Transverse momentum dependent splitting functions at work: quark-to-gluon splitting

Using the recently obtained Pgq splitting function we extend the low x evolution equation for gluons to account for contributions originating from quark-to-gluon splitting. In order to write down a consistent equation we resum virtual corrections coming from the gluon channel and demonstrate that this implies a suitable regularization of the Pgq singularity, corresponding to a soft emitted quark. We also note that the obtained equation is in a straightforward manner generalized to a nonlinear evolution equation which takes into account effects due to the presence of high gluon densities.Comment: 13 pages, 3 figures, published versio

Scattering amplitudes with off-shell quarks

We present a prescription to calculate manifestly gauge invariant tree-level scattering amplitudes for arbitrary scattering processes with off-shell initial-state quarks within the kinematics of high-energy scattering.Comment: 17 pages, references added, calculation included to indicate equivalence with effective action approac

TMD splitting functions in kT factorization: the real contribution to the gluon-to-gluon splitting

We calculate the transverse momentum dependent gluon-to-gluon splitting function within $k_T$-factorization, generalizing the framework employed in the calculation of the quark splitting functions in [1-3] and demonstrate at the same time the consistency of the extended formalism with previous results. While existing versions of $k_T$ factorized evolution equations contain already a gluon-to-gluon splitting function i.e. the leading order Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel or the Ciafaloni-Catani-Fiore-Marchesini (CCFM) kernel, the obtained splitting function has the important property that it reduces both to the leading order BFKL kernel in the high energy limit, to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) gluon-to-gluon splitting function in the collinear limit as well as to the CCFM kernel in the soft limit. At the same time we demonstrate that this splitting kernel can be obtained from a direct calculation of the QCD Feynman diagrams, based on a combined implementation of the Curci-Furmanski-Petronzio formalism for the calculation of the collinear splitting functions and the framework of high energy factorization.Comment: 29 pages, 5 figures, published versio

Z boson production in proton-lead collisions at the LHC accounting for transverse momenta of initial partons

We perform a calculation of inclusive $Z$ boson production in proton-lead collisions at the LHC taking into account the transverse momenta of the initial partons. We use the framework of $k_T$-factorization combining transverse momentum dependent parton distributions (TMDs) with off-shell matrix elements. In order to do it we need to construct appropriate TMDs for lead nuclei which is done using the parton branching method. Our computations are compared with data from CMS taken at $\sqrt{s}=5.02$ TeV. The results are in good agreement with the measurements especially the transverse momentum distribution of the $Z$ boson.Comment: 17 pages, 12 figure

Unintegrated gluon distribution from modified BK equation

We investigate the recently proposed nonlinear equation for the unintegrated gluon distribution function which includes the subleading effects at small $x$. We obtained numerically the solution to this equation in $(x,k)$ space, and also the integrated gluon density. The subleading effects affect strongly the normalization and the $x$ and $k$ dependence of the gluon distribution. We show that the saturation scale $Q_s(x)$, which is obtained from this model, is consistent with the one used in the saturation model by Golec-Biernat and W\"usthoff. We also estimate the nonlinear effects by looking at the relative normalization of the solutions to the linear and nonlinear equations. It turns out that the differences are quite large even in the nominally dilute regime, that is when $Q^2 \gg Q_s^2$. Finally, we calculate the dipole-nucleon cross section.Comment: Comparison with unmodified BK included. To be published in EPJ