Parton Model with Variable Intermediate-State Parton Mass

The parton model is modified by allowing the parton mass to change after absorbing the spacelike photon. Each prescription for the intermediate-state parton mass leads to a model with a definite scaling variable and to a scale-invariance-breaking factor which describes the approach to scaling. The model with Bloom et al.'s variable ${\omega }^{\prime }$ has the required linear zero in $\nu W_2$ as $Q^2\to 0$ for fixed $\omega$, and has a scale-invariance-breaking factor which agrees with experiment for $1\le {\omega }^{\prime }\le 12$. The prescription that the parton mass must vanish after absorbing the photon leads to the scaling variable $\hat{\omega }$, which also occurs in the light-cone-singularity dominance model. Models which allow agreement of the sum rule for the mean squared charge per parton with experiment are given, as are models which have diffractive behavior for $Q^2$ near zero.