Densities, Parton Distributions, and Measuring the Non-Spherical Shape of the Nucleon

Abstract

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 non-spherical shapes. We show that these matrix elements are closely related to specific transverse momentum dependent parton distributions accessible in the angular dependence of the semi-inclusive processes electron plus proton goes to electron plus pion plus anything, and the Drell-Yan reaction proton plus proton goes to a lepton anti-lepton pair plus anything. New measurements or analyses would allow the direct exhibition of the non-spherical nature of the proton.

Figures (2)

• Figure 1: (Color online) Transverse shapes of the nucleon: $\sqrt{2}\hat{\rho}_T({\bf K}_T,{\bf n})/\tilde{f}_1(K_T^2)$. The horizontal axis is the the direction of ${\bf S}_T$ and ${\bf n}=\hat{{\bf S}}_T,\; \phi_n=0$. The shapes vary from circular to highly deformed as $K_T$ is increased from 0 to 2.0 GeV in steps of 0.25 GeV.
• Figure 2: (Color online) Transverse shapes of the nucleon, as in Fig. 1 except that $\phi_n=\pi$.