After a brief review and a more refined analysis of some relevant analyticity properties (when going from Minkowskian to Euclidean theory) of the high–energy parton–parton and hadron–hadron scattering amplitudes in gauge theories, described nonperturbatively, in the eikonal approximation, by certain correlation functions of two Wilson lines or two Wilson loops near the light cone, we shall see ...

Traveltime tomography with shot-based eikonal equation fixes shot positions then relies on inversion to resolve any contradicting information between independent shots and achieve a possible cost-function minimum. On the other hand, the double-square-root (DSR) eikonal equation that describes the whole survey, while providing the same first-arrival traveltimes, allows not only the receivers but...

with k → 0 the gluon momentum, p the quark momentum after emission of the gluon, v a dimensionless vector v ∝ p, and I have omitted overall factors of gs T c F with g 2 s = 4παs and T c F the generators of SU(3) in the fundamental representation. The eikonal approximation has numerous phenomenological applications in QCD, including threshold resummations for a variety of QCD processes [1, 2, 3,...

this paper presents a new numerical method for solution of eikonal equation in two dimensions.in contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. the suggested procedure is based on the geometric properties of the solution surface...

A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion–reaction problem with a diffusion parameter tending to zero. To solve numerically the singularly perturbed diffusion– reaction problem, monotone approximations are employed. Numerical examples are presented f...

I present results for two-loop soft anomalous dimensions, which are derived from dimensionally regularized diagrams with eikonal quark lines and control soft-gluon emission in hard-scattering processes. Detailed results for the UV poles of the eikonal integrals are shown for massive quarks, and the massless limit is also taken. The construction of soft anomalous dimensions at two-loops allows s...

The complex eikonal equation in (3+1) dimensions is investigated. It is shown that this equation generates many multi soliton configurations with arbitrary value of the Hopf index. In general, these eikonal hopfions do not have the toroidal symmetry. For example, a hopfion with topology of the trefoil knot is found. Moreover, we argue that such solitons might be helpful in construction of appro...