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Lattice QCD studies of the $$\Delta$$ baryon resonance and the $$K_0^\ast(700)$$ and $$a_0(980)$$ meson resonances: the role of exotic operators in determining the finite-volume spectrum

https://doi.org/10.22323/1.453.0074

Skinner, Sarah; Bulava, John; Darvish, Danny; Hanlon, Andrew D.; Hoerz, Ben; Morningstar, Colin; Nicholson, Amy; Romero-Lopez, Fernando; Vranas, Pavlos; Walker-Loud, André (December 2023, Pos proceedings of science)

This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel πΣ−K¯N from lattice QCD data. The importance of reliably extracting such spectra lies in the crucial dependence of the hadronic scattering amplitudes analysis on the energy spectrum when using L\"{u}scher's formalism. Results of the methods used are presented and the final finite-volume spectra are shown. The analysis of the scattering amplitude based on these results, exhibits a two-pole structure for the Λ(1405), a virtual bound state below the πΣ threshold and a resonance pole right below the K¯N threshold.
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Low-lying baryon resonances from lattice QCD

Bulava, John; Cid-Mora Barbara; Hanlon, Andrew; Hoerz, Ben; Mohler, Daniel; Morningstar, Colin; Moscoso, Joseph; Nicholson, Amy; Romero-Lopez, Fernando; Skinner, Sarah; et al (October 2023, Nuovo cimento B, to appear)

Recent results studying the masses and widths of low-lying baryon resonances in lattice QCD are presented. The S-wave Nπ scattering lengths for both total isospins I=1/2 and I=3/2 are inferred from the finite-volume spectrum below the inelastic threshold together with the I=3/2 P-wave containing the Δ(1232) resonance. A lattice QCD computation employing a combined basis of three-quark and meson-baryon interpolating operators with definite momentum to determine the coupled channel Σπ-NKbar scattering amplitude in the Λ(1405) region is also presented. Our results support the picture of a two-pole structure suggested by theoretical approaches based on SU(3) chiral symmetry and unitarity.
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The long-distance behaviour of the vector-vector correlator from pion-pion scattering

https://doi.org/10.22323/1.430.0073

Paul, Srijit; Hanlon, Andrew D.; Hoerz, Ben; Mohler, Daniel; Morningstar, Colin; Wittig, Hartmut (April 2023, 39th International Symposium on Lattice Field Theory)

We present the estimation of the long distance behaviour of the vector-vector correlator computed on a lattice QCD ensemble generated with 2 + 1 flavour physical Wilson clover quarks. The long distance regime of the correlator is dominated by multi-hadronic scattering states. We reconstruct the correlator in this regime using the pion-pion scattering states in the 𝐼 = 1 channel. The vector-vector correlator appears in the integrand to estimate the hadronic vacuum polarization contributions to the anomalous magnetic moment of the muon. Therefore, an improved estimation of the correlator will help resolve the tension between (𝑔 − 2)𝜇 experiment and theory.
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D meson -- pion scattering on CLS 2+1 flavor ensembles

https://doi.org/10.22323/1.430.0068

Mohler, Daniel; Bulava, John; Hoerz, Ben; Johnson, Christopher; Morningstar, Colin; Hudspith, Renwick J. (February 2023, Proceedings of Science)

We report progress on finite-volume determinations of heavy light-meson – Goldstone boson scattering phase shifts using the Luescher method on CLS 2+1 flavor gauge field ensembles. In a first iteration we will focus on D-meson – pion scattering in the elastic scattering region at various pion masses using ensembles with three lattice spacings. We employ ensembles on the CLS quark-mass trajectory with a fixed trace of the quark-mass matrix as well as ensembles with a strange-quark mass fixed close to its physical value, which will allow us to study both the light and the strange quark-mass dependence of positive parity heavy-light hadrons close to threshold.
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