Abstract
A Poincar\'e-covariant quark+diquark Faddeev equation is used to compute nucleon elastic form factors on $0\leq Q^2\leq 18 \,m_N^2$ ($m_N$ is the nucleon mass) and elucidate their role as probes of emergent hadronic mass in the Standard Model. The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g. a zero in $G_E^p/G_M^p$; a maximum in $G_E^n/G_M^n$; and a zero in the proton's $d$-quark Dirac form factor, $F_1^d$. Additionally, examination of the associated light-front-transverse number and anomalous magnetisation densities reveals, inter alia: a marked excess of valence $u$-quarks in the neighbourhood of the proton's centre of transverse momentum; and that the valence $d$-quark is markedly more active magnetically than either of the valence $u$-quarks. The calculations and analysis also reveal other aspects of nucleon structure that could be tested with a high-luminosity accelerator capable of delivering higher beam energies than are currently available.
Highlights
Ever since it was found that the proton and neutron are composite systems [1], their elastic electromagnetic form factors have been the focus of extensive programmes in both experiment and theory
The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g., a zero in GpE=GpM, a maximum in GnE=GnM, and a zero in the proton’s d-quark Dirac form factor, Fd1
II guarantee that the calculated nucleon form factors exhibit the large-Q2 scaling behavior predicted by quantum chromodynamics (QCD) [83]; and it is straightforward to ensure that the Schlessinger point method (SPM) interpolants preserve this feature.)
Summary
Ever since it was found that the proton and neutron are composite systems [1], their elastic electromagnetic form factors have been the focus of extensive programmes in both experiment and theory. In reaching high Q2 using this framework, a number of obstacles must be overcome, e.g., one should use inter alia: a large lattice volume to accommodate physically light quarks, small lattice spacing, and high statistics to offset a decaying signal-to-noise ratio as form factors drop rapidly with increasing Q2 To master these challenges, new algorithms are being tested and preliminary results are available [16,17]. Predictions for the large-Q2 behavior of nucleon form factors have been delivered using a fully dynamical quark þ diquark reduction of the Poincare-covariant three-body bound-state problem in relativistic quantum field theory [43]. We reconsider those calculations because questions can be asked about the algorithms used to compute the form factors on x 1⁄4 Q2=m2N ≳ 10.
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