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

Abstract

The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections ${\sigma }_T^{{\gamma }^{\ast }}$ and ${\sigma }_L^{{\gamma }^{\ast }}$) 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 ${\sigma }_T^{{\gamma }^{\ast }}$ and ${\sigma }_L^{{\gamma }^{\ast }}$ is discussed.

arXiv comment37 pages, 1 figure

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