Related papers: An Improved Splitting Function for Small x Evoluti…
Infrared evolution equations for small-$x$ behaviour of the non-singlet structure functions $f_1^{NS}$ and $g_1^{NS}$ are obtained and solved in the next-to-leading approximation, to all orders in $\alpha_s$, and including running…
We construct new smallest parts partition functions and smallest parts crank functions by considering variations of Bailey's Lemma and conjugate Bailey pairs. The functions we introduce satisfy simple linear congruences modulo $3$ and $5$.…
We report an evaluation of subleading eigenvalues and eigenfunctions of the BFKL equation in the color dipole representation with a running gauge coupling. We present an expansion of the small-$x$ proton structure function $F_{2p}(x,Q^2)$…
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.
Starting from the dipole representation of small-$x$ evolution we implement the running of the coupling in a self-consistent way. This results in an evolution equation for the dipole density in Borel $(b)$ space. We show that the Borel…
The small $x$ behavior of the flavor non-singlet $g_{1}$ structure function is analysed numerically by taking into account the all-order resummation of $\alpha_{s} \ln^{2}x $ terms. We include a part of the next-to-leading logarithmic…
Explicit expressions for the non-singlet and singlet structure functions g_1 in the small-x region are obtained. They include the total resummation of the double- and single- logarithms of x and account for the running QCD coupling effects.…
We show that a unified approach to the perturbative evolution of structure functions which sums all logarithms of Q^2 and 1/x at leading and next-to-leading order yields results in full agreement with the 1993 HERA data for F_2. This makes…
We present approximations of varying degree of sophistication to the integral equations for the (gluon) structure functions of a hadron (``the partonic flux factor'') in a model valid in the Leading Log Approximation with a running coupling…
On the basis of a renormalization group analysis of the kernel and of the solutions of the BFKL equation with subleading corrections, we propose and calculate a novel expansion of a properly defined effective eigenvalue function. We argue…
We discuss several methods of calculating the DIS structure functions F_2(x,Q^2) based on BFKL-type small x resummations. Taking into account new HERA data ranging down to small x and low Q^2, the pure leading order BFKL-based approach is…
Recent advances in Schramm-Loewner evolution have driven increasing interest in non-standard Loewner flows. In this work, we propose a novel splitting algorithm to simulate random Loewner curves with rigorous convergence analysis in…
The singlet contribution to the $g_1(x,Q^2)$ structure function is calculated in the double-logarithmic approximation of perturbative QCD in the region $x \ll 1$. Double logarithmic contributions of the type $(\alpha_s \ln ^2 (1/x))^k$…
A recent comparison of the evolution programs QCDNUM and APFEL showed a discrepancy in the time-like evolution of the singlet fragmentation function at NLO. It was found that the splitting functions of this evolution were wrongly assigned…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning $x$-space which is closed under the considered evolution equation. Using these functions as a basis, the…
We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in \phi^3 theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading…
The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation.…
We perform a detailed analysis of the different forms of the kinematical constraint imposed on the low $x$ evolution that appear in the literature. We find that all of them generate the same leading anti-collinear poles in Mellin space…