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Register a new user$I=2$ $pipi$ potential in the HAL QCD method with all-to-all propagators
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In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $pipi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3 times 32$ lattice at the lattice spacing $a approx 0.12$ fm and $m_{pi} approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $pipi$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $rho$ meson by the HAL QCD potential with the hybrid method.
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In this paper, employing an all-to-all quark propagator technique, we investigate the kaon-nucleon interactions in lattice QCD. We calculate the S-wave kaon-nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations at the lattice spacing $a approx 0.09$ fm on $32^3 times 64$ lattices and the pion mass $m_{pi} approx 570$ MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero momentum hadron operators at both source and sink and to smear quark operators at the source. We find the stronger repulsive interaction in the $I=1$ channel than in the $I=0$. The phase shifts obtained by solving the Schr{o}dinger equations with the potentials qualitatively reproduce the energy dependence of the experimental phase shifts, and have the similar behavior to the previous results from lattice QCD without all-to-all propagators. Our study demonstrates that the all-to-all quark propagator technique with the one-end trick is useful to study interactions for meson-baryon systems in the HAL QCD method, so that we will apply it to meson-baryon systems which contain quark-antiquark creation/annihilation processes in our future studies.
In this paper, we report recent developments of the HAL QCD method for two hadron systems which contain quark annihilation processes using all-to-all quark propagators. We employ the hybrid method for all-to-all propagators, which combines a low-mode spectral decomposition of the quark propagator and stochastic estimators for remaining high modes, to evaluate the HAL QCD potentials for the first time. Using this method, we investigate the $I= 1,2$ $pi pi$ scatterings at $m_{pi} approx 870$ MeV. In the $I=2$ study, we study how statistical fluctuations of the HAL QCD potentials are increased due to stochastic estimators in the hybrid method, compared with the conventional one without them. We find that we can reduce statistical fluctuations by dilutions of stochastic noises in order to obtain sufficiently precise results, which turn out to be consistent with conventional results without all-to-all propagators. In the $I=1$ $pi pi$ case, which contains quark annihilation processes, we find that statistical fluctuations are further enhanced due to noise contaminations in annihilation processes. We, however, confirm that we can also reduce such statistical fluctuations to obtain the potential with a reasonable precision as long as we further increase a degree of dilutions at a price of large numerical costs and take an appropriate scheme for the potential.
Hadron spectroscopy on dynamical configurations are faced with the difficulties of dealing with the mixing of single particle states and multi-hadron states (for large spatial volumes and light dynamical quarks masses). It is conceivable that explicit multi-hadron interpolating operators will be necessary for obtaining sufficiently good overlap onto multi-hadron states in order to extract the low-lying excitation spectrum. We explore here the feasibility of using four noise diluted all-to-all quark propagators in the construction of explicit two-hadron operators on quenched, anisotropic lattices. Our longer term goal is to use these operators on large anisotropic, dynamical configurations for hadron spectroscopy.
We measure the ground and excited states for B mesons in the static limit using maximally variance reduced estimators for light quark propagators. Because of the large number of propagators we are able to measure accurately also orbitally excited P, D and F states. We also present some results for Lambda_b.
We present a study of gauge invariant density-density correlators. Density-density correlators probe hadron wave functions and thus can be used to study hadron deformation. Their zero momentum projection requires the computation of all-to-all propagators, which are evaluated with the standard stochastic technique, the dilution method and the stochastic sequential technique. We compare the results to a previous analysis that did not employ the zero momentum projection.
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