Nucleon mass and pion loops

Abstract

Poincare' covariant Faddeev equations for the nucleon and Delta are solved to illustrate that an internally consistent description in terms of confined-quark and nonpointlike confined-diquark-correlations can be obtained. pi N-loop induced self-energy corrections to the nucleon's mass are analysed and shown to be independent of whether a pseudoscalar or pseudovector coupling is used. Phenomenological constraints suggest that this self-energy correction reduces the nucleon's mass by up to several hundred MeV. That effect does not qualitatively alter the picture, suggested by the Faddeev equation, that baryons are quark-diquark composites. However, neglecting the pi-loops leads to a quantitative overestimate of the nucleon's axial-vector diquark component.Comment: 17 pages, 6 figures, REVTEX

Hadron properties and Dyson–Schwinger equations

“…A study of the nucleon's mass and the effect on this of a pseudoscalar meson cloud are detailed in [76]. Lessons learnt were employed in a series of studies of nucleon properties, including form factors [77,78,79].…”

On Nucleon Electromagnetic Form Factors

“…However, since we have already chosen to simplify the calculations by parametrising S(p), we follow Ref. [20] and also employ that expedient with Γ J P , using the following one-parameter forms:…”

“…However, it is also known that such an outcome is undesirable because, Table 1. Mass-scale parameters (in GeV) for the scalar and axial-vector diquark correlations, fixed by fitting nucleon and ∆ masses: for Set A, a fit to the actual masses was required; whereas for Set B the fitted mass was offset to allow for "pion cloud" contributions [20]. We also list ω J P = 1 √ 2 m J P , which is the width-parameter in the (qq) J P Bethe-Salpeter amplitude, Eqs.…”

“…[18,19,20,21]. It has become apparent that the dominant correlations for ground state octet and decuplet baryons are scalar and axial-vector diquarks, primarily because the associated mass-scales are smaller than the masses of these baryons [22,23] and the positive parity of the correlations matches that of the baryons.…”

“…However, that possibility necessitates the incorporation of pseudoscalar meson loop contributions because a credible description of baryon properties is otherwise problematic. Such effects contribute materially: to baryon masses [20,24,25]; and charge and magnetic radii, and magnetic moments [26,27].…”