Related papers: Scheme Dependence at Small x
Effective field theories (EFTs) require regularization and renormalization to gain predictive power. While regularization is inconsequential from the point of view of the observable predictions of EFT -- in a renormalized theory we expect…
Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization…
The nonlinear Balitsky-Kovchegov equation at small x is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of…
Given a renormalization scheme of QCD, one can define a mass scale $\Lambda_{\rm QCD}$ in terms of the beta function. Under a change of the renormalization scheme, however, $\Lambda_{\rm QCD}$ changes by a multiplicative constant. We…
We review the current understanding of the behaviour of inclusive cross sections at small x and large Q^2 in terms of Altarelli-Parisi evolution, the BFKL equation, and Regge theory, asking in particular to what extent they are mutually…
We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…
The impact of the resummation of leading small-$x$ terms in the anomalous dimensions is briefly summarized for the evolution of non--singlet and singlet polarized structure functions.
We show that the diffractive structure function is perturbatively calculable in the domain where the diffractive mass is small but still outside the resonance region. In this domain, which can be characterized by Lambda^2/Q^2 << 1-beta <<…
We propose an approach to DGLAP evolution at small x that circumvents the usual problem that a perturbation expansion is not valid there. The data for the charm structure function are important to motivate the method, and it describes them…
A brief overview is presented of recent developments concerning resummed small-x evolution, based upon the renormalization group equation. The non-singlet and singlet structure functions are discussed for both polarized and unpolarized…
Physical anomalous dimensions are a formulation of the DGLAP evolution of Deep Inelastic structure functions which is independent of factorization scheme and -scale. In this proceedings we provide an outlook on possible applications, in…
The conventional approach to perturbative evolution is illegal because the expansion in powers of $\alpha_s$ of the the DGLAP splitting matrix ${\bf P(z,\alpha_s)}$ breaks down at small $z$. The small-$x$ data for the proton structure…
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…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
We discuss some large effects of dynamical fermions. One is a cutoff effect, others concern the contribution of multi-pion states to correlation functions and are expected to survive the continuum limit. We then turn to the preparation for…
A modification of the saturation model of deep inelastic scattering at small x which includes the Altarelli-Parisi (DGLAP) evolution is presented. Significant improvement of the description of the structure function F_2 at large Q^2 is…
Factorization scheme analysis of $F_2^{\gamma}(x,Q^2)$ in the next-to-leading order QCD is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…
We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…