Related papers: Scheme Dependence at Small x
We define a spatially-dependent fragmentation process, which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, and are also more…
We apply analytic perturbation theory in next-to-next-to-leading order to inclusive semileptonic $\tau$-decay and study the renormalization scheme dependence. We argue that the renormalization scheme ambiguity is considerably reduced in the…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
A survey is given of recent developments on the resummed small-$x$ evolution, in a framework based on the renormalization group equation, of non--singlet and singlet structure functions in both unpolarized and polarized deep--inelastic…
We observe that the DGLAP evolution equations at NNLO analysis predicts a ratio of the structure functions in region of small Bjorken variable $x$. The ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ is obtained and compared with the prediction of…
The problem of precise evaluation of the perturbative QCD predictions at moderate energies is considered. Substantial renormalization scheme dependence of the perturbative predictions obtained with the conventional renormalization group…
We demonstrate the scale dependence of the growth function of cosmological perturbations in dark energy models based on General Relativity. This scale dependence is more prominent on cosmological scales of $100h^{-1}Mpc$ or larger. We…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
We analyse the available data on the polarized asymmetries $A_1$ for proton, neutron and deuteron targets. We use a homogeneous and updated set of unpolarized structure functions to derive $g_1$ from $A_1$, and we accurately correct for the…
It is well known that estimating the expectation of any given bounded random variable with values in $[-B, B]$ has a sample complexity of $\mathrm{O}(B^2/\epsilon^2)$ that is independent of the underlying probability measure. We show that…
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…
We perform an adjust to the most recent structure function data, considering the QCD dipole picture applied to ep scattering. The structure function F2 at small x and intermediate Q2 can be described by the model containing an economical…
In this letter we show that the behaviour of $F_{2}$, at very small $x_B$, agrees with the behaviour expected from the BFKL evolution equation, when screening corrections are included. We obtain a description which is consistent with the…
We use data on the deep inelastic structure function F_2 in order to constrain the cross-section for scattering a colour dipole off a proton. The data seem to prefer parameterisations which include saturation effects. That is they indicate…
We discuss the updated NMC determination of $F_2^n/F_2^p$ and $F_2^p - F_2^n$. Shadowing effects in deuterium make the structure functions determined by the NMC sensibly different from the true ones in the low--$x$ region. We show that the…
We show that if the Lorentz transformation properties of diffraction are other than scalar, the $x \rightarrow 0$ behaviour of $g_1(x,Q^2)$ can grow. We compare with new data on $g_1^p$ from SMC, assess implications for sum rules and for…
Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a…
It is argued that while the scale dependence of the parton distributions in the fixed flavor factorization scheme is governed by three active flavors, the scale dependence of the running coupling should nevertheless be better governed by a…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
The status of the resummation of small x contributions to the unpolarized and polarized deep inelastic structure functions is reviewed.