We present the first attempt of a new method to compute the pion light-cone wave function (LCWF) on the lattice. We compute the matrix element between the pion and the vacuum of a nonlocal operator: the propagator of a “scalar quark” (named, for short a “squark”). A theoretical analysis shows that for some kinematical conditions (an energetic pion and hard squark) this matrix element depends dominantly on the LCWF ${\Phi }_{\pi }\mathrm{}\left(u\right),u\in [0,1].$ On the lattice, the discretization of the parton momenta imposes further constraints on the pion momentum. The two-point Green functions made of squark-quark and squark-squark fields show a hadronlike bound-state behavior and verify the standard energy spectrum. We show some indications that during a short time, after being created, the system of the spectator quark and the squark behave like partons, before they form a hadronlike bound state. This short time is the place where the partonic wave function has to be looked for.

• Received 25 May 2001

DOI:https://doi.org/10.1103/PhysRevD.64.074511