The Stochastic Laplacian Heaviside Method in Lattice QCD and its First Applications to Hadron Spectroscopy

Currently, the best way to extract the low-energy predictions of quantum chromodynamics (QCD) is by estimating the QCD path integrals using the Monte Carlo method formulated on a space-time lattice. Determining the hadron mass spectrum is one of the major applications of such an approach. To study a particular state of interest, the energies of all states lying below that state must first be extracted, and many of the levels lying below the masses of the excited resonances are multihadron states. Reliably extracting multi-hadron energies is challenging since quark propagators that begin and end on the same final time-slice are essential. A novel method of estimating such quark propagators is proposed. This method, known as the ‘stochastic Laplacian Heaviside’ algorithm, combines Laplacian-Heaviside quark smearing with a new stochastic estimator of quark propagators. The method works well even in large spatial volumes. The implementation of the method is discussed in detail and its effectiveness is demonstrated in various systems, such as in determining the isovector and isoscalar meson energies, and calculating the energies of two-pion states. The inclusion of the scalar glueball is also studied.