Dipole factorization for DIS at NLO: Loop correction to the ${\gamma }_{T,L}^{*}\to q\overline{q}$ light-front wave functions

The one-loop QCD corrections to the light-front wave function for the quark-antiquark Fock state inside a transverse or longitudinal off-shell photon are explicitly calculated, both in full momentum space and in mixed space (also known as dipole space). These results provide one of the main contributions to virtual next-to-leading-order (NLO) corrections to many deep inelastic scattering (DIS) observables (inclusive or not) in the dipole factorization formalism at low Bjorken $x$. In a follow-up article, these one-loop corrections are combined with earlier results on the wave function for the quark-antiquark-gluon Fock state, in order to get the full set of NLO corrections to the DIS structure functions $F_2$ and $F_L$ in the dipole factorization formalism, valid at low Bjorken $x$.

Figure 1

Tree-level contribution to the $q\overline{q}$ Fock component inside an incoming transverse photon.

Figure 2

Left: LFWF (at a given order in perturbation theory) for a Fock state $\mathcal{F}$ inside a physical incoming state $i$. A quark is singled out from the Fock state $\mathcal{F}$, as $\mathcal{F}=q_0+\widehat{\mathcal{F}}$. Right: One-loop quark self-energy diagram correcting the contribution shown on the left.

Figure 3

One-gluon-loop diagrams contributing to the light-front wave function of the $q\overline{q}$ Fock component inside an incoming transverse photon.