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Acknowledgments We thank the participants of the FPF meetings and the Snowmass working groups for discussions that have contributed both directly and indirectly to this study. We gratefully acknowledge the invaluable support of the CERN Physics Beyond Colliders study group and the work of CERN technical teams related to civil engineering studies (SCE-DOD), safety discussions (HSE-OHS, HSE-RP, EP-DI-SO), integration (EN-ACE), and discussions on services (EN-CV, EN-EL, EN-AA) and simulations (SY-STI). L. A. Anchordoqui is supported by U.S. National Science Foundation (NSF) Grant PHY-2112527. A. Ariga is supported by JSPS, Japan KAKENHI Grant JP20K23373 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant 101002690). T. Ariga acknowledges support from JSPS, Japan KAKENHI Grant JP19H01909. B. Batell is supported by U.S. Department of Energy (DOE) Grant DE–SC0007914 and by PITT PACC, USA. The work of J. Bramante is supported by NSERC, Canada. F. G. Celiberto acknowledges support from the INFN/NINPHA project, USA and thanks the Università degli Studi di Pavia, Italy for the warm hospitality. G. Chachamis is supported by the Fundação para a Ciência e a Tecnologia (Portugal) under project CERN/FIS-PAR/0024/2019 and contract ‘‘Investigador auxiliar FCT - individual Call, Portugal CEECIND/03216/2017 and acknowledges funding from the European Union’s Horizon 2020 research and innovation programme (Grant 824093). P. B. Denton is supported by DOE, USA Grant DE-SC0012704. Y. Du was supported by National Science Foundation of China (NSFC) Grants 12022514 and 11875003. The work of J. L. Feng is supported in part by NSF, USA Grants PHY- 1915005 and PHY-2111427, Simons Investigator Award, USA #376204, Simons Foundation, USA Grant 623683, and Heising-Simons Foundation, USA Grants 2019-1179 and 2020-1840. The work of M. Fieg, T. B. Smith, and Y.-D. Tsai is supported in part by NSF Grant PHY-1915005. M. Fucilla, M. M. A. Mohammed, and A. Papa acknowledge support from the INFN/QFT@COLLIDERS, Italy project. The work of M. V. Garzelli was supported in part by the Bundesministerium für Bildung und Forschung (BMBF), Germany. V. P. Goncalves was partially financed by the Brazilian funding agencies CNPq, FAPERGS, and INCT-FNA (process number 464898/2014-5). M. Guzzi is supported in part by NSF, USA Grants PHY- 1820818 and PHY-2112025. J. C. Helo acknowledges support from ANID FONDECYT-Chile Grant 1201673 and from ANID Millennium Science Initiative Program ICN2019 044. K. Jodłowski is supported by the National Science Centre, Poland, Grant 2015/18/A/ST2/00748. Ahmed Ismail and R. Mammen Abraham are supported by DOE, USA Grant DE-SC0016013. Ameen Ismail is supported by NSERC, Canada (reference number 557763) and by NSF, USA Grant PHY-2014071. Y. S. Jeong is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT: Ministry of Science and ICT) (2021R1A2C1009296). The work of F. Kling is supported by DOE, USA Grant DE-AC02-76SF00515 and by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy – EXC 2121 Quantum Universe – 390833306. P. Nadolsky is supported by DOE, USA Grant DE-SC0010129. H. Otono acknowledges support from JSPS, Japan KAKENHI Grant JP20H01919. V. Pandey is supported by DOE, USA Grant DE-SC-0009824. M. H. Reno is supported in part by DOE, USA Grant DE-SC-0010113. The work of A. Ritz is supported by NSERC, Canada, Canada. The work of D. Sengupta is supported by NSF, USA Grant PHY-1915147. T. Sjöstrand is supported by Swedish Research Council Grant 2016-05996. D. Soldin acknowledges support from the NSF, USA Grant PHY-1913607. S. Trojanowski is supported by the grant ‘‘AstroCeNT: Particle Astrophysics Science and Technology Centre’’ carried out within the International Research Agendas programme of the Foundation for Polish Science financed by the European Union under the European Regional Development Fund, and by the Polish Ministry of Science and Higher Education through its scholarship for young and outstanding scientists (decision 1190/E-78/STYP/14/2019). K. Xie is supported by DOE, USA Grant DE-FG02-95ER40896, NSF, USA Grant PHY- 1820760, and in part by PITT PACC. Parts of this work have been supported by Fermi Research Alliance, LLC, USA under Contract DE-AC02-07CH11359 with the DOE., The Forward Physics Facility (FPF) is a proposal to create a cavern with the space and infrastructure to support a suite of far-forward experiments at the Large Hadron Collider during the High Luminosity era. Located along the beam collision axis and shielded from the interaction point by at least 100 m of concrete and rock, the FPF will house experiments that will detect particles outside the acceptance of the existing large LHC experiments and will observe rare and exotic processes in an extremely low-background environment. In this work, we summarize the current status of plans for the FPF, including recent progress in civil engineering in identifying promising sites for the FPF and the experiments currently envisioned to realize the FPF's physics potential. We then review the many Standard Model and new physics topics that will be advanced by the FPF, including searches for long-lived particles, probes of dark matter and dark sectors, high-statistics studies of TeV neutrinos of all three flavors, aspects of perturbative and non-perturbative QCD, and high-energy astroparticle physics., ANID FONDECYT-Chile 1201673, Fermi Research Alliance DE-AC02-07CH11359, HSE-OHS, HSE-RP, NINPHA, PITT PACC, SY-STI, National Science Foundation PHY-2112527, U.S. Department of Energy DE–SC0007914, Simons Foundation 376204, 623683, Fuel Cell Technologies Program 824093, DE-SC0012704, Horizon 2020 Framework Programme, First Peoples Fund, Heising-Simons Foundation 2019-1179, 2020-1840, Natural Sciences and Engineering Research Council of Canada, European Commission, European Research Council, Deutsche Forschungsgemeinschaft 390833306, DE-SC-0009824, DE-SC-0010113, DE-SC0010129, JP20H01919, PHY-1915147, Japan Society for the Promotion of Science JP20K23373, National Natural Science Foundation of China 11875003, 12022514, PHY-1915005, PHY-2111427, Fundação para a Ciência e a Tecnologia CERN/FIS-PAR/0024/2019, Bundesministerium für Bildung und Forschung, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Ministry of Science, ICT and Future Planning 2021R1A2C1009296, DE-AC02-76SF00515, National Research Foundation of Korea, Instituto Nazionale di Fisica Nucleare, Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul, Narodowe Centrum Nauki 2015/18/A/ST2/00748, 557763, DE-SC0016013, PHY-2014071, Vetenskapsrådet 2016-05996, PHY-1913607, Ministerstwo Edukacji i Nauki 1190/E-78/STYP/14/2019, DE-FG02-95ER40896, PHY-1820760, Università degli Studi di Pavia, Horizon 2020 101002690, JP19H01909, European Regional Development Fund, Instituto Nacional de Ciência e Tecnologia: Física Nuclear e Aplicações 464898/2014-5, PHY-1820818, PHY-2112025, Agencia Nacional de Investigación y Desarrollo ICN2019 044

