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Nucleon and Roper electromagnetic elastic and transition form factors

D. J. Wilson, I. C. Cloët, L. Chang, and C. D. Roberts
Phys. Rev. C 85, 025205 – Published 22 February 2012
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  • INTRODUCTION
  • ELECTROMAGNETIC CURRENTS
  • NUCLEON ELASTIC
  • NUCLEON→ROPER TRANSITION AND ROPER…
  • ANOMALOUS MAGNETIC MOMENTS
  • MESON CLOUD
  • EPILOGUE
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    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 behavior 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*(Q2) exhibits a zero at Q2≈0.5mN2. 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<Q2≲2GeV2, 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.

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    • Received 9 December 2011

    DOI:https://doi.org/10.1103/PhysRevC.85.025205

    ©2012 American Physical Society

    Authors & Affiliations

    D. J. Wilson1, I. C. Cloët2, L. Chang1, and C. D. Roberts1,3,4

    • 1Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
    • 2CSSM and CoEPP, School of Chemistry and Physics University of Adelaide, Adelaide SA 5005, Australia
    • 3Institut für Kernphysik, Forschungszentrum Jülich, DE-52425 Jülich, Germany
    • 4Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616, USA

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    Vol. 85, Iss. 2 — February 2012

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    Images

    • Figure 1
      Figure 1
      Poincaré covariant Faddeev equation [Eq. (B10)] employed herein to calculate baryon properties. Ψ in Eq. (B1) is the Faddeev amplitude for a baryon of total momentum P=pq+pd. It expresses the relative momentum correlation between the dressed-quark and -diquarks within the baryon. The shaded region demarcates the kernel of the Faddeev equation (Appendix B ), in which: the single line denotes the dressed-quark propagator (Appendix A 1); Γ is the diquark Bethe-Salpeter amplitude (Appendix A 4); and the double line is the diquark propagator [Eqs. (B4) and (B9)].Reuse & Permissions
    • Figure 2
      Figure 2
      Interaction vertex that ensures a conserved current for the elastic and transition form factors in Eqs. (2) and (3). The single line represents the dressed-quark propagator, S(p) in Appendix A 1; the double line, the diquark propagators in Eqs. (B4) and (B9); and the vertices are described in Appendix C. From top to bottom, the diagrams describe the photon coupling: directly to the dressed-quark, to a diquark in an elastic scattering event, or inducing a transition between scalar and axial-vector diquarks.Reuse & Permissions
    • Figure 3
      Figure 3
      Proton Dirac (top) and Pauli (bottom) form factors, as a function of x=Q2/mN2. Solid curve, result obtained herein using the contact-interaction and hence a dressed-quark mass function and diquark Bethe-Salpeter amplitudes that are momentum-independent; dashed curve, result obtained in Ref. [34], which employed QCD-like momentum-dependence for the dressed-quark propagators and diquark Bethe-Salpeter amplitudes in solving the Faddeev equation; dot-dashed curve, a parametrization of experimental data [35].Reuse & Permissions
    • Figure 4
      Figure 4
      Neutron Dirac (top) and Pauli (bottom) form factors, as a function of x=Q2/mN2. Solid curve, result obtained herein using the contact interaction and hence a dressed-quark mass function and diquark Bethe-Salpeter amplitudes that are momentum-independent; dashed curve, result obtained in Ref. [34], which employed QCD-like momentum dependence for the dressed-quark propagators and diquark Bethe-Salpeter amplitudes in solving the Faddeev equation; dot-dashed curve, a parametrization of experimental data [35].Reuse & Permissions
    • Figure 5
      Figure 5
      Flavor separation of the proton's Dirac form factor, as a function of x=Q2/mN2; normalization: F1pu(0)=2, F1pd(0)=1. Solid curve, u quark obtained using the contact interaction; short-dashed curve, d quark, contact interaction; dot-dashed curve, u quark obtained from QCD-like momentum dependence for the dressed-quark propagators and diquark Bethe-Salpeter amplitudes in the Faddeev equation [34]; and long-dashed curve, d quark obtained similarly. The data are from Refs. [42, 43]: u quark, circles; and d quark, diamonds. The dotted curves are determined from the parametrization of data in Ref. [44].Reuse & Permissions
    • Figure 6
      Figure 6
