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

Silvi, Giorgio; Paul, Srijit; Alexandrou, Constantia; Krieg, Stefan; Leskovec, Luka; Meinel, Stefan; Negele, John; Petschlies, Marcus; Pochinsky, Andrew; Rendon, Gumaro; Syritsyn, Sergey; Todaro, Antonino

doi:10.1103/PhysRevD.103.094508

Title: $P$ -wave nucleon-pion scattering amplitude in the $Δ (1232)$ channel from lattice QCD

Journal Article · Fri May 14 00:00:00 EDT 2021 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.103.094508· OSTI ID:1782981

Silvi, Giorgio; Paul, Srijit; Alexandrou, Constantia;

;

; Meinel, Stefan;

; Petschlies, Marcus; Pochinsky, Andrew;

;

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 $$\Delta \rightarrow \pi N$$ 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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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division; USDOE Office of Science (SC), High Energy Physics (HEP); German Research Foundation (DFG); European Union’s Horizon 2020

Grant/Contract Number:: AC02-05CH11231; SC0019229; AC05-06OR23177; SC0009913; SC-0011090; SC0018121; SC0012704; SC0011090; 642069; 765048; CRC-110; SFB-TRR 55

OSTI ID:: 1782981

Alternate ID(s):: OSTI ID: 1784909; OSTI ID: 1798469; OSTI ID: 1907979

Report Number(s):: JLAB-THY-21-3408; DOE/OR/23177-5226; arXiv:2101.00689; BNL-221693-2021-JAAM; PRVDAQ; 094508

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 103 Journal Issue: 9; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: P -wave nucleon-pion scattering amplitude in the Δ ( 1232 ) channel from lattice QCD

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Title: $P$ -wave nucleon-pion scattering amplitude in the $Δ (1232)$ channel from lattice QCD