Completing the Picture of the Roper Resonance

Abstract

We employ a continuum approach to the three valence-quark bound-state problem in relativistic quantum field theory to predict a range of properties of the proton's radial excitation and thereby unify them with those of numerous other hadrons. Our analysis indicates that the nucleon's first radial excitation is the Roper resonance. It consists of a core of three dressed-quarks, which expresses its valence-quark content and whose charge radius is 80% larger than the proton analogue. That core is complemented by a meson cloud, which reduces the observed Roper mass by roughly 20%. The meson cloud materially affects long-wavelength characteristics of the Roper electroproduction amplitudes but the quark core is revealed to probes with Q 2 3m 2 N .

Baryons as relativistic three-quark bound states

“…They exhibit a strong Q 2 dependence of the transverse helicity amplitude A 1/2 including a zero crossing, which also translates into a zero of the corresponding Pauli form factor F 2 (Q 2 ). Such a behavior is typically expected for radial excitations and it has been recovered by a number of approaches, from constituent [23] and light-front constituent-quark models [24] to Dyson-Schwinger calculations [25], effective field theory [26], lattice QCD [27] and AdS/QCD [28]. Although none of them has yet achieved pointwise agreement with the data they all predict the correct signs and orders of magnitude of the amplitude.…”

“…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].…”

“…to drastically simplified wave functions for the baryon. An alternative strategy that aims at the preservation of such dynamics has been pursued in [302,327,350] for ground-state baryons and very recently also for the Roper [25]. Here one works again with the quark-diquark Bethe-Salpeter equation from Fig.…”

“…In particular, it seems that a rainbow-ladder based scheme cannot resolve the level ordering issue between the Roper and the negative parity ground state discussed in the beginning of this review. One should also note that the superficial disagreement between the model results of [25,344] and the rainbowladder calculation of [421] is not a matter of principle but merely the consequence of a different perspective on setting the scale and interpreting the corresponding results. For the negative parity ground states, a similar effect is seen in the quark-diquark rainbow-ladder framework also shown in the left panel of Fig.…”

“…[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. m N = 1.14 and m N = 1.18 GeV, respectively.…”