3,995 research outputs found
QCD Factorization for Spin-Dependent Cross Sections in DIS and Drell-Yan Processes at Low Transverse Momentum
Based on a recent work on the quantum chromodynamic (QCD) factorization for
semi-inclusive deep-inelastic scattering (DIS), we present a set of
factorization formulas for the spin-dependent DIS and Drell-Yan cross sections
at low transverse momentum.Comment: 12 pages, two figures include
Spin Decomposition of Electron in QED
We perform a systematic study on the spin decomposition of an electron in QED
at one-loop order. It is found that the electron orbital angular momentum
defined in Jaffe-Manohar and Ji spin sum rules agrees with each other, and the
so-called potential angular momentum vanishes at this order. The calculations
are performed in both dimensional regularization and Pauli-Villars
regularization for the ultraviolet divergences, and they lead to consistent
results. We further investigate the calculations in terms of light-front wave
functions, and find a missing contribution from the instantaneous interaction
in light-front quantization. This clarifies the confusing issues raised
recently in the literature on the spin decomposition of an electron, and will
help to consolidate the spin physics program for nucleons in QCD.Comment: 8 page
Threshold Resummation for Higgs Production in Effective Field Theory
We present an effective field theory to resum the large double logarithms
originated from soft-gluon radiations at small final-state hadron invariant
masses in Higgs and vector boson (\gamma^*, and ) production at hadron
colliders. The approach is conceptually simple, indepaendent of details of an
effective field theory formulation, and valid to all orders in sub-leading
logarithms. As an example, we show the result of summing the
next-to-next-to-next leading logarithms is identical to that of standard pQCD
factorization method.Comment: A version to appear in Phys. Rev.
Comments on "Graphon Signal Processing''
This correspondence points out a technical error in Proposition 4 of the
paper [1]. Because of this error, the proofs of Lemma 3, Theorem 1, Theorem 3,
Proposition 2, and Theorem 4 in that paper are no longer valid. We provide
counterexamples to Proposition 4 and discuss where the flaw in its proof lies.
We also provide numerical evidence indicating that Lemma 3, Theorem 1, and
Proposition 2 are likely to be false. Since the proof of Theorem 4 depends on
the validity of Proposition 4, we propose an amendment to the statement of
Theorem 4 of the paper using convergence in operator norm and prove this
rigorously. In addition, we also provide a construction that guarantees
convergence in the sense of Proposition 4
Generalized Graphon Process: Convergence of Graph Frequencies in Stretched Cut Distance
Graphons have traditionally served as limit objects for dense graph
sequences, with the cut distance serving as the metric for convergence.
However, sparse graph sequences converge to the trivial graphon under the
conventional definition of cut distance, which make this framework inadequate
for many practical applications. In this paper, we utilize the concepts of
generalized graphons and stretched cut distance to describe the convergence of
sparse graph sequences. Specifically, we consider a random graph process
generated from a generalized graphon. This random graph process converges to
the generalized graphon in stretched cut distance. We use this random graph
process to model the growing sparse graph, and prove the convergence of the
adjacency matrices' eigenvalues. We supplement our findings with experimental
validation. Our results indicate the possibility of transfer learning between
sparse graphs
- …