Breakdown of the operator-product expansion in the 't Hooft model

We consider deep inelastic scattering in the 't Hooft model. Being solvable, this model allows us to directly compute the moments associated with the cross section at next-to-leading order in the 1/Q2 expansion. We perform the same computation using the operator-product expansion. We find that all the terms match in both computations except for one in the hadronic side, which is proportional to a nonlocal operator. The basics of the result suggest that a similar phenomenon may occur in four dimensions in the large Nc limit. © 2008 The American Physical Society.