Ridge effect, azimuthal correlations, and other novel features of gluonic string collisions in high energy photon-mediated reactions

One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two “ridges”, opposite in azimuthal angle $\varphi$, with approximately flat rapidity distributions. This phenomenon can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper, we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic tube string collisions in the context of two examples: electron-proton scattering at a future electron-ion collider or the peripheral scattering of protons accessible at the LHC. A striking prediction of our analysis is that the azimuthal angle of the produced ridges will be correlated with the scattering plane of the electron or proton producing the virtual photon. In the case of $ep\to eX$, the final state $X$ is expected to exhibit maximal multiplicity when the elliptic flow in $X$ is aligned with the electron scattering plane. In the $pp\to ppX$ example, the multiplicity and elliptic flow in $X$ are estimated to exhibit correlated oscillations as functions of the azimuthal angle $\mathrm{\Phi }$ between the proton scattering planes. In the minimum-bias event samples, the amplitude of oscillations is expected to be on the order of 2% to 4% of the mean values. In the events with highest multiplicity, the oscillations can be three times larger than in the minimum-bias event samples.