6533b862fe1ef96bd12c6af3

RESEARCH PRODUCT

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

Stefan MeinelMarcus PetschliesJohn W. NegeleStefan KriegStefan KriegAntonino TodaroAntonino TodaroAntonino TodaroSergey SyritsynSergey SyritsynSrijit PaulGumaro RendonAndrew PochinskyConstantia AlexandrouConstantia AlexandrouLuka LeskovecLuka LeskovecGiorgio SilviGiorgio Silvi

subject

Physics010308 nuclear & particles physicsNuclear TheoryLattice (group)Lattice QCDCoupling (probability)01 natural sciencesScattering amplitudeIsospinIrreducible representation0103 physical sciences010306 general physicsNucleonEnergy (signal processing)Mathematical physics

description

We determine the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance parameters using lattice QCD and the L\"uscher 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 $L\ensuremath{\approx}2.8\text{ }\text{ }\mathrm{fm}$. The pion and nucleon masses are ${m}_{\ensuremath{\pi}}=255.4(1.6)\text{ }\text{ }\mathrm{MeV}$ and ${m}_{N}=1073(5)\text{ }\text{ }\mathrm{MeV}$, respectively, and the strong decay channel $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}\ensuremath{\pi}N$ 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 $\stackrel{\ensuremath{\rightarrow}}{P}=\frac{2\ensuremath{\pi}}{L}(1,1,1)$, 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 ${m}_{\mathrm{\ensuremath{\Delta}}}=1378(7)(9)\text{ }\text{ }\mathrm{MeV}$ and the coupling ${g}_{\mathrm{\ensuremath{\Delta}}\ensuremath{-}\ensuremath{\pi}N}=23.8(2.7)(0.9)$.

https://doi.org/10.1103/physrevd.103.094508