Understanding nonperturbative deep-inelastic scattering: Instanton-induced inelastic dipole-dipole cross section

We derive the semiclassical (instanton-induced) contribution to the inelastic cross section of two color dipoles at large [Formula Presented] We study its dependence on the dipole sizes, orientations, and most importantly the impact parameter. The inelastic cross section is approximately quadratic in the dipole sizes and Gaussian like in the impact parameter with a width of the order of the instanton size. These results are directly relevant to double DIS [Formula Presented] as well as [Formula Presented] and standard DIS [Formula Presented] at small x when a real photon and a hadron can be approximated by a dipole. For such cases, with one small dipole scattering on a large dipole, the impact parameter profile exhibits a width of about 1/2 fm, which is in good agreement with the impact parameter profile recently extracted from DIS DESY HERA data, including diffractive [Formula Presented]