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

Abstract

We determine the $\Delta (1232)$ resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering with $J^P=3/2^{+}$ in the isospin $I=3/2$, $P$-wave channel. Our calculation is performed with $N_f=2+1$ flavors of clover fermions on a lattice with $L\approx 2.8$ fm. The pion and nucleon masses are $m_{\pi }=255.4(1.6)$ MeV and $m_N=1073(5)$ MeV, and the strong decay channel $\Delta \to \pi N$ is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $\vec{P}=\frac{2\pi }{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass $m_{\Delta }=1378(7)(9)$ MeV and the coupling $g_{\Delta \text{-}\pi N}=23.8(2.7)(0.9)$.

References in corpus (17)

• Extended Partial-Wave Analysis of piN Scattering Data
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• Electromagnetic excitation of the Delta(1232)-resonance
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Chiral dynamics of the S11(1535) and S11(1650) resonances revisited
• Multichannel one-to-two transition amplitudes in a finite volume
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
• Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon
• Lattice QCD determination of patterns of excited baryon states
• Hadron Spectroscopy with Dynamical Chirally Improved Fermions
• Singularity structure of the pi N scattering amplitude in a meson-exchange model up to energies W < 2.0 GeV
• Phase-shift analysis of low-energy ${\pi }^{\pm }p$ elastic-scattering data
• Lattice operators for scattering of particles with spin
• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• On the definition of the Δmass and width

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