Impulse approximation partons

The essence of the parton model is the assumption that, when a sufficiently high momentum transfer reaction takes place, the projectile, be it a lepton or a parton inside a hadron, sees the target as made up of almost free constituents, and is scattered by a single, free, effectively massless constituent. Moreover the scattering from individual constituents is incoherent. The picture thus looks much like the impulse approximation of nuclear physics. 

Finally we warn the reader that to meet the phenomenal accuracy of recent experiments it is necessary to give careful attention to kinematic details which to some extent detract from the elegant simplicity of the original picture. These effects are treated in the appendix to this chapter (Section 16.9) in which the parton model is reformulated as an impulse approximation which allows better control of the kinematic factors. The chapter can be perfectly well understood without reading the appendix. 

In the appendix to this chaper we shall develop a picture of the parton model as an impulse approximation in which better control of kinematic effects is possible. It turns out from eqn (16.9.36) that for CC reactions involving a transition from a light quark j to a heavy qumrk k the principal kinematic corrections are the following ... 

We now go to the reference frame in which the impulse approximation is supposed to hold. In this frame we shall calculate the inelastic nucleon tensor W (N) in terms of the partonic tensors W° k,j) for a lepton scattering on a quark j and turning it into a quark of type k. Although the impulse approximation is a simple idea, there are subtleties in the derivation so we shall go through the analysis in some detail. 

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