HERA-data in the light of small x evolution with state of the art NLO input

TL;DR

The paper develops and tests a state-of-the-art small-x framework based on JIMWLK evolution with NLO input (notably running coupling and energy-conservation corrections) against HERA data for both total and diffractive gamma*-p cross sections. By employing BK/GT truncations and careful treatment of impact factors and impact-parameter profiles, the authors show that energy-conservation corrections are essential for achieving an accurate, perturbatively driven fit up to Q^2 ≈ 1200 GeV^2 in the x < 0.02 regime. The analysis highlights the critical role of nonperturbative b-dependence and the need for full NLO impact factors to sharpen diffractive predictions, while demonstrating that asymptotic, pseudo-scaling solutions can describe the data robustly when NLO effects are properly included. Overall, the work solidifies the CGC/JIMWLK approach as a viable framework for interpreting small-x HERA data and provides clear directions for future refinements, including more complete NLO inputs and refined nonperturbative modeling.

Abstract

Both total and diffractive cross sections from HERA are successfully confronted with JIMWLK evolution equations in the asymptotic pseudo-scaling region. We present a consistent, simultaneous description of both types of cross sections that includes NLO corrections in the form of running coupling and energy conservation corrections. The inclusion of energy conservation corrections allows to match all available data with x below .02 i.e. up to Q^2 of 1200 GeV^2. We discuss the effects of quark masses including charm, contrast asymptotic and pre-asymptotic fit strategies, and survey non-perturbative uncertainties related to impact parameter dependence.

Figures (23)

• Figure 1: Diagrammatic representation of the amplitude for $\gamma^* A$ scattering at small $x$ at momentum transfer $Q^2=-q^2$. Light cone "time" $x^-$ runs from right to left. The interacting "out-state" (left) contain nontrivial interaction between projectile and target, which is marked by a vertical bar (blue online) at $x^-=0$ that indicates the interaction region and markers for the Wilson lines picked up by the projectile constituents. The non-interacting "in-state" (right) instead has no interactions and correspondingly trivial Wilson line factors at $x^-=0$.
• Figure 2: Rapidity gap events differ from generic events contributing to the total cross section by a target side rapidity gap of size $Y_{\rm{gap}}=\ln(1/x_{\mathbb{P}})$ into which no gluons are emitted. This gap is complemented by a projectile fragmentation range of size $Y_{\rm{frag}}=\ln(1/\beta)$, such that $Y=Y_{\rm{gap}}+Y_{\rm{frag}}$.
• Figure 3: Left: The evolution speed $\lambda$ as a function of dimensionless units $R_s \Lambda$ for two different approaches mentioned in text. Middle: Evolution speed after adding in the energy conservation correction on top of running coupling Right: The running couplings (regulated vs. unregulated) used in different BK schemes plotted against the parent dipole size $r$. The vertical lines bracket approximately the region of saturation corresponding to HERA, $0.8 < R_s < 3.7$ for $5\times 10^{-7} < x_{\text{bj}} < 0.02$.
• Figure 4: Left: LO i.e. fixed coupling BK evolution: asymptotically the evolution speed $\lambda \rightarrow \text{\bf{const}}\times\alpha_s$ for any relevant initial state. Middle: NLO BK evolution: the running coupling slows down the evolution. After the initial state effects are erased, the evolution speed settles on the same asymptotic line. Right: DGLAP type NLO corrections slow down the evolution further.
• Figure 5: Relative size of the energy conservation correction: the contributions to the r.h.s. of Eq. \ref{['eq:GT_modified']} at a fixed $R_s(Y)$ (left: $1/R_s\ll \Lambda$, right: $R_s$ near $\Lambda$) are split up into the contribution without the energy conservation correction, labeled $[\text{R.H.S.}]_{\text{rc}}$ (it contains only the running coupling corrections) and the energy conservation correction $\frac{d}{dY}[\text{R.H.S.}]_{\text{rc}}$. In the scaling regime, the the energy conservation correction is subleading. Away from the scaling regime (exemplified by a Gaussian correlator shape at the same correlation length) the energy conservation correction dominates.