Calm Multi-Baryon Operators

Abstract

Outstanding problems in nuclear physics require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolators. Very early in Euclidean time this linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions. To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ $\sim$ 800 MeV --- the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

8 pages, 3 figures, proceedings for LATTICE 2017

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• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD
• Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Unified contraction algorithm for multi-baryon correlators on the lattice
• Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

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