Parton interpretation and twist-4 parton distributions

Through explicit examples we show that twist-4 parton distributions have no parton interpretation in the sense that parton or partons inside a hadron can carry the momentum fraction x of the hadron with x>1 or x<−1. The studied twist-4 parton distributions of collinear factorization are power-divergent for |x|>1. The corresponding transverse momentum dependent parton distributions have finite contributions for |x|>1 and they have hence no parton interpretation. Parton distributions are defined with products of field operators. In the case of twist-4, different orderings give different results. The differences are determined by commutation relations of field operators. This has been explicitly checked in the studied case. The implications of our results are discussed.