Hamiltonian effective field theory study of the N*(1440) resonance in lattice QCD

Abstract

We examine the phase shifts and inelasticities associated with the N * (1440) Roper resonance and connect these infinite-volume observables to the finite-volume spectrum of lattice QCD using Hamiltonian effective field theory. We explore three hypotheses for the structure of the Roper resonance. All three hypotheses are able to describe the scattering data well. In the third hypothesis the Roper resonance couples the low-lying bare basis-state component associated with the ground state nucleon with the virtual meson-baryon contributions. Here the non-trivial superpositions of the meson-baryon scattering states are complemented by bare basis-state components explaining their observation in contemporary lattice QCD calculations. The merit of this scenario lies in its ability to not only describe the observed nucleon energy levels in large-volume lattice QCD simulations but also explain why other low-lying states have been missed in today's lattice QCD results for the nucleon spectrum.

The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD

“…While we do not perform continuum and chiral extrapolations here, our data can be used for future such extrapolations. Chiral extrapolations of lattice scattering data using unitarized extensions of chiral effective theory [65,[67][68][69][70][71][72][73][74] have been performed, although to date cutoff effects have not been considered. Nonetheless, it is evident in our data that cutoff effects in both the scattering amplitude (shown in Fig.…”

“…In order to extrapolate to the physical point and continuum, a range of pion masses m π = 200 − 280 MeV and lattice spacings a = 0.050 − 0.086 fm are employed. Such extrapolations have been performed recently using chiral perturbation theory and its extensions [63][64][65][66][67][68][69][70][71][72][73][74] and treat all scattering data simultaneously. As these extrapolations are somewhat involved and have not yet treated cutoff effects, we present the determination of the amplitudes only in this work and leave extrapolation to the physical quark masses and continuum for the future.…”

Valence quark contributions for the γ*N→N(1440) form factors from light-front holography

“…It is worth mentioning that some authors interpret the Roper as a dynamically-generated baryon-meson resonance, without an explicit reference to three-quark systems, except for the nucleon and the Δð1232Þ [105][106][107][108]. As far as we know, there are no calculations of γ Ã N → Nð1440Þ transition form factors for intermediate and large Q 2 , based on dynamically-generated resonance models for the Roper.…”

“…As far as we know, there are no calculations of γ Ã N → Nð1440Þ transition form factors for intermediate and large Q 2 , based on dynamically-generated resonance models for the Roper. Future lattice QCD simulations can help to understand the role of the baryon-meson contribution for the transition form factors at low Q 2 [107,108].…”

Genuine quark state versus dynamically generated structure for the Roper resonance

“…The Graz-Ljubljana group has concluded that πN channel alone does not render a low-lying resonance and that coupling with ππN channels seems to be important, which supports the dynamical origin of the Roper. The Adelaide group analyzed two scenarios of the resonance formation in the framework of the Hamiltonian effective field theory [30,31], the dynamical generation and the generation through a lowlying bare-baryon resonant state: while both these effective models reproduce well the experimental phase shift by suitably adjusting model parameters, only the former scenario provides an adequate interpretation of the lattice results of the GrazLjubljana group [28]. The width of the Roper resonance and the quark mass dependence of its mass has also been investigated in relativistic baryon ChiPT [32,33].…”