Related papers: The difficulties involved in calculating $\delta\r…
We use the operator product expansion (OPE) to show that non-perturbative QCD corrections to $\Delta\rho$ can be calculated using unsubtracted dispersion relations for either the transverse or the longitudinal vacuum polarization functions.…
Various forms of derivative dispersion relations, in which the dispersion integral is replaced by a series of derivatives of the imaginary part of a scattering amplitude, are reviewed. Conditions of their validity and practical…
Dispersion Relations (DR) are known to be a powerful instrument for studying scattering amplitudes. In particular, they often apply to calculations in Perturbative QCD and Standard Model. We argue that applying DR to amplitudes with…
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
We produce an explicit formula for the dispersion relation for the Dirac Equation in the Standard Model Extension (SME) in the presence of Lorentz violation. Our expression is obtained using a novel techniques which exploit the algebra of…
To calculate dilepton rates in a Monte Carlo simulation of ultrarelativistic heavy ion collisions, one usually scales the number of similar QCD processes by a ratio of the corresponding differential probabilities. We derive the formula for…
Complex response function obtained in reflection spectroscopy at terahertz range is examined with algorithms based on dispersion relations for integer powers of complex reflection coefficient, which emerge as a powerful and yet uncommon…
There is a result related to the average number of the $(\delta, \eta)$-LLL bases in dimension $n$ in theoretical sense but the formula seems to be complicated and computing in high dimension takes a long time. In practical sense, we…
A forward dispersion calculation is implemented for the spin polarizabilities $\gamma_1, ... ,\gamma_4$ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are…
Premixed flames are susceptible to hydrodynamic and thermodiffusive instabilities that wrinkle the flame front and lead to complex multiscale patterns. They strongly impact the flame propagation and dynamics, increasing the speed of a…
We present a calculation of the polarized rho meson cloud in a nucleon using time-ordered perturbation theory in two different variants advocated in the literature. We calculate the induced difference between the distributions Delta…
We briefly summarize the main points made during the discussion session on the determination of $\Delta G/G$, where all Workshop participants were strongly encouraged to contribute.
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We present the numerical dispersion effects in solving the convected Helmholtz equation by the conforming and nonconforming quadrilateral finite elements. Particularly, we evaluate the dispersion relations for the numerical schemes. The…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion…
I discuss our current understanding of parton distributions. I begin with the underlying theoretical framework, and the way in which different data sets constrain different partons, highlighting recent developments. The methods of examining…
We present the model for determination of pulsar distances or average electron distribution using a method similar to the widely used dependence of A$_V$ on distances in different directions. To have reliable pulsar distances, we have used…
A hitherto difficult and unsolved issue in plasma physics is how to give a general numerical solver for complicated plasma dispersion relation, although we have long known the general analytical forms. We transform the task to a full-matrix…