Dipole factorization for DIS at NLO: Combining the $q\bar{q}$ and $q\bar{q}g$ contributions

TL;DR

This paper extends dipole factorization to NLO for DIS structure functions at low x, explicitly calculating both $q\bar{q}$ and $q\bar{q}g$ contributions, demonstrating divergence cancellation, and discussing high-energy logarithm resummation.

Contribution

It provides the first direct calculation of both $q\bar{q}$ and $q\bar{q}g$ contributions at NLO in dipole factorization for DIS, including divergence cancellation and resummation insights.

Findings

Both $q\bar{q}$ and $q\bar{q}g$ contributions calculated at NLO.

UV divergences cancel between $q\bar{q}$ and $q\bar{q}g$ contributions.

Resummation of high-energy logarithms discussed.

Abstract

The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections $\sigma^{\gamma^*}_{T}$ and $\sigma^{\gamma^*}_{L}$) at low $x_{Bj}$ are obtained, as a generalization of the dipole factorization formula. For the first time, the contributions of both the $q\bar{q}$ and the $q\bar{q}g$ Fock states in the photon are directly calculated, using earlier results for the $q\bar{q}$ light-front wave-functions at one loop inside a dressed virtual photon. Both the $q\bar{q}$ and the $q\bar{q}g$ contributions have UV divergences, which are shown to cancel each other, using conventional dimensional regularization as UV regulator. Finally, the resummation of high-energy logarithms on top of the NLO results for $\sigma^{\gamma^*}_{T}$ and $\sigma^{\gamma^*}_{L}$ is discussed.