Saturation and BFKL dynamics in the HERA data at small x

Abstract

We show that the HERA data for the inclusive structure function F_2(x,Q^2) for x < 0.01 and 0.045 < Q^2 < 45 GeV^2 can be well described within the color dipole picture, with a simple analytic expression for the dipole-proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x_0 of x at which the saturation scale Q_s equals 1GeV, and the logarithmic derivative of the saturation momentum λ. The value of λextracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.

Figures (3)

• Figure 1: The $F_2$ structure function in bins of $Q^2$ for small (upper part) and moderate (lower part) values of $Q^2$. The experimental points are the latest published data from the H1 and ZEUS collaborations New_HERA. (The H1 data have been rescaled by a factor $1.05$ which is within the normalization uncertainty.) The few data points at the lowest available $Q^2$ (0.045, 0.065 and $0.085 \hbox{GeV}^2$) are not displayed although they are included in the fit. The full line shows the result of the CGC fit with ${\mathcal{N}}_0=0.7$ to the ZEUS data for $x\leq 10^{-2}$ and $Q^2\leq 45\ \hbox{GeV}^2$. The dashed line shows the predictions of the pure BFKL part of the fit (no saturation).
• Figure 2: The same as in Fig. 1, but for large $Q^2$. Note that in the bins with $Q^2\ge 60 \,{\rm GeV}^2$, the CGC fit is extrapolated outside the range of the fit ($Q^2<50\ \hbox{GeV}^2$ and $x\leq 10^{-2}$), to better emphasize its limitations.
• Figure 3: The dipole amplitude for two values of $x$, compared to the pure scaling functions with "anomalous dimension" $\gamma=\gamma_s=0.63$ and $\gamma=0.84$.