Effects of self-organized criticality in small−xB deep-inelastic scattering

It is pointed out that self-organized criticality (SOC) in systems of soft gluons manifest itself not only in large-rapidity gap (LRG) events, but also in normal events in small-xB deep-inelastic lepton-nucleon scattering processes. It is suggested that the following empirical facts are direct consequences of SOC in systems of interacting soft gluons which dominate the small-xB region: The structure function F2(xB , Q 2) can be well described by the Haidt-plot, which implies in particular that (a) F2(xB , Q 2) increases like log (1/xB) for decreasing xB at fixed Q 2. (b) F2(xB , Q 2) increases like logQ2 for increasing Q2 at fixed xB . Deep inelastic lepton-nucleon scattering utilizing electron, muon, and neutrino beams is an extremely useful tool in studying the structure of matter and its interactions. Since the operation of HERA, the first electron-proton collider, the kinematical region of such experiments has been significantly extended. In terms of the difference (q) between the initial and the final four-momenta (k and k) of the electron, and the four momentum (p) of the proton, the kinematical region in which data are now available is: 0 ≤ Q ≤ 9 · 10GeV and 10 ≤ xB ≤ 1, where Q 2 ≡ −q, and xB ≡ −q /(2pq). Physics of deep-inelastic lepton-nucleon scattering (DIS) in the “small-xB region (xB ≤ 10, say)” for sufficiently large Q-values plays a very special role. In fact, “Small-xB