Conformal field theories and deep inelastic scattering

We consider deep inelastic scattering thought experiments in unitary conformal field theories. We explore the implications of the standard dispersion relations for the operator product expansion data. We derive positivity constraints on the operator product expansion coefficients of minimal-twist operators of even spin s >= 2. In the case of s = 2, when the leading-twist operator is the stress tensor, we reproduce the Hofman-Maldacena bounds. For s > 2, the bounds are new.