Masses of Ground- and Excited-State Hadrons

Abstract

We present the first Dyson-Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground-and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector-vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degreeof freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and ∆ masses and those of the dressed-quark and diquark correlations they contain.

Baryons as relativistic three-quark bound states

“…These features are clearly visible in the contact interaction model of Refs. [333,344] and also persist in rainbow-ladder calculations as we will see in Sec. 3.6.…”

“…For reviews on the physics of the NJL model see e.g. [337,338]; applications for ground states of baryons are discussed in [339][340][341][342][343] and recent applications also to excited states and baryons with strangeness can be found in [333,344]. We discuss some of these results below in Sec.…”

“…An interesting perspective on the baryon spectrum can be drawn from the inherent connection between meson and diquark properties [344]. Their Bethe-Salpeter equations (3.48) and (3.92) in rainbow-ladder are in fact so similar that after working out the Dirac, colour and flavour traces they only differ by a factor 1 /2 -diquarks are 'less bound' than mesons.…”

“…In the NJL/contact model the first radial excitations of the positive-and negative-parity N , ∆ and Ω baryons have been studied in Ref. [344] and the properties of the Roper were calculated within a momentum dependent diquark model [25]. Very recently, results for nucleon and ∆ resonances have also become available in the rainbow-ladder three-body framework [421].…”

“…In both the NJL/contact interaction based work [344] and the momentum-dependent quark-diquark model of Ref. [25] a similar strategy to determine the properties of the Roper has been employed: anticipating attractive mass shifts from a meson cloud that is not explicitly contained in the models, the model parameters (in particular the scale) were tuned to overestimate the nucleon mass, i.e.…”