Sum rules and their experimental tests

Let us now look at some of the relations amongst the scaling functions in the quark-parton model. We shall see that where these have been tested the results are, with one exception at present, generally in agreement with the predictions. 

There is a set of sum rules, based upon the relations (16.4.2-4), which involve integrating the scaling functions over the region 0 x 1. The presence of production thresholds in the formulae for the Fi x, complicates the results at finite Q in addition there are sometimes QCD corrections. It is only in the limit oo that truly simple results 

Firstly, because (16.4.36) involves only valence contributions, we obtain via (16.4.28) 

These results were originally derived by Adler, prior to the invention of 

At finite the result is not simple. But because of the dominance of the full expression in (16.4.36) will lead to a result differing from (17.1.2) and (17.1.3) by at most a few per cent. There are no QCD corrections. The Adler sum rule has been tested by the WA25 Group (WA25, 1985) and is in agreement with the data for 1 40 (GeV/c).  

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