Parton distribution amplitudes: Revealing correlations within the proton and Roper

Cédric Mezrag,Jorge Segovia,Lei Chang,Craig D Roberts

doi:10.1016/j.physletb.2018.06.062

Abstract

Constrained by solutions of the continuum three-valence-body bound-state equations, we use perturbation theory integral representations (PTIRs) to develop algebraic Ansätze for the Faddeev wave functions of the proton and its first radial excitation, delivering therewith a quantum field theory calculation of the pointwise behaviour of their leading-twist parton distribution amplitudes (PDAs). The proton's PDA is a broad, concave function, with its maximum shifted relative to the peak in QCD's conformal limit expression for this PDA. The size and direction of this shift signal the presence of both scalar and pseudovector diquark correlations in the nucleon, with the scalar generating around 60% of the proton's normalisation. The radial-excitation is constituted similarly, and the pointwise form of its PDA, which is negative on a material domain, is the result of marked interferences between the contributions from both types of diquark; particularly, the locus of zeros that highlights its character as a radial excitation. These features originate with the emergent phenomenon of dynamical chiral-symmetry breaking in the Standard Model.

Highlights

Estimates of low-order Mellin moments exist, obtained using sum rules [14, 15] or latticeQCD (lQCD) [16,17,18], but there are no quantum field theory computations of this parton distribution amplitudes (PDAs)’s pointwise behaviour; and nothing is known about the PDA of the proton’s radial excitation
We present the first quantum field theory calculation of the pointwise behaviour of the leadingtwist parton distribution amplitudes (PDAs) of the proton and its lightest radial excitation
The radial-excitation is constituted and the pointwise form of its PDA, which is negative on a material domain, is the result of marked interferences between the contributions from both types of diquark; the locus of zeros that highlights its character as a radial excitation

Summary

Introduction

Estimates of low-order Mellin moments exist, obtained using sum rules [14, 15] or latticeQCD (lQCD) [16,17,18], but there are no quantum field theory computations of this PDA’s pointwise behaviour; and nothing is known about the PDA of the proton’s radial excitation. The proton’s Faddeev wave function, χ, is obtained from Eqs.

Results

Conclusion