Self-Similarity, Current Commutators, and Vector Dominance in Deep Inelastic Lepton-Hadron Interactions

Constraints given by the atmospheric neutrino-induced muon flux on the neutrinonucleon interactions at high energies

“…Similar bounds were found by BJOI~XEN [20] using the locality of the Iepton current [22]. Especially, if the constituents of the nucleon have spin 1/2 and the sign of the third structure funetion is negative we obtain k = 0.53 q-0.03 (in agreement with the data of the CERN experiments [19]). It was shown that if the linear rise of the total cross section could be attributed to the scaling behaviour of the structure functions, then at a confidence level of more than 99% the slope of the linear rise had to be less than 0.8 (a = cE X 10 -3s cm 2 GeV-1).…”

“…The cross section for this process is determined by a second rank Lorentz tensor as follows where y = v/ME. Assuming that the "scale invariance" found in the SLAC-MIT experiments [16] for the structure functions of the deep-inelastic electroproduction (20 GeV 2 > Q2 > 1 GeV 2, v/M < 12 GeV) can be extended for the invariant functions of the process (17), we obtain that as Q2 __~ co at fixed to (BJORKE~ limit or automodelity [17], [19])the Gi functions approach a finite nonzero value at all values of to lim G~(to, Q2) = Fi(to) (…”

“…where N(v + ~, E, 19) is the intensity of the atmospheric r~ and ~, at horizontal angle O (measured to the vertical), dcrA/dE~, is the differential cross section per nucleus for the reaction v~,+Z-+lz + anything, 3) (--dE~,/dx) is the average energy loss of muons in the rock, s is the threshold energy for detection, NA is Avogadro's number, A is the number of nucleons in the nucleus. If we assume 1) If we know the effeetive range-energy relations of muons for a rock, then the depth can be labelled by the energy which corresponds to the effective range equal to the depth.…”

“…The theoretical developments concerning the deep-inelastic leptonnucleon scattering stimulated by the SLAC-MIT experiments [16,17,18,19], however, called for the revision of these analyses.…”

“…We use the Cabibbo current 4) J~, (x) = (V~(x) + A~(x) ~s=~ cos 0 c + (V~(x) + A~(x)) zs=l sin 0 c (19). Assuming P, T, PT and Lorentz invariance, W ~/~ can be expanded in terms of"" ~tV five invariant functions: 1 W~/~(p, q) = --g~,W7/~(q 2, r) + ~ 91 (q2, v) ----ie~'"~~q~pe W~/~(q 2, v) + %q" W~/~(q 2, v) -?…”