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Geometric scaling in inclusive e A reactions and nonlinear perturbative QCD

A. Freund, K. Rummukainen, H. Weigert, A. Schaefer

TL;DR

The work tests whether geometric scaling, established for the proton in deep inelastic scattering, extends to inclusive electron-nucleus reactions within a nonlinear pQCD framework that includes saturation. By modeling nuclear shadowing as a rescaling of the saturation scale and evaluating a generalized scaling form, the authors analyze NMC and E665 data to show that 1/A F2^A exhibits scaling when expressed in terms of the scaling variable $\tau=(x/x_0)^{2\lambda} Q^2 / A^{1/3}$, with fit parameters $\lambda\approx0.18$, $\gamma\approx0.09$, and $\delta\approx0.25$. The Ca data appear compatible with $A^{1/3}$ scaling, supporting a universal saturation picture across nucleons and nuclei, though some dataset inconsistencies and phase-space limitations are noted. The study underscores the potential of geometric scaling as a robust indicator of saturation effects in eA scattering and calls for future Electron-Ion Collider data to definitively map the $x$ and $A$ dependences.

Abstract

In this note we report on geometric scaling in inclusive e A scattering data from the NMC and E665 experiments. We show that this scaling, as well as nuclear shadowing, is expected in the framework of nonlinear pQCD at small x based on a simple rescaling argument for e p scattering.

Geometric scaling in inclusive e A reactions and nonlinear perturbative QCD

TL;DR

The work tests whether geometric scaling, established for the proton in deep inelastic scattering, extends to inclusive electron-nucleus reactions within a nonlinear pQCD framework that includes saturation. By modeling nuclear shadowing as a rescaling of the saturation scale and evaluating a generalized scaling form, the authors analyze NMC and E665 data to show that 1/A F2^A exhibits scaling when expressed in terms of the scaling variable , with fit parameters , , and . The Ca data appear compatible with scaling, supporting a universal saturation picture across nucleons and nuclei, though some dataset inconsistencies and phase-space limitations are noted. The study underscores the potential of geometric scaling as a robust indicator of saturation effects in eA scattering and calls for future Electron-Ion Collider data to definitively map the and dependences.

Abstract

In this note we report on geometric scaling in inclusive e A scattering data from the NMC and E665 experiments. We show that this scaling, as well as nuclear shadowing, is expected in the framework of nonlinear pQCD at small x based on a simple rescaling argument for e p scattering.

Paper Structure

This paper contains 5 sections, 5 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Geometric scaling and nuclear shadowing within nonlinear pQCD.
  3. Geometric scaling in $\frac{1}{A}F^A_2$
  4. Geometric scaling in $\frac{1}{A}F^A_2$
  5. Conclusions

Figures (4)

  • Figure 1: Ratio of $2F_2^A/AF_2^D$ vs. $\tau$ for NMC and E665. Note the increasing steepness with $A$ within the NMC and E665 datasets respectively.
  • Figure 2: Comparative phase space of HERA, NMC and E665.
  • Figure 3: Scaling behavior of NMC and E665 $F^A_2$ data vs. $\tau = \left(\frac{x_{\text{bj}}}{x_0}\right)^{2\lambda}\frac{Q^2}{A^{1/3}}$. The vertical axis corresponds to the l.h.s. of Eq. \ref{['eq:F2fit']}. The dashed line corresponds to the geometric scaling curve obtained from HERA data. These are shown offset by a factor of 5.
  • Figure 4: Plot of scaled NMC and E665 $F^A_2/AF_2^p$ data vs. $\tau = \left(\frac{x_{\text{bj}}}{x_0}\right)^{2\lambda}\frac{Q^2}{A^{1/3}}$. This corresponds to "dividing the data shown in Fig. \ref{['fig:scaling']} by the dashed line."