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Helicity Dependent Distribution Functions of the Proton and $Λ$ and $Σ^0$ Baryons

Yang Yu, Peng Cheng, Hui-Yu Xing, Daniele Binosi, Craig D. Roberts

TL;DR

This work uses continuum Schwinger function methods to generate a coherent set of helicity-dependent and unpolarised distribution functions for the proton, Λ, and Σ^0 baryons, emphasizing the impact of diquark correlations and SU(3) flavor breaking on spin and momentum distributions. It situates these predictions within the Emergent Hadron Mass framework, linking hadron structure to a momentum-dependent gluon mass and a process-independent running coupling that feed the quark gap equation and the Faddeev description of baryons. A key result is that gluons contribute about 40% to the spin of each octet baryon at a typical measurement scale, with axialvector diquarks playing a crucial role in enabling valence-strange spin in Σ^0. The results guide future experimental tests of QCD in baryon structure and suggest extensions to spin-transfer observables in Λ electroproduction, moving toward a unified, parameter-free description of hadron DFs and FFs.

Abstract

Using continuum Schwinger function methods, a coherent set of predictions for proton, $Λ$ and $Σ^0$ distribution functions (DFs) has been made available -- both helicity dependent and unpolarised. The results and comparisons between them reveal impacts of diquark correlations and SU$(3)$-flavour symmetry breaking, some of which are highlighted in this contribution. For instance: in-proton ratios of helicity-dependent/unpolarised valence-quark DFs are presented; it is highlighted that, were it not for the presence of axialvector diquarks in the $Σ^0$, the valence strange quark would carry none of the $Σ^0$ spin; and the sign and size of polarised gluon DFs is discussed -- at a scale typical of modern measurements, gluon partons carry roughly 40% of each octet baryon's spin.

Helicity Dependent Distribution Functions of the Proton and $Λ$ and $Σ^0$ Baryons

TL;DR

This work uses continuum Schwinger function methods to generate a coherent set of helicity-dependent and unpolarised distribution functions for the proton, Λ, and Σ^0 baryons, emphasizing the impact of diquark correlations and SU(3) flavor breaking on spin and momentum distributions. It situates these predictions within the Emergent Hadron Mass framework, linking hadron structure to a momentum-dependent gluon mass and a process-independent running coupling that feed the quark gap equation and the Faddeev description of baryons. A key result is that gluons contribute about 40% to the spin of each octet baryon at a typical measurement scale, with axialvector diquarks playing a crucial role in enabling valence-strange spin in Σ^0. The results guide future experimental tests of QCD in baryon structure and suggest extensions to spin-transfer observables in Λ electroproduction, moving toward a unified, parameter-free description of hadron DFs and FFs.

Abstract

Using continuum Schwinger function methods, a coherent set of predictions for proton, and distribution functions (DFs) has been made available -- both helicity dependent and unpolarised. The results and comparisons between them reveal impacts of diquark correlations and SU-flavour symmetry breaking, some of which are highlighted in this contribution. For instance: in-proton ratios of helicity-dependent/unpolarised valence-quark DFs are presented; it is highlighted that, were it not for the presence of axialvector diquarks in the , the valence strange quark would carry none of the spin; and the sign and size of polarised gluon DFs is discussed -- at a scale typical of modern measurements, gluon partons carry roughly 40% of each octet baryon's spin.
Paper Structure (5 sections, 3 equations, 1 figure)

This paper contains 5 sections, 3 equations, 1 figure.

Table of Contents

  1. Foundation
  2. Emergent Hadron Mass
  3. Distribution Functions - Proton
  4. Distribution Functions - $\mathbf \Lambda$ and $\mathbf \Sigma^{\mathbf 0}$
  5. Conclusion

Figures (1)

  • Figure 1: CSM predictions for a collection of in-proton DFs, all CSM results at the scale $\zeta=2\,$GeV. Panel a. Isovector in-proton DFs compared with preliminary results from numerical simulations of lattice-regularised QCD Lin:2020fsjLin:2018pvv. Panels b, c. CSM predictions for in-proton isovector and isoscalar DF ratios.