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

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
OriginalsprogUdefineret/Ukendt
TidsskriftJHEP
ISSN1126-6708
DOI
StatusUdgivet - 7. feb. 2009

Bibliografisk note

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

Emneord

  • hep-lat

Citer dette

Blossier, Benoit ; Morte, Michele Della ; Hippel, Georg von ; Mendes, Tereza ; Sommer, Rainer. / On the generalized eigenvalue method for energies and matrix elements in lattice field theory. I: JHEP. 2009.
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On the generalized eigenvalue method for energies and matrix elements in lattice field theory. / Blossier, Benoit; Morte, Michele Della; Hippel, Georg von; Mendes, Tereza; Sommer, Rainer.

I: JHEP, 07.02.2009.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - On the generalized eigenvalue method for energies and matrix elements in lattice field theory

AU - Blossier, Benoit

AU - Morte, Michele Della

AU - Hippel, Georg von

AU - Mendes, Tereza

AU - Sommer, Rainer

N1 - (1+28) pages, 9 figures; minor corrections to table 1 and figures, main results unaffected

PY - 2009/2/7

Y1 - 2009/2/7

N2 - 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.

AB - 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.

KW - hep-lat

U2 - 10.1088/1126-6708/2009/04/094

DO - 10.1088/1126-6708/2009/04/094

M3 - Tidsskriftartikel

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

ER -