On the generalized eigenvalue method for energies and matrix elements in lattice field theory

By B. Blossier, M. Morte, G. Hippel, T. Mendes, Rainer Sommer. 2009

382 citations recorded by the source corpus.

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(−(EN+1 − En) t). The gap EN+1 − En can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/mb in HQET.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bb852e71f9fff955bd3a7146e4563b04b278074e

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In Nuclear and High Energy Physics

Citations in the corpus

Light Hadron Masses from Lattice QCD (2012, methodology): “One can overcome these problem by using a variational method (Blossier et al., 2009; Luscher and Wolff, 1990; Michael, 1985).”
Scattering processes and resonances from lattice QCD (2017, methodology): “A technique that has proven extremely effective is to compute a matrix of correlation functions using a basis of operators, Cij(t) ≡ ∫ L dx ∫ L dy e−iP·(x−y) [ 〈0|Ai(x, t)A†j(y, 0)|0〉 ] L , which can be analyzed variationally (Blossier et al., 2009; Luscher and Wolff, 1990; Michael, 1985).”