Towards the P-wave nucleon-pion scattering amplitude in the $\Delta$ (1232) channel

Abstract

We use lattice QCD and the Lüscher method to study elastic pion-nucleon scattering in the isospin I = 3/2 channel, which couples to the ∆ (1232) resonance. Our N f = 2 + 1 flavor lattice setup features a pion mass of m π ≈ 250 MeV, such that the strong decay channel ∆ → πN is close to the threshold. We present our method for constructing the required lattice correlation functions from single-and two-hadron interpolating fields and their projection to irreducible representations of the relevant symmetry group of the lattice. We show preliminary results for the energy spectra in selected moving frames and irreducible representations, and extract the scattering phase shifts. Using a Breit-Wigner fit, we also determine the resonance mass m ∆ and the g ∆ −πN coupling.

Meson-Nucleon Scattering Amplitudes from Lattice QCD

“…Preliminary results from Ref. [68] are also shown in Fig. 2, which result in a value of the coupling g ∆Nπ compatible with Ref.…”

“…Preliminary results on the ∆(1232) resonance are also found in Ref. [68] on a single ensemble of N f = 2 + 1 dynamical fermions at m π = 250MeV. There the leading partial wave approximation is applied and all necessary Wick contractions are evaluated using a combination of sequential, stochastic and point-to-all propagators.…”

I=3/2Nπ scattering and the ∆(1232) resonance on $N_f=2+1$ CLS ensembles using the stochastic LapH method

“…[13], but other preliminary work can be found in Refs. [23][24][25]. The ∆baryons decay almost exclusively to Nπ states [26], so we need only worry about a single open channel.…”

Recent highlights with baryons from lattice QCD

“…then below 3-particle thresholds, there is a quantization condition det(1 − B (P) K) = det(1 − KB (P) ) = 0 (16) or det( K −1 − B (P) ) = 0 (17) where the Hermitian "box matrix" B (P) encodes the effects of the cubic finite-volume. Details about the box matrix may be found in Ref.…”

“…Preliminary results for the Δ resonance in another recent study using a lattice with length L = 2.8 fm, spacing a = 0.116 fm and pion mass m π = 260 MeV has appeared in Ref. [16]. No slice-to-slice propagators were used, three total momenta were studied, the ground and excited states were extracted, and their analysis included only a single partial wave.…”