Abstract
There are many outstanding problems in nuclear physics which 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 so far 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 interpolating fields. Very early in Euclidean time this optimal 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~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly 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.
Highlights
To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ ∼ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions
With only different choices of smearing at the sink, we have observed that extending this method to three or more correlation functions makes the analysis unstable: more noise was introduced through the linear combination of more than two correlation functions, offsetting any extra gain in early time; beyond two solutions, the Matrix Prony (MP) method can produce unphysical complex eigenvalues which arise from the numerical data as small oscillations in time that often appear with high statistics calculations
We observe that the reduction of the excited state contamination in the two-nucleon correlation function is more significantly improved in this case, and more importantly, the stochastic noise is not much larger than the original correlation function
Summary
The best technique for constructing a set of good multi-particle operators is the variational method based on the Generalized Eigenvalue Problem (GEVP) [16]. A large basis of operators is constructed and used at both source and sink to create a matrix of correlators, which is diagonalized to produce the best overlap onto the true eigenstates of the system This method has been used extensively and very successfully in the mesonic sector [17,18,19,20,21,22,23]. Multi-nucleon correlators are generally only projected onto definite momentum at the sink, which is sufficient to eliminate overlap onto states with different total momentum These issues have led to investigations of alternative methods that capture some of the benefits of the variational methods without the need for a symmetric matrix of correlation functions. One method which has been used successfully for nucleons (and multi-baryons) is known as the Matrix Prony method, and will be discussed
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