Neutrino cross-sections in the quark-parton model for

2 Neutrino cross-sections in the quark—parton model for 

In Chapters 15 and 16 we developed the theory of deep inelastic scattering from a very general point of view, using the general structure of the cross-section in terms of the three scaling functions Fj x). FVom their experimental behaviour we were led to the quark-parton picture in which a virtual photon, or emitted at the lepton vertex interacts with a quark or antiquark in the target hadron. At the level of the simple 

Once we assume that we are dealing with lepton scattering on point-like spin-half objects, we expect, on the basis of our results for ue — i/e and ue — ue [see Section 5.1 and (5.1.26 and 29)] to find that our angular distribution is a sum of two terms, with the characteristic structure of the scattering off left-handed and right-handed objects. So for neutrino reactions we expect 1 from uL — uL and (1 — from i R — i/R and vice versa for antineutrino reactions. [For electromagnetic reactions we would expect 1 -I- (1 - y) .  

We now substitute the various formulae for the Fj x) (16.4.26-30) into the cross-section expressions (15.5.7), and ignoring the term xym /s, obtain for CC reactions initiated hy u or u -. 

We see that for y large, y 1, the x dependence in neutrino and antineutrino reactions determines the quark and antiquark distribution respectively. 

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