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Calculation of fermion loops for $η^\prime$ and nucleon scalar and electromagnetic form factors

C. Alexandrou, K. Hadjiyiannakou, G. Koutsou, A. 'O Cais, A. Strelchenko

TL;DR

This work benchmarks exact GPU-based evaluation of disconnected fermion loops against stochastic dilution schemes and the truncated solver method for $N_f=2$ Wilson lattice QCD on a $16^3\times32$ lattice. By studying loops entering the $\eta'$ mass, nucleon electromagnetic form factors, and nucleon scalar form factors, the authors quantify how many noise vectors are required for convergence and identify the truncated solver method as the most efficient approach across operator insertions, with notable speedups for scalar operators. They report an $\eta'$ mass of $am_{\eta'}=0.54(10)$ ($m_{\eta'}=1.17(22)\ \text{GeV}$) and a nucleon sigma-term $\sigma_l=0.50(8)$ GeV at $m_\pi\approx750$ MeV, along with precise assessments of the noisy disconnected contributions to EM form factors. Overall, the results provide practical guidance on selecting stochastic techniques for disconnected diagrams and illustrate the benefits of GPU-accelerated exact benchmarks for lattice QCD observables.

Abstract

The exact evaluation of the disconnected diagram contributions to the flavor-singlet pseudoscalar meson mass, the nucleon sigma term and the nucleon electromagnetic form factors, is carried out utilizing GPGPU technology with the NVIDIA CUDA platform. The disconnected loops are also computed using stochastic methods with several noise reduction techniques. Various dilution schemes as well as the truncated solver method are studied. We make a comparison of these stochastic techniques to the exact results and show that the number of noise vectors depends on the operator insertion in the fermionic loop.

Calculation of fermion loops for $η^\prime$ and nucleon scalar and electromagnetic form factors

TL;DR

This work benchmarks exact GPU-based evaluation of disconnected fermion loops against stochastic dilution schemes and the truncated solver method for Wilson lattice QCD on a lattice. By studying loops entering the mass, nucleon electromagnetic form factors, and nucleon scalar form factors, the authors quantify how many noise vectors are required for convergence and identify the truncated solver method as the most efficient approach across operator insertions, with notable speedups for scalar operators. They report an mass of () and a nucleon sigma-term GeV at MeV, along with precise assessments of the noisy disconnected contributions to EM form factors. Overall, the results provide practical guidance on selecting stochastic techniques for disconnected diagrams and illustrate the benefits of GPU-accelerated exact benchmarks for lattice QCD observables.

Abstract

The exact evaluation of the disconnected diagram contributions to the flavor-singlet pseudoscalar meson mass, the nucleon sigma term and the nucleon electromagnetic form factors, is carried out utilizing GPGPU technology with the NVIDIA CUDA platform. The disconnected loops are also computed using stochastic methods with several noise reduction techniques. Various dilution schemes as well as the truncated solver method are studied. We make a comparison of these stochastic techniques to the exact results and show that the number of noise vectors depends on the operator insertion in the fermionic loop.

Paper Structure

This paper contains 7 sections, 24 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Lattice ensemble and simulation parameters
  3. Evaluation of the $\eta^\prime$ mass
  4. Nucleon Electromagnetic form factors
  5. Nucleon scalar form factors
  6. Conclusions
  7. Acknowledgment

Figures (12)

  • Figure 1: Left panel: The error on the disconnected part of the $\eta^\prime$ correlator $D(t)$ at $t/a=3$ as a function of the number of inversions. The line shows the statistical error. Right panel: The disconnected part of the $\eta^\prime$ correlator $D(t)$ at $t/a=3$ computed stochastically as a function of the number of inversions. The lines show the mean value and error band of the exact result for $D(t)$ at the same time slide. In both graphs we show, from top to bottom, results using: color, spin, even-odd and cubic dilution.
  • Figure 2: In the left panel we show the error on the disconnected and on the right the disconnected part of the $\eta^\prime$ correlator $D(t)$ at $t/a=3$ using the truncated solver method as a function of the number of low precision noise vectors for: 10 (top), 50 (middle) and 120 (bottom) high precision noise vectors. The lines show the mean value and error band of the exact result for $D(t)$ at the same time slide.
  • Figure 3: The ratio $R(t)=\frac{D(t)}{C_{\pi}(t)}$ computed using the truncated solver method and the exact approach. With the filled (red) squares we show the exact calculation and with the filled (green) circles, the filled (blue) triangles and the filled (magenta) rhombus when using 10, 50 and 120 high precision noise vectors, respectively.
  • Figure 4: The mass of $\eta^\prime$ as a function of computational cost (high precision inversions). The exact result is shown with the filled (red) squares and the results of the stochastic truncated solver method with the filled (green) circles as a function of the number of high precision vectors.
  • Figure 5: Left: Connected nucleon three-point function. Right: Disconnected nucleon three-point function.
  • ...and 7 more figures