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

This title appears in the Scientific Report : 2021

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

We 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 l...

Personal Name(s):	Silvi, Giorgio (Corresponding author)
	Paul, Srijit / Alexandrou, Constantia / Krieg, Stefan / Leskovec, Luka / Meinel, Stefan / Negele, John / Petschlies, Marcus / Pochinsky, Andrew / Rendon, Gumaro / Syritsyn, Sergey / Todaro, Antonino
Contributing Institute:	Jülich Supercomputing Center; JSC
Published in:	Physical Review D Physical review / D, 103 103 (2021 2021) 9 9, S. 094508 094508
Imprint:	Melville, NY Inst. 2021 2021-05-14 2021-05-01
DOI:	10.1103/PhysRevD.103.094508
Document Type:	Journal Article
Research Program:	Enabling Computational- & Data-Intensive Science and Engineering
Link:	OpenAccess
	Publikationsportal JuSER

Please use the identifier: http://dx.doi.org/10.1103/PhysRevD.103.094508 in citations.
Please use the identifier: http://hdl.handle.net/2128/27916 in citations.

We 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 $g_{\Delta\text{-}\pi N}=23.8(2.7)(0.9)$.