Speaker
Description
In recent years, numerous studies have aimed at improving the precision of the theoretical description of the nonlinear QCD regime of gluon saturation in high-energy collisions, in order to match the precision of the data coming from the LHC and the future EIC. In particular, NLO QCD corrections have been calculated for many high-energy processes sensitive to gluon saturation.
In most of such NLO calculations, the chosen regularization procedure is dimensional regularization for the transverse integrals complemented by a naive cut-off for the light-cone momentum k^+ integrals. Although convenient in that context, this regularization procedure has disadvantages. On the one hand, it does not allow us to disentangle soft and rapidity divergences, which are then both regulated by the cut-off. On the other hand, it complicates the comparison with results obtained in other formalisms for QCD valid in different kinematical regimes, for example collinear or TMD factorizations, which typically use other regularization schemes.
As an alternative, we discuss how to implement in these NLO gluon saturation calculations various rapidity regulators similar to the ones used by the TMD or SCET communities. As a first application and consistency check, we revisit the calculation of the NLO corrections to the DIS structure function at low x in the dipole factorization approach, now with these rapidity regulators together with dimensional regularization. When combining the results from all diagrams, we find as expected that the UV divergences are canceling each other, as well as the soft divergences. The only surviving divergence is the rapidity divergence associated with the Balitsky-Kovchegov evolution of the dipole operator.
Among the finite NLO corrections to the structure functions, the ones which are found to depend on the rapidity regularization scheme are compatible with the expected scheme dependence concerning the choice of evolution variable for the BK equation. This suggests that choosing one of the three rapidity regulators we propose amounts to choosing the precise evolution variable in the definition of the low x evolution: light-cone momentum k^+ or k^- or rapidity.
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