Probing the high-energy dynamics of QCD: selected theoretical and phenomenological studies

The center-of-mass energies available at modern accelerators, such as the Large Hadron Collider (LHC), and at forthcoming generation accelerators, such as the Electron-Ion Collider (EIC), offer us a unique opportunity to investigate hadronic matter under the most extreme conditions ever reached. In particular, we can access the Regge-Gribov regime of QCD, described by the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach along with its non-linear generalizations (the set of B-JIMWLK equations). The aim of these approaches is to resum large-energy logarithmic corrections which spoil the convergence of perturbative series at high-energy. The aforementioned approaches are theoretically developed both in the leading (LL) and the next-to-leading (NLL) approximation, but precise full NLL predictions still remains an open challenge. Furthermore, extending BFKL beyond the NLL approximation has been an open problem for more than twenty years. We face the task of hunting precision in this field from different perspectives. In particular, within the BFKL approach, we calculate the next-to-leading order (NLO) impact factor for the Higgs boson production. This is the necessary ingredient to study the inclusive forward emissions of a Higgs boson in association with a backward identified jet. Moreover, by using already known NLO impact factors, we propose a series of new semi-hard reactions that can be used to investigate BFKL dynamics at the LHC within NLL accuracy. We consider also the problem of extending BFKL beyond the NLL approximation and compute one of the ingredients entering the BFKL kernel at the next-to-NLL (NNLL) accuracy. Finally, in the saturation (non-linear) framework, we calculate the diffractive double hadron photo- or electroproduction cross sections with full NLL accuracy, useful to detect saturation effects, at both the future EIC or already at LHC (via Ultra Peripheral Collisions).