      Flavor separation of the proton's Pauli form factor, as a function of x=Q2/mN2: d quark, top; and u quark, bottom. Solid curve, result obtained using the contact interaction; dashed curve, obtained from QCD-like momentum-dependence for the dressed-quark propagators and diquark Bethe-Salpeter amplitudes in the Faddeev equation [34]; dotted curve, determined from the parametrization of data in Ref. [44]; data from Refs. [42, 43, 46].Reuse & Permissions
    • Figure 7
      Figure 7
      (Top) Normalized ratio of proton Pauli and Dirac form factors. Solid curve, contact interaction; long-dashed curve, result from Ref. [41], which employed QCD-like momentum-dependence for the dressed-quark propagators and diquark Bethe-Salpeter amplitudes; long-dash-dotted curve, drawn from parametrization of experimental data in Ref. [35]; and dotted curve, softened contact-interaction result, described in connection with Eq. (6). (Bottom) Normalized ratio of proton Sachs electric and magnetic form factors. Solid curve and long-dashed curve, as above; dot-dashed curve, linear fit to data in Refs. [51, 52, 53, 54, 55], constrained to one at Q2=0; short-dashed curve, [1,1]-Padé fit to that data; and dotted curve, softened contact-interaction result, described in connection with Eq. (6). In addition, we have represented a selection of data explicitly: solid squares [52], circles [54], triangles [55], and open squares [56].Reuse & Permissions
    • Figure 8
      Figure 8
      Comparison of charged-Roper and proton Dirac (top) and Pauli (bottom) form factors, as a function of x=Q2/mN2. Solid curve, Roper; dashed-curve, proton. All results obtained using the contact interaction, and hence a dressed-quark mass function and diquark Bethe-Salpeter amplitudes that are momentum independent.Reuse & Permissions
    • Figure 9
      Figure 9
      Comparison of neutral-Roper and neutron Dirac (top) and Pauli (bottom) form factors, as a function of x=Q2/mN2: Solid curve, neutral-Roper; and dashed-curve, neutron. All results obtained using the contact-interaction, and hence a dressed-quark mass-function and diquark Bethe-Salpeter amplitudes that are momentum-independent.Reuse & Permissions
    • Figure 10
      Figure 10
      (Top) F1* [solid and dot-dashed curves with dressed-quark anomalous magnetic moment (Sec. 5)] and F2* (dashed and dotted curves with dressed-quark anomalous magnetic moment) as a function of x=Q2/mN2, computed using the framework described herein. (Bottom) Computed form of F1*(x) compared with available data [18, 19, 20]. The squares, triangles, and stars are preliminary results [62] from a simulation of Nf=2+1 lattice-QCD at, respectively, mπ2/mπexpt.2≃8, 10, 40.Reuse & Permissions
    • Figure 11
      Figure 11
      Comparison between F2*(x) computed using the framework described herein and available data [18, 19, 20], with x=Q2/mN2. (Top) Normalized to unity at x=0; (bottom) as computed. In both panels the dashed curve was computed with a model for the dressed-quark anomalous electromagnetic moment (Sec. 5). The squares, triangles, and stars are preliminary results from a simulation of Nf=2+1 lattice-QCD at, respectively, mπ2/mπexpt.2≃8, 10, 40 [62].Reuse & Permissions
    • Figure 12
      Figure 12
      Separation of F2*(x) into contributions from different diagrams, with x=Q2/mN2: solid curve, photon on u-quark with scalar diquark spectator; dashed curve, photon on scalar diquark with u-quark spectator; dot-dashed curve, photon on axial-vector diquark with quark spectator; dotted curve, photon-induced transition between scalar and axial-vector diquarks with u-quark spectator. N.B. Owing to Eq. (C5), there is no contribution involving an axial-vector diquark spectator.Reuse & Permissions
    • Figure 13
      Figure 13
      (Top) F1R0→n (solid curve) as a function of x=Q2/mN2 compared with F1R+→p (dashed curve), computed using the framework described herein. (Bottom) Analog for F2R0→n.Reuse & Permissions
    • Figure 14
      Figure 14
      Helicity amplitudes for the γ*p→P11(1440) transition, with x=Q2/mN2: A1/2 (top) and S1/2 (bottom). Solid curves, computed using the treatment of the contact interaction described herein, including the dressed-quark anomalous magnetic moment (Appendix C 6); dashed curves, the light-front constituent-quark model results from Ref. [63]; long-dash-dotted curves, the light-front constituent-quark model results from Ref. [64]; short-dashed curves, our smooth fit to the bare form factors inferred in Ref. [30, 31, 32]; data, Refs. [18, 19, 20].Reuse & Permissions
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