We investigate the inclusive emission in unpolarized proton collisions of a charm-flavored hadron in association with a Higgs boson, featuring large transverse momenta and produced with a large rapidity distance. Taking advantage of a narrow timing coincidence between the ATLAS detector and the future FPF ones, we study the behavior of cross sections and azimuthal correlations for ultraforward rapidities of the detected hadron. We provide evidence that the hybrid high-energy and collinear factorization, encoding the BFKL resummation of large energy logarithms and supplemented by collinear densities and fragmentation functions, offers a fair description of this process and comes out as an important tool to deepen our understanding of strong interactions in ultraforward production regimes., 27 pages, 5 figures, version published in Phys. Rev. D

Pursuing the goal to single out the validity region of the high-energy resummation, better known as BFKL approach, and to possibly disentangle BFKL effects from the ones coming from a DGLAP-inspired, fixed-order description, new predictions for the forward inclusive hadron-jet production, tailored on the CMS and CASTOR acceptances, are given., 6 pages, 2 figures; contribution to the proceedings of the XXVII International Workshop on Deep Inelastic Scattering and Related Subjects (DIS2019), Torino, Italy, 8-12 April, 2019; to appear on Proceedings of Science

We suggest the inclusive detection at the LHC of a light charged hadron and of a jet widely separated in rapidity as a new probe channel for the study of the BFKL resummation. Predictions for cross section and azimuthal correlations, shaped on the CMS and CASTOR acceptances, are presented., 6 pages, 2 figures; presented by F.G. Celiberto at "Diffraction and Low-x 2018", Reggio Calabria, Italy, August 26 - September 1, 2018; to be published in the conference proceedings by Acta Phys. Polon. B

The inclusive production at the LHC of a charged light hadron and of a jet, featuring a wide separation in rapidity, is suggested as a new probe process for the investigation of the BFKL mechanism of resummation of energy logarithms in the QCD perturbative series. We present some predictions, tailored on the CMS and CASTOR acceptances, for the cross section averaged over the azimuthal angle between the identified jet and hadron and for azimuthal correlations., Comment: 19 pages, 6 figures; few typos corrected and one reference updated during proof reading; version published on Eur. Phys. J. C. arXiv admin note: text overlap with arXiv:1701.05077