Parton Reggeization Approach (PRA) is a generalized scheme of kT-factorization which uses the formalism of Reggeized gluons and quarks to define gauge-invariant hard-scattering matrix elements with off-shell partons in the initial state (See Ref. [1] for more detailed discussion). The calculations in PRA are performed in the framework of Lipatov's gauge invariant effective theory for Multi-Regge processes in QCD. LO calculations in PRA combine this matrix elements with unintegrated PDFs, defined by the Kimber-Martin-Ryskin (KMR) formula, which resums leading doubly-logarithmic corrections ~log^2(t/mu^2), where t is the virtuality of the parton and mu^2 is the hard scale.

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The aim of PRA is to improve order-by-order stability of the predictions for multi-scale observables which are sensitive to the radiation of additional hard partons, such as azimuthal decorrelations of pairs of jets and vector bosons or mesons, containing heavy quarks or polarization observables in the Drell-Yan process. Some of these observables can be successfully described already in the LO of PRA, while in the conventional Collinear Parton Model (CPM), the NLO and even NNLO corrections to this observables are found to be significant. See Refs. [1-4] for examples.
The calculation of real and virtual NLO corrections in PRA significantly differs form the similar calculations in CPM. The discussion of real corrections has ben started in [5]. In the Lipatov's theory, one encounters the new type of divergences of loop integrals -- so called rapidity divergences, which are related with Reggeization of the parton in the t-channel. See Ref. [6] and references therein for the initial discussion of rapidity divergences in PRA.
New results to be presented in this talk include: the self-consistent implementation of regularization of rapidity divergences by tilting the Wilson lines in the Lipatov's effective action off the light cone, general classification of one-loop integrals with logarithmic rapidity divergences and some new results for the specific integrals. In particular, the 3 point functions with two scales of virtuality and one or two light-cone propagators will be discussed.
References:
[1] A. V. Karpishkov, M. A. Nefedov and V. A. Saleev,``$B{\bar B}$ angular correlations at the LHC in parton Reggeization approach merged with higher-order matrix elements,'' Phys. Rev. D96, no. 9, 096019 (2017) [arXiv:1707.04068 [hep-ph]].
[2] M. Nefedov and V. Saleev, "Diphoton production at the Tevatron and the LHC in the NLO* approximation of the parton Reggeization approach", Phys. Rev. D 92, no. 9, 094033 (2015) [arXiv:1505.01718 [hep-ph]].
[3] M.A.Nefedov, V.A.Saleev and A.V.Shipilova, "Dijet azimuthal decorrelations at the LHC in the parton Reggeization approach", Phys. Rev. D 87, no. 9, 094030 (2013) [arXiv:1304.3549 [hep-ph]].
[4] M.A.Nefedov, N.N.Nikolaev and V.A.Saleev, "Drell-Yan lepton pair production at high energies in the Parton Reggeization Approach", Phys. Rev. D 87, no. 1, 014022 (2013) [arXiv:1211.5539 [hep-ph]].
[5] M. Nefedov and V. Saleev, ``DIS structure functions in the NLO approximation of the Parton Reggeization Approach,'' EPJ Web Conf. 158, 03011 (2017) [arXiv:1709.06378 [hep-ph]].
[6] M. Nefedov and V. Saleev, ``On the one-loop calculations with Reggeized quarks,'' Mod. Phys. Lett. A 32, no. 40, 1750207 (2017) [arXiv:1709.06246 [hep-th]].
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