Spin-dependent quark densities, matrix elements of specific density operators in proton states of definite spin-polarization, indicate that the nucleon may harbor an infinite variety of nonspherical shapes. We show that these matrix elements are closely related to specific transverse-momentum-dependent (TMD) parton distributions accessible in the angular dependence of the semi-inclusive processes $\mathit{ep}\to e\pi X$ and the Drell-Yan reaction $\mathit{pp}\to l\overline{l}X$. New measurements or analyses would allow the direct exhibition of the nonspherical nature of the proton.

• Received 17 August 2007

DOI:https://doi.org/10.1103/PhysRevC.76.065209