Deep inelastic scattering in the dipole picture at next-to-leading order

We study quantitatively the importance of the recently derived next-to-leading-order corrections to the deep inelastic scattering structure functions at small $x$ in the dipole formalism. We show that these corrections can be significant and depend on the factorization scheme used to resum large logarithms of energy into renormalization group evolution with the Balitsky-Kovchegov equation. This feature is similar to what has recently been observed for single inclusive forward hadron production. Using a factorization scheme consistent with the one recently proposed for the single inclusive cross section, we show that it is possible to obtain meaningful results for the deep inelastic scattering cross sections.

Figure 1

LO and NLO contributions to $F_L$ (left) and $F_T$ (right) as a function of $Q^2$ at $x_{Bj}={10}^{-3}$ with ${\alpha }_{\mathrm{s}}=0.2$.

Figure 2

LO and NLO contributions to $F_L$ (left) and $F_T$ (right) as a function of $Q^2$ at $x_{Bj}={10}^{-3}$ with ${\alpha }_{\mathrm{s}}=0.2$ and using the $x_{Bj}$-subtraction procedure.

Figure 3

LO and NLO contributions to $F_L$ as a function of $x_{Bj}$ at $Q^2=1{\mathrm{GeV}}^2$ (left) and $Q^2=50{\mathrm{GeV}}^2$ (right) with ${\alpha }_{\mathrm{s}}=0.2$.

Figure 4

LO and NLO contributions to $F_T$ as a function of $x_{Bj}$ at $Q^2=1{\mathrm{GeV}}^2$ (left) and $Q^2=50{\mathrm{GeV}}^2$ (right) with ${\alpha }_{\mathrm{s}}=0.2$.

Figure 5

Left: NLO/leading-order ratio for $F_L$ and $F_T$ as a function of $Q^2$ at $x_{Bj}={10}^{-3}$ with fixed (solid) and running (dashed) coupling. Right: NLO/leading-order ratio for $F_L$ and $F_T$ as a function of $x_{Bj}$ at $Q^2=1{\mathrm{GeV}}^2$ (solid) and $Q^2=50{\mathrm{GeV}}^2$ (dashed) with running coupling.