An alternative to the dimensional counting rules

Abstract

The asymptotic behaviour of hadron form factors and the threshold behaviours of structure functions are investigated in a model based on i) unitarity with\(q\bar q\) intermediate states in thet =q2 channel, and dispersion relations; ii) asymptotic behaviour of the quark-hadron amplitude governed by the spins of the exchanged (spectators) partons; iii) Bloom-Gilman duality. Our model emphasizes the infra-red region of the impulse diagram and is supposed to work in an intermediateq2 region in which scaling violation and gluon jets are not too important. We find, fort → ∞,\(\bar f_\lambda ^{hadron} (t) \sim \bar f_\lambda ^{quark} (t)\prod\limits_i {t^{S_i - 1} } \prod\limits_j {t^{\alpha _j (0)} } \), where\(\bar f_\lambda \) is the form factor for the current helicity ι, summed over the hadronic helicities,8i the spin of thei-th elementary spectator and α3 the Regge trajectory of thej-th composite spectator. The threshold behaviours of the structure functions are given by the Drell-Yan-West relation. For mesons we predict\(\bar f_0 \sim t^{ - 1} , \bar f_{ \pm 1} \sim t^{ - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} } \) (in contradiction with helicity selection rules),νW2 (ω = 1) ≠ 0. For baryons, the dipole fit suggests the existence of a spin-zero neutral parton in addition to the quarks. The deuteron data are compatible with our predictions,\(F^d \sim F^\mathcal{N} t^{ - 1.3} \),vW2d∼(ω − 1)−5.6.