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

TL;DR

This paper explores the non-spherical shapes of the nucleon by linking spin-dependent quark densities to measurable transverse momentum dependent parton distributions in semi-inclusive and Drell-Yan processes.

Contribution

It establishes a connection between nucleon shape indicators and experimentally accessible distributions, proposing new ways to observe the non-spherical structure of the proton.

Findings

Matrix elements relate to specific transverse momentum dependent distributions.

Potential for new measurements to reveal proton's non-spherical shape.

Provides a theoretical framework for experimental exploration.

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.