$\Delta$-baryon axialvector and pseudoscalar form factors, and associated PCAC relations

Abstract

A quark+diquark Faddeev equation treatment of the baryon bound state problem in Poincaré-invariant quantum field theory is used to deliver parameter-free predictions for all six $\Delta$-baryon elastic weak form factors. Amongst the results, it is worth highlighting that there are two distinct classes of such $\Delta$-baryon form factors, $(g_1,g_3,G_{\pi \Delta \Delta })$, $(h_1,h_3,H_{\pi \Delta \Delta })$, the functions within each of which are separately linked via partial conservation of axial current (PCAC) and Goldberger-Treiman (GT) relations. Respectively within each class, the listed form factors possess qualitatively the same structural features as the nucleon axial, induced pseudoscalar, and pion-nucleon coupling form factors. For instance, the $\Delta$-baryon $g_1$ axial form factor can reliably be approximated by a dipole function, characterised by an axial charge $g_A^{{\Delta }^{+}}=0.71(9)$ and mass-scale $m_A^{\Delta }=0.95(2)m_{\Delta }$. Moreover, the two distinct $\Delta$-baryon PCAC form factor relations are satisfied to a high degree of accuracy on a large range of $Q^2$; the associated GT relations present good approximations only on $Q^2/m_{\Delta }^2\simeq 0$; and pion pole dominance approximations are reliable within both classes. There are two $\pi \Delta \Delta$ couplings: $g_{\pi \Delta \Delta }=10.46(1.88)$; $h_{\pi \Delta \Delta }=35.73(3.75)$; and the associated form factors are soft. Such couplings commonly arise in phenomenology, which may therefore benefit from our analyses. A flavour decomposition of the axial charges reveals that quarks carry $71$\% of the $\Delta$-baryon spin. The analogous result for the proton is $\approx 65$\%.

arXiv comment19 pages, 9 figures, 2 tables

References in corpus (41)

• Baryons as relativistic three-quark bound states
• The 1/N Expansion for Baryons
• NuSTEC White Paper: Status and Challenges of Neutrino-Nucleus Scattering
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Coupled-channel dynamics in the reactions piN --> piN, etaN, KLambda, KSigma
• Distribution Functions of the Nucleon and Pion in the Valence Region
• Nucleon mass from a covariant three-quark Faddeev equation
• Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report
• Diquark Correlations in Hadron Physics: Origin, Impact and Evidence
• On unifying the description of meson and baryon properties
• Nucleon and $\Delta$ elastic and transition form factors
• The Spin Structure of the Nucleon
• Masses of ground and excited-state hadrons
• Neutrino Interactions with Nucleons and Nuclei: Importance for Long-Baseline Experiments
• Perspective on rainbow-ladder truncation
• Electromagnetic Form Factors of Charged and Neutral Kaons
• Natural constraints on the gluon-quark vertex
• Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances
• Nucleon axial structure from lattice QCD
• Gauge Sector Dynamics in QCD
• Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
• On Nucleon Electromagnetic Form Factors
• Quark transverse charge densities in the $\Delta (1232)$ from lattice QCD
• Emergent Hadron Mass in Strong Dynamics
• Nucleon electromagnetic form factors using lattice simulations at the physical point
• Model Analysis of the $ep\to e{p}^{\prime }{\pi }^{+}{\pi }^{-}$ Electroproduction Reaction on the Proton
• Elastic and transition form factors of the Δ(1232)
• Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach
• Transition between nuclear and quark-gluon descriptions of hadrons and light nuclei
• Strong QCD Insights from Excited Nucleon Structure Studies with CLAS and CLAS12
• Emergence of mass in the gauge sector of QCD
• Axial charges of hyperons and charmed baryons using $N_f=2+1+1$ twisted mass fermions
• Axial form factor of the nucleon at large momentum transfers
• The relativistic chiral Lagrangian for decuplet and octet baryons at next-to-leading order
• Electromagnetic form factors of the baryon decuplet with flavor SU(3) symmetry breaking
• Determination of the $\Delta (1232)$ axial and pseudoscalar form factors from lattice QCD
• Nucleon axial form factor at large momentum transfers
• Determining the helicity structure of the nucleon at the Electron Ion Collider in China
• The $\Delta (1232)$ axial charge and form factors from lattice QCD
• Isovector axial vector and pseudoscalar transition form factors of $\Delta$ in QCD
• A unified approach to hadron phenomenology at zero and finite temperatures in a hard-wall AdS/QCD model

Cited by in corpus (1)

• Space-like Electromagnetic Form Factors of Lambda- and Sigma-Baryons from Quark-Diquark Faddeev Equations