of our
method in test applications to the O(N) \Phi^4 theory, and on variations in the
details of our estimation method, which goes beyond conventional Pade
approximants by estimating and correcting for subasymptotic deviations from
exact results.Comment: 11 pages, LaTeX, including 2 figures in 3 ps files; requires
epsfig.sty; added comparison with recent exact result
The conjugacy problem for automorphism groups of countable homogeneous structures
We consider the conjugacy problem for the automorphism groups of a number of
countable homogeneous structures. In each case we find the precise complexity
of the conjugacy relation in the sense of Borel reducibility
Application of Pade Approximants to Determination of alpha_s(M_Z^2) from Hadronic Event Shape Observables in e+e- Annihilation
We have applied Pade approximants to perturbative QCD calculations of event
shape observables in e+e- --> hadrons. We used the exact O(alpha_s^2)
prediction and the [0/1] Pade approximant to estimate the O(alpha_s^3) term for
15 observables, and in each case determined alpha_s(M_Z^2) from comparison with
hadronic Z^0 decay data from the SLD experiment. We found the scatter among the
alpha_s(M_Z^2) values to be significantly reduced compared with the standard
O(alpha_s^2) determination, implying that the Pade method provides at least a
partial approximation of higher-order perturbative contributions to event shape
observables.Comment: 15 pages, 1 EPS figure, Submitted to Physics Letters
The Anomalous Magnetic Moments of the Electron and the Muon - Improved QED Predictions Using Pade Approximants
We use Pade Approximants to obtain improved predictions for the anomalous
magnetic moments of the electron and the muon. These are needed because of the
very precise experimental values presently obtained for the electron, and soon
to be obtained at BNL for the muon. The Pade prediction for the QED
contribution to the anomalous magnetic moment of the muon differs significantly
from the naive perturbative prediction.Comment: 8 pages (LateX); SLAC-PUB-6670, CERN-TH-7451/94, TAUP-2201-94,
OSU-RN-393/94. Typo correcte
Estimate of the Three-Loop MS bar Contribution to sigma(W_L^+ W_L^- --> Z_L Z_L)
The three-loop contribution to the MS bar single-Higgs-doublet standard-model
cross-section at s = (5M_H)^2 is estimated
via least-squares matching of the asymptotic Pade-approximant prediction of the
next order term, a procedure that has been previously applied to QCD
corrections to correlation functions and decay amplitudes. In contrast to these
prior applications, the expansion parameter for the W_L^+ W_L^- \to Z_L Z_L
process is the non-asymptotically-free quartic scalar-field coupling of the
standard model, suggesting that the least-squares matching be performed over
the "infrared" mu^2 <= s region of the scale parameter. All three coefficients
of logarithms within the three-loop term obtained by such matching are found to
be within 6.6% relative error of their true values, as determined via
renormalization-group methods. Surprisingly, almost identical results are
obtained by performing the least squares matching over the mu^2 >= s region.Comment: 9 pages, LaTeX, 3 figures adde
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