Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

New Scaling at High Energy DIS

E. Levin, K. Tuchin

TL;DR

The paper addresses high-energy DIS in the low-$x_B$ regime using the dipole formalism, focusing on a non-linear evolution equation that encompasses saturation effects. By modeling the BFKL kernel and introducing a scaling variable $\xi$, it reduces the problem to a one-dimensional scaling equation, solving for the amplitude in both the saturation and diffusion regions. The main result is that the dipole amplitude exhibits geometric scaling over a broad kinematic domain, with corrections to scaling shown to be small in realistic regions, aligning with experimental observations and offering insights beyond the GBW phenomenology. The work also discusses the implications for nuclear targets and sets the stage for future extensions to DIS on heavy nuclei at high rapidity.

Abstract

We develop a new approach for solving the non-linear evolution equation in the low $x_B$ region and show that the remarkable "geometric" scaling of its solution holds not only in the saturation region, but in much wider kinematical region. This is in a full agreement with experimental data (Golec-Biernat, Kwiecinski and Stasto).

New Scaling at High Energy DIS

TL;DR

The paper addresses high-energy DIS in the low- regime using the dipole formalism, focusing on a non-linear evolution equation that encompasses saturation effects. By modeling the BFKL kernel and introducing a scaling variable , it reduces the problem to a one-dimensional scaling equation, solving for the amplitude in both the saturation and diffusion regions. The main result is that the dipole amplitude exhibits geometric scaling over a broad kinematic domain, with corrections to scaling shown to be small in realistic regions, aligning with experimental observations and offering insights beyond the GBW phenomenology. The work also discusses the implications for nuclear targets and sets the stage for future extensions to DIS on heavy nuclei at high rapidity.

Abstract

We develop a new approach for solving the non-linear evolution equation in the low region and show that the remarkable "geometric" scaling of its solution holds not only in the saturation region, but in much wider kinematical region. This is in a full agreement with experimental data (Golec-Biernat, Kwiecinski and Stasto).

Paper Structure

This paper contains 6 sections, 40 equations, 4 figures.

Table of Contents

  1. Introduction.
  2. Definition of the problem.
  3. The model for the kernel.
  4. Solution to the scaling equation.
  5. Corrections to the scaling solution.
  6. Discussion.

Figures (4)

  • Figure 1: The eigenvalue of the BFKL evolution equation kernel as a function of the anomalous dimension of the gluon structure function. Solid line is the exact $\chi$ as given by Eq. (\ref{['CHI']}), dashed line corresponds to the model Eq. (\ref{['I2']}) and perfectly fits $\chi$ (it is almost indistinguishable from solid line), the dotted line is model for the right branch Eq. (\ref{['MODEL']}). The different kinematical regions are shown.
  • Figure 2:
  • Figure 3: The ratio $\delta\tilde{N}(y,\xi)/\tilde{N}(\xi)$.
  • Figure 4: (a)Dipole -- target scattering amplitude $N(z)$ and (b) dipole -- target cross section $\hat{\sigma}(z')$ in the scaling approximation versus scaling variable (a) $z$ and (b) $z'$: Solid line is a Fourier transform of $\tilde{N}(\xi)$ given in Fig. 2(a), dashed line is a Golec-Biernat -- Wusthoff model as explained in text and dotted line is the $z\gg1$ asymptotic calculated in Ref. LT.