Toward the global fit of the TMD gluon density in the proton from the LHC data

Abstract

We propose a new analytical expression for the transverse-momentum-dependent (TMD, or unintegrated) gluon density in the proton. Essential phenomenological parameters are extracted from the LHC data on inclusive hadron production in $pp$ collisions at low transverse momenta ${p}_{T}\ensuremath{\le}1\text{ }\text{ }\mathrm{GeV}$. The latter are described in the framework of a modified soft quark-gluon string model, where the gluonic state and nonzero transverse momentum of partons inside the proton are taken into account. To determine the parameters important at moderate and large $x$, we use the measurements of inclusive $b$-jet and Higgs boson production at the LHC as well as the latest HERA data on proton structure functions ${F}_{2}^{c}(x,{Q}^{2})$ and ${F}_{2}^{b}(x,{Q}^{2})$ and reduced cross sections ${\ensuremath{\sigma}}_{\mathrm{red}}^{c}(x,{Q}^{2})$ and ${\ensuremath{\sigma}}_{\mathrm{red}}^{b}(x,{Q}^{2})$. The Catani-Ciafaloni-Fiorani-Marchesini evolution equation is applied to extend the initial gluon distribution to the whole kinematical region. We achieve a simultaneous description of all considered processes with ${\ensuremath{\chi}}^{2}/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.2$, thus moving toward the global fit of the TMD gluon density from collider data. The obtained TMD gluon distribution in a proton is available for public usage and implemented in the tmdlib package and Monte Carlo event generator pegasus.