Non-Spherical Shapes of the Proton: Existence, Measurement and Computation

TL;DR

This paper explores the non-spherical shapes of the proton through spin-dependent quark density operators, linking theoretical calculations with experimental measurements via TMD distributions to reveal the proton's shape.

Contribution

It introduces a framework connecting proton shape, spin-dependent densities, and TMDs, proposing new measurements and lattice QCD computations to observe non-spherical proton shapes.

Findings

TMDs relate to non-spherical proton shapes

Lattice QCD can compute relevant TMDs

New experiments could directly observe proton shape

Abstract

The nature of the proton wave function can be elucidated by studying the matrix elements of spin-dependent quark density operators SDDs, defined as matrix elements of density operators in proton states of definite spin-polarization. These have an infinite variety of non-spherical shapes. The matrix elements of the SDDs are closely related to specific transverse momentum dependent TMD parton distributions accessible in the angular dependence of certain semi-inclusive processes. New measurements would allow the direct exhibition of the non-spherical nature of the proton. The TMDs can be computed using lattice QCD so that the non-spherical shapes could eventually be measured experimentally and computed using fundamental theory.