Speculations on the breakdown of scaling at10−15cm

We discuss the hypothesis that scaling in deep-inelastic electron-nucleon scattering is a "preasymptotic" phenomenon, which will be broken at energies large enough to probe the structure of the constituents of the nucleon. In particular, we consider a model in which the constituents are light (i.e., $M\lesssim M_p$) and are bound by a very heavy gluon ($M_G\gg M_p$), which induces a small "size" in the constituents of order ${M_G}^{-1\mathrm{}}$. The experimental implications of this hypothesis are discussed, primarily for the region of momentum transfers $M^2\ll Q^2\ll {M_G}^2$. In a bound-state model, using the Bethe-Salpeter equation in ladder approximation, we show that the deviations from simple scaling behavior in spacelike scattering and timelike annihilation processes are correlated and measure the "size" of the constituent. Finally, we show that the hypothesis that the constituent has structure is not inconsistent with local current algebra and, in particular the Adler sum rule for neutrino-nucleon scattering.