Related papers: Reflection Identities of Harmonic Sums and pole de…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
Recent concerns about the very large next-to-leading logarithmic (NLL) corrections to the BFKL equation are addressed by the introduction of a physical rapidity-separation parameter $\Delta$. At the leading logarithm (LL) this parameter…
We study some analytic properties of the BFKL ladder at next-to-leading logarithmic accuracy (NLLA). We use a procedure by Chirilli and Kovchegov to construct the NLO eigenfunctions, and we show that the BFKL ladder can be evaluated order…
Let $\mathfrak{g}$ be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible $\mathfrak{g}$-module. It is argued that the character of…
We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator…
A calculation of the non-singlet part of spin dependent structure function, $xg_1^{NS}(x,Q^2)$ and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge…
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas…
We solve the Balitsky-Fadin-Kuraev-Lipatov equation in the next-to-leading logarithmic approximation for forward scattering with all conformal spins using an iterative method.
The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the solution of the BFKL equations both in the transverse coordinate and momentum spaces. This result is…
This is a summary of the contributions on the next-to-leading order corrections to the BFKL equation which were presented to the `Small-x and Diffraction' working group at the 1998 Durham Workshop on HERA Physics.
We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.
It is shown that the existing four-loop result for the Bjorken polarized sum rule for deep inelastic electron-nucleon scattering obtained within perturbative Quantum Chromodynamics should be supplemented by the calculation of the diagrams…
The procedure to improve the convergence in transverse momentum space of the NLL BFKL kernel using a w-shift is revisited. An accurate approximation to this shift only depending on transverse momenta is presented. This approximation is…
Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the L\"owenheim-Skolem Theorems of stationary logics. In this paper, we mainly analyze the…
In this work we prove a new combinatorial identity and applying it we establish many finite harmonic sum identities. Among many others, we prove that \begin{equation*}…
Of late, the field of BFKL physics has been the subject of significant developments. The calculation of the NLL terms was recently completed, and they turned out to be very large. Techniques have been proposed to resum these corrections.…
The solution to the non-forward BFKL equation in the Leading Logarithmic approximation is expressed in terms of a sum of iterations of its kernel directly in transverse momentum and rapidity space. Several studies of the non-forward…
We show that the forward-jet measurements performed at HERA allow for a detailed study of corrections due to next-to-leading logarithms (NLL) in the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach. While the description of the d\sigma/dx data…
The representation of the total cross section at high energy $\sqrt s$ in the next-to-leading $\ln s$ approximation is given with definition of the impact factors and explicit expression for the BFKL kernel. The estimate of the Pomeron…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…