Calm Multi-Baryon Operators

Abstract

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 m π ∼ 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.Speaker,

Lattice QCD input for nuclear structure and reactions

“…Further, the exponential degradation of the signal to noise in systems involving multiple hadrons remains an issue. Nonetheless, new ideas have been suggested in recent years to alleviate these problems, and the results presented previously and in this conference have proven to be promising [71,97,99,100]. As the community moves towards the Exascale computing era [1], and with the advent of new algorithms and novel ideas along the way, the LQCD and QED calculations with physical masses of the light quarks, at larger lattice volumes and with multiple lattice spacings, may become a reality in upcoming years.…”

“…This also means that the two-nucleon systems in the P-wave can benefit from a considerable improvement, as is suggested in Ref. [97].…”

“…The CalLatt collaboration implemented this approach during the past year for the two-nucleon systems, and the preliminary results, shown in the right panel of Fig. 13, demonstrate that the expected improvement is achieved (plot taken from a proceedings to this conference [97]). Even a more significant improvement is observed in the two-nucleon correlation functions that are formed from displaced sources for the nucleons, potentially pointing to the suggestion by the collaboration that the dominant excited-state contributions to a multi-nucleon correlation function (with the present sink-source structures) arise from the excitations of a single nucleon.…”

Towards grounding nuclear physics in QCD

“…For example, a deeply bound state will have a compact wave function and thus couple poorly to a creation operator that is spread out [234]. A further improvement was achieved by using Matrix Prony methods [254,255] to optimize the single-nucleon interpolating fields prior to constructing the two-nucleon states [235,256]. However, this only suppresses contamination from the inelastic single-nucleon excited state and does not address the issue of the closely packed elastic scattering states.…”

On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods

“…For more recent references see Refs. [9][10][11] and also Appendix A. For an application of the Prony method in real time dynamics with Tensor networks see Ref.…”