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000893066 1001_ $$0P:(DE-Juel1)171116$$aSilvi, Giorgio$$b0$$eCorresponding author$$ufzj
000893066 245__ $$a$P$-wave nucleon-pion scattering amplitude in the $\Delta(1232)$ channel from lattice QCD
000893066 260__ $$aMelville, NY$$bInst.$$c2021
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000893066 520__ $$aWe determine the $\Delta(1232)$ resonance parameters using lattice QCD and the L{\"u}scher 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, respectively, and the strong decay channel $\Delta \rightarrow \pi N$ 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 $g_{\Delta\text{-}\pi N}=23.8(2.7)(0.9)$.
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000893066 7001_ $$00000-0002-5713-0039$$aNegele, John$$b6
000893066 7001_ $$0P:(DE-HGF)0$$aPetschlies, Marcus$$b7
000893066 7001_ $$0P:(DE-HGF)0$$aPochinsky, Andrew$$b8
000893066 7001_ $$00000-0002-6807-6760$$aRendon, Gumaro$$b9
000893066 7001_ $$00000-0003-1189-2940$$aSyritsyn, Sergey$$b10
000893066 7001_ $$00000-0003-3736-9410$$aTodaro, Antonino$$b11
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000893066 773__ $$0PERI:(DE-600)2844732-3$$a10.1103/PhysRevD.103.094508$$gVol. 103, no. 9, p. 094508$$n9$$p094508$$tPhysical review / D$$v103$$x2470-0010$$y2021
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