Hadron constituents ande+e−colliding-beam experiments

In order to test the idea that hadrons are made out of some fundamental constituents, it is most important to state precisely, in a general way, what we mean by the hadronic constituents. We call the constituents partons and state a set of basic assumptions. They are weaker than any of the assumptions previously used in connection with the model. With these assumptions, we show that if $R\equiv \frac{\sigma (e^{+}{e}^{-}\to \mathrm{hadrons})}{\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})}$ increases faster than or equal to $\ln \left(\frac{Q}{M}\right)$ at large $Q$, then the multiplicity of hadrons in $e^{+}{e}^{-}\to$ hadrons must increase at least as fast as $\frac{\left(\frac{Q}{M}\right)}{\ln \left(\frac{Q}{M}\right)}$. $Q$ is the center-of-mass energy of the colliding beam. The increase in $R$ with $Q$, itself, does not violate the basic concept of the parton model. If the above relations between the increase in the cross section and the multiplicity are contradicted by experiments at large $Q$, however, the parton model requires a major overhaul.