Elastic Nucleon-Pion scattering amplitudes in the $\Delta$ channel at physical pion mass from Lattice QCD

Abstract

We present an investigation of pion-nucleon elastic scattering in the $I(J^P)=\frac{3}{2}({\frac{3}{2}}^{+})$ channel using lattice QCD with degenerate up and down, strange and charm quarks with masses tuned to their physical values. We use an ensemble of twisted mass fermions with box size $L=5.1\mathrm{fm}$ and lattice spacing $a=0.08\mathrm{fm}$ and we consider the $\pi N$ system in rest and moving frames up to total momentum ${\vec{P}}^2=3(2\pi /L{)}^2$ = 0.17 GeV${}^2$. We take into account the finite volume symmetries and $S$- and $P$-wave mixing, and use the Lüscher formalism to simultaneously constrain the $J=1/2,\ell =0$ and $J=3/2,\ell =1$ scattering amplitudes. We estimate the $\Delta$ resonance pole in the $P$-wave channel as well as the $S$-wave isospin-3/2 scattering length.

18 pages, 18 figures, 10 tables; v2 matches published version

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Cited by in corpus (2)

• Investigation of pion-nucleon contributions to nucleon matrix elements
• Higher order quantization conditions for two-body scattering with spin