相关论文: Factorization and Regularization by Dimensional Re…

I review the known approaches to two-body nonleptonic $B$ meson decays, including factorization assumption, modified factorization assumption, QCD factorization, and perturbative QCD factorization. Important phenomenological aspects of…

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…

A nonperturbative approach to two-dimensional covariant gauge QCD is presented in the context of the Schwinger-Dyson equations and the corresponding Slavnov-Taylor identities. The distribution theory, complemented by the dimensional…

A complication in proving factorization theorems in Feynman gauge is that individual graphs give a super-leading power of the hard scale when all the gluons inducing the hard scattering are longitudinally polarized. With the aid of an…

We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to the nonrelativistic QCD (NRQCD) factorization for heavy quarkonium production or decay, which means that for any given process these two factorization…

This is the third one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups in odd dimension.

We study the gauge symmetry factorizability by boundary conditions on intervals of any dimensions. With Dirichlet-Neumann BCs, the Kaluza-Klein decomposition in five-dimension for arbitrary gauge group can always be factorized into that for…

We compute the relativistic corrections to the color-singlet contribution to gluon fragmentation into a J/psi at relative order v^4, making use of the nonrelativistic QCD (NRQCD) factorization approach. The corresponding full-QCD process…

The factorization theorems of quantum chromodynamics (QCD) apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler…

Let G be a semisimple algebraic group over an algebraically-closed field of characteristic zero. In this note we show that every regular face of the Littlewood-Richardson cone of G gives rise to a reduction rule: a rule which, given a…

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…

QCD factorization approach in the field-theoretic description of the semi-inclusive hadronic processes in the large Bjorken $x$ approximation implies extraction of the three-dimensional parton distribution functions as a convolution of a…

Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and quarks and gluons within it. We propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD…

We compute the relative-order-v^4 contribution to gluon fragmentation into quarkonium in the 3S1 color-singlet channel, using the nonrelativistic QCD (NRQCD) factorization approach. The QCD fragmentation process contains infrared…

We discuss the very rare, exclusive hadronic decays of a Z boson into a meson and a photon. The QCD factorization approach allows to organize the decay amplitude as an expansion in powers of $\Lambda_{\rm QCD}/m_Z\,$, where the leading…

Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…

We estimate the potential size of the weak annihilation amplitudes in QCD factorization as allowed by experimental data. To achieve this goal, we establish a connection between the amplitudes in the QCD factorization and the so-called…

This is a self-contained purely algebraic treatment of desingularization of fields of fractions $\mathbf{L}:=Q(\mathbf{A})$ of $d$-dimensional domains of the form \[\mathbf{A}:=\bar{\mathbf{F}}[\underline{x}]/\langle…

In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real…

We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…