Abstract
Transverse momentum dependent (TMD) parton distributions in a proton are important in high energy physics from both theoretical and phenomenological points of view. Using the latest RHIC and LHC data on the inclusive soft hadron production in $pp$ and $AA$ collisions at small transverse momenta, we determine the parameters of the initial TMD gluon density, derived in the framework of quark-gluon string model at the low scale $\mu_0 \sim 1 - 2$ GeV and refine its large-$x$ behaviour using the LHC data on the $t \bar t$ production at $\sqrt s = 13$ TeV. Then, we apply the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation to extend the obtained TMD gluon density to the whole kinematical region. In addition, the complementary TMD valence and sea quark distributions are generated. The latter are evaluated in the approximation where the gluon-to-quark splitting occurs at the last evolution step using the TMD gluon-to-quark splitting function. Several phenomenological applications of the proposed TMD quark and gluon densities to the LHC processes are discussed.
Highlights
In recent years, an understanding has been obtained that a theoretical description of a number of processes at high energies and large momentum transfer containing multiple hard scales requires unintegrated, or transverse momentum dependent (TMD) parton density functions [1], which encode nonperturbative information on a proton structure, including transverse momentum and polarization degrees of freedom
The Transverse momentum dependent (TMD) parton densities are related to the physical cross sections and other observables measured in the collider experiments via TMD factorization theorems in quantum chromodynamics (QCD)
The factorization theorems provide the necessary framework to separate hard partonic physics described with a perturbative QCD expansion from soft hadronic physics and allow one to determine the TMD parton distributions from collider data
Summary
An understanding has been obtained that a theoretical description of a number of processes at high energies and large momentum transfer containing multiple hard scales requires unintegrated, or transverse momentum dependent (TMD) parton density functions [1], which encode nonperturbative information on a proton structure, including transverse momentum and polarization degrees of freedom. In the high-energy factorization, the production cross sections at low transverse momenta are governed by the nonperturbative input to the TMD parton density functions The latter being used as an initial condition for the subsequent QCD evolution could play an important role in phenomenological applications [5,6,7,8]. The TMD quark and gluon densities in a proton were determined [14] from fits to precision measurements of deep inelastic scattering cross sections at HERA and evolved by the Dokshitzer-Gribov-Lipatov-AltarelliParisi (DGLAP) evolution [15] with NLO splitting functions using the parton branching method [16,17].
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