QCD traveling waves phenomenology revisited

In this paper, we review and update the Amaral-Gay Ducati-Betemps-Soyez saturation model, by testing it against the recent H1-ZEUS combined data on deep inelastic scattering, including heavy quarks in the dipole amplitude. We obtain that this model, which is based on traveling wave solutions of the Balitsky-Kovchegov equation and built in the momentum space framework, yields very accurate descriptions of the reduced cross section, ${\sigma }_r(x,y,Q^2)$, as well as DIS structure functions such as $F_2(x,Q^2)$ and $F_L(x,Q^2)$, all measured at HERA. Additionally, it provides good descriptions of heavy quark structure functions, $F_2^{cc}$ and $F_2^{bb}$ at small-$x$ and $Q^2\lesssim 60{\mathrm{GeV}}^2$. We also use the improved model to make predictions for structure functions to be measured in the near future at LHeC.

Figure 1

Red circles: H1-ZEUS $e^{\pm }p$ combined $F_2(x,Q^2)$ data in the range $x\le 0.01$ and $0.045{\mathrm{GeV}}^2\le Q^2\le 150{\mathrm{GeV}}^2$ [35]. $F_2$ uncertainties are estimated, considering $\delta F_2\approx \delta {\sigma }_r$. Curves: black solid and blue dashed curves are the predictions of variants $V_1{B}_2$ and $V_3{B}_2$, following from fits to ${\sigma }_r(x,y,Q^2)$ including heavy quarks and only with light ones. Fit parameters of these curves are given in Table 3.

Figure 2

Charm structure function, $F_2^{cc}(x,Q^2)$, estimates from HERA in the range $2.5{\mathrm{GeV}}^2\le Q^2\le 120{\mathrm{GeV}}^2$ [45], assuming $F_2^{cc}\approx {\sigma }_r^{cc}$. Predictions of variants $V_3{B}_1$ and $V_3{B}_2$ are given by blue dashed and black solid curves, respectively.

Figure 3

Bottom structure function, $F_2^{bb}(x,Q^2)$, estimates from HERA in the range $2.5{\mathrm{GeV}}^2\le Q^2\le 120{\mathrm{GeV}}^2$ [45], assuming $F_2^{bb}\approx {\sigma }_r^{bb}$. Predictions of variants $V_3{B}_1$ and $V_3{B}_2$ are given by blue dashed and black solid curves, respectively.

Figure 4

Longitudinal structure function, $F_L(x,Q^2)$, from HERA in the range $1.5{\mathrm{GeV}}^2\le Q^2\le 120{\mathrm{GeV}}^2$ [46] Predictions of variants $V_3{B}_1$ and $V_3{B}_2$ are given by blue dashed and black solid curves, respectively.

Figure 5

$F_2(x,Q^2)$ and $F_L(x,Q^2)$ predictions at LHeC for $Q^2=10{\mathrm{GeV}}^2$ and ${10}^{-6}\le x\le {10}^{-2}$. Pseudodata within this kinematic window was extracted from predictions of the Monte Carlo RAPGAP in Fig. 4.13 of Ref. [47].

Figure 6

$F_2^{cc}$ and $F_2^{bb}$ predictions (model $V_3{B}_2$) at LHeC, in the range ${10}^{-6}\le x\le {10}^{-2}$ and $2.0{\mathrm{GeV}}^2\le Q^2\le 200{\mathrm{GeV}}^2$ alongside pseudodata extracted from the Monte Carlo RAPGAP (Figs. 3.23 and 3.24 of Ref. [47]).