Precision QCD, Hadronic Structure & Forward QCD, Heavy Ions: Report of Energy Frontier Topical Groups 5, 6, 7 submitted to Snowmass 2021

This report was prepared on behalf of three Energy Frontier Topical Groups of the Snowmass 2021 Community Planning Exercise. It summarizes the status and implications of studies of strong interactions in high-energy experiments and QCD theory. We emphasize the rich landscape and broad impact of these studies in the decade ahead. Hadronic interactions play a central role in the high-luminosity Large Hadron Collider (LHC) physics program, and strong synergies exist between the (HL-)LHC and planned or proposed experiments at the U.S. Electron-Ion Collider, CERN forward physics experiments, high-intensity facilities, and future TeV-range lepton and hadron colliders. Prospects for precision determinations of the strong coupling and a variety of nonperturbative distribution and fragmentation functions are examined. We also review the potential of envisioned tests of new dynamical regimes of QCD in high-energy and high-density scattering processes with nucleon, ion, and photon initial states. The important role of the high-energy heavy-ion program in studies of nuclear structure and the nuclear medium, and its connections with QCD involving nucleons are summarized. We address ongoing and future theoretical advancements in multi-loop QCD computations, lattice QCD, jet substructure, and event generators. Cross-cutting connections between experimental measurements, theoretical predictions, large-scale data analysis, and high-performance computing are emphasized.