Dipole factorization for DIS at NLO I: Loop correction to the photon to quark-antiquark 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 (a.k.a. dipole space). These results provide one of the main contributions to virtual NLO corrections to many 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.