Positivity and an analysis of asymptotic and nonasymptotic effects in electron-positron annihilation processes

Abstract

A detailed positivity analysis of e+e− → hadrons and e+e− →\(\bar p\)+x is made within a framework of light-cone expansion/parton theory. A positivity bound for the asymptotic ratio $$R_\infty = \mathop {\lim }\limits_{s \to \infty } \frac{{\sigma (e^ + e^ - \to {\text{hadrons)}}}}{{\sigma (e^ + e^ - \to \mu ^ + \mu ^ - {\text{)}}}}$$ is derived and the stability of such a bound is studied by including nonleading terms up to third order. Corresponding positivity domains for the nonasymptotic ratios $$R\left( s \right) = \frac{{\sigma (e^ + e^ - \to {\text{hadrons)}}}}{{\sigma (e^ + e^ - \to \mu ^ + \mu ^ - {\text{)}}}}$$ (s finite), inclusive distributions(dσ/dx)(e+e− →\(\bar p\)+x) and inclusive angular distributions(dσ/dx d cosϑ)(e+e− →\(\bar p\)+x) are also estimated in the present accelerator energies and predictions are made for future energies. The extra assumption is the validity of the Gribov-Lipatov reciprocity relation for e+e− →\(\bar p\)+x in the asymptotic region. Our analysis suggests that scaling ofσ(e+e− → hadrons) will set in within the SPEAR II limit (∼81 (GeV)2), while that ofσ(e+e− →\(\bar p\)+x) will set in beyond this limit for slow particles in the centre-of-mass frame (i.e. for the pionization region).