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Lattice calculation of hadronic tensor of the nucleon
We report an attempt to calculate the deep inelastic scattering structure
functions from the hadronic tensor calculated on the lattice. We used the
Backus-Gilbert reconstruction method to address the inverse Laplace
transformation for the analytic continuation from the Euclidean to the
Minkowski space.Comment: 8 pages, 5 figures; Proceedings of the 35th International Symposium
on Lattice Field Theory, 18-24 June 2017, Granada, Spai
Variance Reduction and Cluster Decomposition
It is a common problem in lattice QCD calculation of the mass of the hadron
with an annihilation channel that the signal falls off in time while the noise
remains constant. In addition, the disconnected insertion calculation of the
three-point function and the calculation of the neutron electric dipole moment
with the term suffer from a noise problem due to the
fluctuation. We identify these problems to have the same origin and the
problem can be overcome by utilizing the cluster decomposition
principle. We demonstrate this by considering the calculations of the glueball
mass, the strangeness content in the nucleon, and the CP violation angle in the
nucleon due to the term. It is found that for lattices with physical
sizes of 4.5 - 5.5 fm, the statistical errors of these quantities can be
reduced by a factor of 3 to 4. The systematic errors can be estimated from the
Akaike information criterion. For the strangeness content, we find that the
systematic error is of the same size as that of the statistical one when the
cluster decomposition principle is utilized. This results in a 2 to 3 times
reduction in the overall error.Comment: 7 pages, 5 figures, appendix added to address the systematic erro
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