DOUBLE ASYMPTOTIC SCALING AT HERA

Perturbative QCD predicts that at sufficiently large Q2 and small x nucleon structure functions should exhibit scaling in the two variables square-root ln 1/x ln ln Q2 and square-root ln 1/x/ln ln Q2, provided only that the small-x behaviour of the input to the perturbative QCD evolution is sufficiently soft. We derive these asymptotic results by writing the gluonic Altarelli-Parisi equation at small x as a two-dimensional wave equation, which propagates the gluon distribution from its boundaries into the asymptotic region. We then show that the existing experimental data on F(2)p (x, Q2) from HERA provide a remarkable confirmation of both of these scaling predictions. The 'hard' pomeron, which does not scale, is thereby excluded by more than three standard deviations; only a very small admixture of it is permitted by the data. We propose that existing and future data from HERA should be binned in the two scaling variables, in order to facilitate the search for small scaling violations.