PoS - Proceedings of Science
Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Hadron Spectroscopy and Interactions
Towards the P-wave nucleon-pion scattering amplitude in the $\Delta$ (1232) channel
S. Paul*, G. Silvi, C. Alexandrou, G. Koutsou, S. Krieg, L. Leskovec, S. Meinel, J. Negele, M. Petschlies, A. Pochinsky, G. Rendon and S. Syritsyn
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Published on: May 29, 2019
We use lattice QCD and the L\"uscher method to study elastic pion-nucleon scattering in the isospin $I = 3/2$ channel, which couples to the $\Delta(1232)$ resonance. Our $N_f=2+1$ flavor lattice setup features a pion mass of $m_\pi \approx 250$ MeV, such that the strong decay channel $\Delta \rightarrow \pi N$ 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 $m_\Delta$ and the $g_{\Delta-\pi N}$ coupling.
DOI: https://doi.org/10.22323/1.334.0089
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