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

Benoit Blossier, Michele Della Morte, Georg von Hippel, Tereza Mendes, Rainer Sommer

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Abstract

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 $\exp(-(E_{N+1}-E_n) t)$. The gap $E_{N+1}-E_n$ 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 $1/m_b$ in HQET.
Original languageUndefined/Unknown
JournalJHEP
ISSN1126-6708
DOIs
Publication statusPublished - 7. Feb 2009

Bibliographical note

(1+28) pages, 9 figures; minor corrections to table 1 and figures, main results unaffected

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