We calculate the one-loop corrections to dihadron production in Deep Inelastic Scattering (DIS) at small x using the Color Glass Condensate formalism. We show that all UV and soft singularities cancel while the collinear divergences are absorbed into quark and anti quark-hadron fragmentation functions. Rapidity divergences lead to JIMWLK evolution of dipoles and quadrupoles describing multiple-scatterings of the quark anti-quark dipole on the target proton/nucleus. The resulting cross section is finite and can be used for phenomenological studies of dihadron angular correlations at small x in a future Electron-Ion Collider (EIC).

The goal of this white paper is to give a comprehensive overview of the rich field of forward physics. We discuss the occurrences of BFKL resummation effects in special final states, such as Mueller-Navelet jets, jet gap jets, and heavy quarkonium production.It further addresses TMD factorization at low x and the manifestation of a semi-hard saturation scale in (generalized) TMD PDFs. More theoretical aspects of low x physics, probes of the quark gluon plasma, as well as the possibility to use photon-hadron collisions at the LHC to constrain hadronic structure at low x, and the resulting complementarity between LHC and the EIC are also presented. We also briefly discuss diffraction at colliders as well as the possibility to explore further the electroweak theory in central exclusive events using the LHC as a photon-photon collider. CONTENTS I. Introduction II. Manifestations of BFKL evolution A. Mueller-Navelet jets B. Toward precision studies of BFKL dynamics C. Unintegrated gluon distribution (UGD) D. BFKL resummation of NLO collinear factorization: Heavy quarkonium production E. Diffraction: Gaps between jets III. Hadronic Structure at low x and gluon saturation A. Color Glass Condensate and high gluon densities B. Transverse Momentum Dependent Parton Distribution Functions C. Complementarity between EIC and LHC D. Forward dijets: from LHC to EIC E. Color Glass Condensate beyond high energy factorization IV. Imprints of high gluon densities at low x at the LHC. A. Open QCD questions at a hadron-hadron collider: Parton fragmentation, mini-jets and their interplay with high parton densities B. Forward direct photon measurements 27 C. Top quark pair production as a tool to probe Quark-Gluon -Plasma formation 29 V. Ultra-peripheral collisions at hadronic colliders and exclusive reactions at the EIC 31 A. Existing measurements on diffractive vector meson photoproduction in UPCs 31 B. Future measurements on diffractive vector meson photoproduction in UPCs 33 C. The ratio of Ψ(2s) and J/Ψ photoproduction cross-sections as a tool to quantify non-linear QCD evolution 34 D. Planned measurements at the Electron Ion Collider 36 VI. Odderon discovery and diffractive jets 38 A. Soft diffraction and the Odderon discovery by the D0 and TOTEM experiments 38 B. Inclusive diffraction measurements at the LHC and sensitivity to the Pomeron structure 39 VII. Electroweak and Beyond the Standard Model Physics 41 A. Precision Proton Spectrometer (PPS) and ATLAS Forward Proton detector (AFP) at high luminosity 41 B. Non-elastic contribution in photon-photon physics 44 C. Exclusive production of Higgs boson 47 D. Anomalous quartic couplings with proton tagging 49 VIII. Conclusions 53 Acknowledgements 54 References 55

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We calculate the next to leading order corrections to dihadron production in Deep Inelastic Scattering (DIS) at small x using the Color Glass Condensate formalism for the case when the virtual photon is transverse polarized. Similar to the case of longitudinal photon exchange all UV and soft singularities cancel while the collinear divergences are absorbed into quark and antiquarkhadron fragmentation functions. Rapidity divergences lead to JIMWLK evolution of dipoles and quadrupoles which describe multiple-scatterings of the quark antiquark dipole on the target proton/nucleus and contain all the QCD dynamics of the target leading to a finite final result for the dihadron production cross section.

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