Nucleon and Roper electromagnetic elastic and transition form factors

Abstract

We compute nucleon and Roper electromagnetic elastic and transition form factors using a Poincaré-covariant, symmetry-preserving treatment of a vector × vector contact-interaction. Obtained thereby, the electromagnetic interactions of baryons are typically described by hard form factors. In contrasting this behaviour with that produced by a momentum-dependent interaction, one achieves comparisons which highlight that elastic scattering and resonance electroproduction experiments probe the evolution of the strong interaction's running masses and coupling to infrared momenta. For example, the existence, and location if so, of a zero in the ratio of nucleon Sachs form factors are strongly influenced by the running of the dressed-quark mass. In our description of the nucleon and its first excited state, diquark correlations are important. These composite and fully-interacting correlations are instrumental in producing a zero in the Dirac form factor of the proton's d-quark; and in determining the ratio of d-to-u valence-quark distributions at x = 1, as we show via a simple formula that expresses dv/uv(x = 1) in terms of the nucleon's diquark content. The contact interaction produces a first excitation of the nucleon that is constituted predominantly from axial-vector diquark correlations. This impacts greatly on the γ * p → P11(1440) form factors, our results for which are qualitatively in agreement with the trend of available data. Notably, our dressed-quark core contribution to F2 * (Q 2 ) exhibits a zero at Q 2 ≈ 0.5 m 2 N . Faddeev equation treatments of a hadron's dressed-quark core usually underestimate its magnetic properties, hence we consider the effect produced by a dressed-quark anomalous electromagnetic moment. Its inclusion much improves agreement with experiment. On the domain 0 < Q 2 2 GeV 2 , meson-cloud effects are conjectured to be important in making a realistic comparison between experiment and hadron structure calculations. We find that our computed helicity amplitudes are similar to the bare amplitudes inferred via coupled-channels analyses of the electroproduction process. This supports a view that extant hadron structure calculations, which typically omit meson-cloud effects, should directly be compared with the bare-masses, -couplings, etc., determined via coupled-channels analyses.

Baryons as relativistic three-quark bound states

“…Closely related is the contactinteraction model developed in Refs. [344,509] which requires some modifications to the kernels to make it applicable to excited states; it has since been applied to nucleon, ∆ and Roper elastic and transition form factors [510][511][512]. A compilation of results together with a comparison with the quark-diquark model using momentum-dependent ingredients can be found in [506].…”

Dynamical chiral symmetry breaking and the fermion–gauge-boson vertex

“…III A, no Ansatz for the transverse part of the fermion-photon vertex is completely satisfactory if it does not express what might be called leakage into the spacelike region of spectral strength from both the two-pion continuum and the region of the ρ-meson pole. If one concentrates on the spacelike domain, then such effects are maximal near q 2 = 0 and may be characterised by observing that they alter charge radii by 20% [28,56,[65][66][67]. Related, and more important perhaps, are the limitations of the tensor basis in Eqs.…”

“…Namely, whilst expressed solely in terms of the functions in the dressed-fermion propagator, it nevertheless produces a magnetic moment distribution in fair agreement with the most realistic symmetry-preserving solution of the inhomogeneous vector Bethe-Salpeter equation that is currently available. It is therefore worth employing this Ansatz more widely; e.g., in the computation of hadron electromagnetic form factors [20,21,25,28].…”

“…[13][14][15][16], insights from which have subsequently been exploited; e.g., Refs. [17][18][19][20][21][22][23][24][25][26][27][28].…”

Features and flaws of a contact interaction treatment of the kaon

“…This study is an integral part of a larger programme, aimed at charting the interaction between light-quarks by explicating the impact of differing assumptions about the behaviour of the Bethe-Salpeter kernel upon the spectrum of hadrons, and also upon their elastic and transition form factors on a large domain of momentum transfer. Material progress has been made in connection with u, d-quark systems [15][16][17][18][19]; and a spectrum of mesons and baryons with one or more s-quarks was recently computed [20]. In order to extend the latter to predictions for elastic and transition form factors of baryons containing s-quarks, it is necessary to compute such form factors for mesons containing s-quarks.…”