17,628 research outputs found
Cancellation of Infrared Divergence in Inclusive Production of Heavy Quarkonia
A scheme is presented here to cancel out the topologically unfactorized
infrared divergences in the inclusive production of heavy quarkonia, which
affect the NRQCD factorization of these processes. The heavy quarkonia are
defined as resonance states of QCD instead of color singlet heavy quark pair.
Thus the final heavy quark pair is nor necessarily to be color singlet. In
addition, the heavy quarkonia are reconstructed by their decay products. As the
result, transition between states containing containing heavy quarks caused by
exchanges of soft gluons are also taken into account here. Such cancellation is
crucial for the NRQCD factorization of these processes.Comment: 17 pages, 26 figure
A method for getting a finite in the IR region from an all-order beta function
The analytical method of QCD running coupling constant is extended to a model
with an all-order beta function which is inspired by the famous
Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric
gau\-g\-e theories. In the approach presented here, the running coupling is
determined by a transcendental equation with non-elementary integral of the
running scale . In our approach , which reads 0.30642,
does not rely on any dimensional parameters. This is in accordance with results
in the literature on the analytical method of QCD running coupling constant.
The new "analytically im\-p\-roved" running coupling constant is also
compatible with the property of asymptotic freedom.Comment: 5 pages, 3 figure
Quantization of Yang-Mills Theories without the Gribov Ambiguity
A gauge condition is presented here to quantize non-Abelian gauge theory on
the manifold , which is free from the
Gribov ambiguity. Perturbative calculations in the new gauge behave like the
axial gauge in ultraviolet region, while infrared behaviours of the
perturbative series are quite nontrivial. The new gauge condition, which reads
, may not satisfy the requirement that
in conventional perturbative calculations. However, such
contradiction is not harmful for gauge theories constructed on the manifold
.Comment: 11page
Failure-informed adaptive sampling for PINNs
Physics-informed neural networks (PINNs) have emerged as an effective
technique for solving PDEs in a wide range of domains. It is noticed, however,
the performance of PINNs can vary dramatically with different sampling
procedures. For instance, a fixed set of (prior chosen) training points may
fail to capture the effective solution region (especially for problems with
singularities). To overcome this issue, we present in this work an adaptive
strategy, termed the failure-informed PINNs (FI-PINNs), which is inspired by
the viewpoint of reliability analysis. The key idea is to define an effective
failure probability based on the residual, and then, with the aim of placing
more samples in the failure region, the FI-PINNs employs a failure-informed
enrichment technique to adaptively add new collocation points to the training
set, such that the numerical accuracy is dramatically improved. In short,
similar as adaptive finite element methods, the proposed FI-PINNs adopts the
failure probability as the posterior error indicator to generate new training
points. We prove rigorous error bounds of FI-PINNs and illustrate its
performance through several problems.Comment: 21 pages, 18 figure
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