TMD parton shower effects in associated $\gamma$ + jet production at LHC

We investigate associated prompt photon and hadronic jet production at the LHC energies using the $k_T$-factorization approach. Our consideration is based on the $\mathcal O(\alpha\alpha_s^2)$ off-shell gluon-gluon fusion subprocess $g^*g^*\to \gamma q\bar q$ and several subleading quark-initiated contributions from $\mathcal O(\alpha\alpha_s)$ and $\mathcal O(\alpha\alpha_s^2)$ subprocesses, taken into account in the conventional (collinear) QCD factorization. The transverse momentum dependent (or unintegrated) gluon densities in a proton are derived from Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation. We achieve reasonably good agreement with the experimental data taken by CMS and ATLAS Collaborations and demonstrate the importance of initial state parton showers for jet determination in the $k_T$-factorization approach.