The color dipole picture of low-x DIS

TL;DR

This paper presents a model-independent analysis of low-x deep inelastic scattering, demonstrating how photon fluctuations into quark-antiquark dipoles interact with the gluon field, leading to scaling behaviors and saturation effects consistent with experimental data.

Contribution

It provides a model-independent framework for understanding low-x DIS phenomena, including scaling and saturation, without relying on specific dipole cross section ansatzes.

Findings

Validation of low-x scaling behavior of photoabsorption cross section.

Determination of the saturation scale exponent C_2 ≈ 0.29.

Prediction of the longitudinal-to-transverse cross section ratio R = 1/2 ρ.

Abstract

Deep inelastic electron scattering (DIS) from nucleons at low values of the Bjorken variable $x \cong Q^2/W^2 \lsim ~ 0.1$ proceeds via fluctuations of the photon into quark-antiquark dipole states that subsequently interact with the gluon field in the nucleon. Dependent on the interaction energy, $W$, the color-gauge-invariant dipole interaction with the gluon field in the nucleon, for any fixed dipole size, contains the limits of i) color transparency and ii) saturation, where "saturation" stands for the approach to a hadronlike dipole-proton interaction cross section. All essential features of the experimental results on low-x DIS, as a consequence of the color-gauge-invariant dipole interaction follow model independently i.e. without specific ansatz for the dipole cross section. The model-independent results in particular include the low-x scaling behavior of the photoabsorption cross section, $\sigma_{\gamma^*p} (W^2,Q^2) = \sigma_{\gamma^*p} (\eta (W^2,Q^2))$, with definite functional dependence on the low-x scaling variable $\eta (W^2,Q^2) \cong Q^2/\Lambda^2_{sat} (W^2)$ in the limits of $\eta (W^2,Q^2) \gg 1$ and $\eta (W^2,Q^2) \ll 1$, respectively. Consistency with the pQCD-improved parton model implies the definite value of $C_2 \cong 0.29$ for the exponent in the "saturation scale", $\Lambda^2_{sat} (W^2) \approx (W^2)^{C_2}$. The longitudinal-to-transverse ratio of the photoabsorption cross section at large $Q^2$ has the definite value of $R = 1/2 \rho$ with $\rho = 4/3$. For $W^2 \to \infty$ at any fixed $Q^2$, the photoabsorption cross section converges towards a $Q^2$-independent saturation limit that coincides with the cross section for $Q^2 = 0$ photoproduction.