Collinearly-improved BK evolution meets the HERA data

TL;DR

The paper tests a collinearly-improved BK evolution, which resums large double and single collinear logarithms, against HERA small-x DIS data. By including running-coupling effects and DGLAP-like single-log corrections, the authors produce a stable, improved evolution equation (collinearly-improved BK) and perform fits to the HERA reduced cross-section using GBW and rcMV initial conditions. They find good qualitative and quantitative agreement (χ^2 ~ 1.1–1.2) with rcMV initial conditions and particular RC prescriptions, and show that the approach yields a reliable description up to Q^2 ≈ 400 GeV^2 while remaining competitive for saturation physics. The work demonstrates the phenomenological viability of resummed high-energy QCD evolution and sets the stage for future full-NLO fits and matching to DGLAP at large Q^2.

Abstract

In a previous publication, we have established a collinearly-improved version of the Balitsky-Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD coupling. The equation thus obtained includes all the next-to-leading order corrections to the BK equation which are enhanced by (single or double) collinear logarithms. We then use numerical solutions to this equation to fit the HERA data for the electron-proton reduced cross-section at small Bjorken x. We obtain good quality fits for physically acceptable initial conditions. Our best fit, which shows a good stability up to virtualities as large as Q^2=400 GeV^2 for the exchanged photon, uses as an initial condition the running-coupling version of the McLerran-Venugopalan model, with the QCD coupling running according to the smallest dipole prescription.

Figures (3)

• Figure 1: Running coupling for various schemes and configurations. (a) As a function of the daughter dipole size $|\bm{x}-\bm{z}|$, with $\phi=0$ the angle between the parent dipole $\bm{x}-\bm{y}$ and the daughter one $\bm{x}-\bm{z}$. (b) The same with $\phi = \pi/6$. (c) As a function of the angle $\phi$ for fixed daughter dipole size $|\bm{x}-\bm{z}|=1.5$. Black (continuous): The minimal dipole scheme as defined in Eq. \ref{['amin']}. Red (dashed): The "fac" scheme as given in Eq. \ref{['azero']}. Blue (dotted): The Balitsky scheme Balitsky:2006wa. In all cases the parent dipole size is $|\bm{x}-\bm{y}|=1$, the coupling is smoothly frozen at the value 0.7 and $\Lambda_{\rm QCD} = 0.2$.
• Figure 2: Description of the HERA data obtained by the fits using the rcMV initial condition. Each box corresponds to a given value of $Q^2$ as indicated (in GeV$^2$) in the top-right corner. For each fit we plot the ratio of the prediction to the central experimental value. The (green) band represents the experimental uncertainty.
• Figure 3: Left: value of the saturation momentum, defined for each rapidity as $2/r_s(Y)$ with $T(r_s(Y), Y)=1/2$. For comparison, we have overlaid the experimental data points from the HERA dataset. Right: plot of the corresponding initial conditions for the rapidity evolution.