Pion-nucleon scattering in the Roper channel from lattice QCD

Abstract

We present a lattice QCD study of N π scattering in the positive-parity nucleon channel, where the puzzling Roper resonance N * (1440) resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with N f = 2+1 Wilson-clover dynamical fermions, mπ 156 MeV and L 2.9 fm. In addition to a number of qqq interpolating fields, we implement operators for N π in p-wave and N σ in s-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by N (0), N (0)π(0)π(0) (mixed with N (0)σ(0)) and N (p)π(−p) with p 2π/L, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental N π phase-shift would -in the approximation of purely elastic N π scattering -imply an additional eigenstate near the Roper mass mR 1.43 GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that N π elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with N ππ, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of previous lattice studies based just on qqq interpolators, that did not find a Roper eigenstate below 1.65 GeV. The study of the coupled-channel scattering including a three-particle decay N ππ remains a challenge.

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].…”

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data

“…As a prominent example, we cite the numerous attempts to calculate the mass of the Roper resonance and solve the problem of the level ordering between this resonance and the N * (1535) [41][42][43][44][45][46][47][48][49][50]. It is a well known experimental fact that the Roper resonance decays with a significant probability (up to 40%) into the final state of a nucleon and two pions.…”

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

“…Evaluating the integrals and expressing p 0 through A 2 , we finally get 3 10) where at the final stage we have expressed the non-relativistic couplings through the physical observables. Below, we briefly summarize the lessons learned:…”

“…As an example, we quote the calculation of the parameters of the Roper resonance [1][2][3][4][5][6][7][8][9][10], which decays -at a substantial rate -into a nucleon and two pions. The finite-volume effects in such few-body systems are expected to be rather pronounced.…”