The missing constituents—gluons

We defined qj x ) dx as the number of partons of type j whose mass lies between x mj and x + dx )mjq. As already mentioned, it is more fundamental to define qj x )dx as the number of partons of type j whose Z component of momentum, as measured in the CM reference frame in which the nucleon is travelling very fast (we call this an infinite momentum frame ), lies between x pzjq and x + dx )pzj. Generally, a parton with Z component of momentum x pzN in an infinite momentum frame will not have mass x mj. The two statements are equivalent only if the parton is at rest in the rest frame of the nucleon. (This is explained in the appendix to this chapter.) But the latter property was effectively assumed when in Section 16.1 we identified the time comp)onent of q in the partons rest frame as ty. Thus the two interpretations of the physical meaning of qj x ) are equivalent, and this equivalence is essential for the derivation of many of the detailed formulae of the model. 

Granted this, it is clear that the total Z component of momentum carried by a given type of parton is dx[p2Nxgj(x)]. Thus the fraction of the proton s CM momentum carried by a given constituent is /J xqj x) dx. 

The total fraction of the proton s CM momentum carried by the quarks and antiquarks is thus 

Now from (16.4.9), (16.4.12) and (16.4.27) we see that to a very good approximation, below charm threshold, 

Experimentally, the RHS is measured over a wide range of to be 0.45 0.03. We are forced to conclude that the quarks and antiquarks carry only about 50% of the momentum of the proton  

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