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Non-perturbatively Determined Relativistic Heavy Quark Action
High Energy Physics - Lattice · Submitted 9 Aug 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This apparent non-uniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction $c_E=c_B$ is permitted through order $a|\vec p|$ and to all orders in $m a$ where $\vec p$ is the heavy quark's spatial momenta.
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The abstract, sentence by sentence
We present a method to non-perturbatively determine the parameters of the on-shell, $O(a)$-improved relativistic heavy quark action. These three parameters, $m_0$, $\zeta$, and $c_B=c_E$ are obtained by matching finite-volume, heavy-heavy and heavy-light meson masses to the exact relativistic spectrum through a finite-volume, step-scaling recursion procedure. We demonstrate that accuracy on the level of a few percent can be achieved by carrying out this matching on a pair of lattices with equal physical spatial volumes but quite different lattice spacings. A fine lattice with inverse lattice spacing $1/a=5.4$ GeV and $24^3 \times 48$ sites and a coarse, $1/a=3.6$ GeV, $16^3 \times 32$ lattice are used together with a heavy quark mass $m$ approximately that of the charm quark. This approach is unable to determine the initially expected, four heavy-quark parameters: $m_0$, $\zeta$, $c_B$ and $c_E$. This apparent non-uniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction $c_E=c_B$ is permitted through order $a|\vec p|$ and to all orders in $m a$ where $\vec p$ is the heavy quark's spatial momenta.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a method to non-perturbatively determine the parameters of the on-shell, $O(a)$-improved relativistic heavy quark action. | contribution 0.99 | 0.94 | 0.23 | asserted 1.00 |
| s1 | These three parameters, $m_0$, $\zeta$, and $c_B=c_E$ are obtained by matching finite-volume, heavy-heavy and heavy-light meson masses to the exact relativistic spectrum through a finite-volume, step-scaling recursion procedure. | method 0.99 | 0.89 | 0.18 | asserted 1.00 |
| s2 | We demonstrate that accuracy on the level of a few percent can be achieved by carrying out this matching on a pair of lattices with equal physical spatial volumes but quite different lattice spacings. | result 0.96 | 0.90 | 0.25 | asserted 0.99 |
| s3 | A fine lattice with inverse lattice spacing $1/a=5.4$ GeV and $24^3 \times 48$ sites and a coarse, $1/a=3.6$ GeV, $16^3 \times 32$ lattice are used together with a heavy quark mass $m$ approximately that of the charm quark. | method 0.99 | 0.89 | 0.03 | asserted 0.99 |
| s4 | This approach is unable to determine the initially expected, four heavy-quark parameters: $m_0$, $\zeta$, $c_B$ and $c_E$. | limitation 0.76 | 0.82 | 0.16 | asserted 1.00 |
| s5 | This apparent non-uniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction $c_E=c_B$ is permitted through order $a|\vec p|$ and to all orders in $m a$ where $\vec p$ is the heavy quark's spatial momenta. | interpretation 0.84 | 0.58 | 0.26 | asserted 0.99 |
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The paper
Original abstract
We present a method to non-perturbatively determine the parameters of the on-shell, $O(a)$-improved relativistic heavy quark action. These three parameters, $m_0$, $\zeta$, and $c_B=c_E$ are obtained by matching finite-volume, heavy-heavy and heavy-light meson masses to the exact relativistic spectrum through a finite-volume, step-scaling recursion procedure. We demonstrate that accuracy on the level of a few percent can be achieved by carrying out this matching on a pair of lattices with equal physical spatial volumes but quite different lattice spacings. A fine lattice with inverse lattice spacing $1/a=5.4$ GeV and $24^3 \times 48$ sites and a coarse, $1/a=3.6$ GeV, $16^3 \times 32$ lattice are used together with a heavy quark mass $m$ approximately that of the charm quark. This approach is unable to determine the initially expected, four heavy-quark parameters: $m_0$, $\zeta$, $c_B$ and $c_E$. This apparent non-uniqueness of these four parameters motivated the analytic result, presented in a companion paper, that this set is redundant and that the restriction $c_E=c_B$ is permitted through order $a|\vec p|$ and to all orders in $m a$ where $\vec p$ is the heavy quark's spatial momenta.
Human review
References
How the literature uses it
37 arXiv papers cite this in 43 sentences
Papers citing it · 13 sentences without a confident label
Uses its method or tool 23 papers
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The bottom quark has been simulated at its physical mass using the Columbia formulation of the relativistic-heavy-quark (RHQ) action [ref] , which is based on the Fermilab heavy quark action [ref] .
Approaches to inclusive semileptonic $B_{(s)}$-meson decays from Lattice QCD · Numerical setup · 0.99
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In particular, we use the relativistic heavy quark (RHQ) action [ref] , which allows us to simulate the $b$ quark at its physical mass.
Inclusive semi-leptonic $B_{(s)}$ mesons decay at the physical $b$ quark mass · Introduction · 1.00
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For the $b$ quarks we use the anisotropic Sheikholeslami-Wohlert (clover) action with the relativistic heavy-quark (RHQ) interpretation [ref] .
Calculating B-meson decay constants using domain-wall light quarks and nonperturbatively tuned relativistic b-quarks · Computational setup · 1.00
Cites it as background 4 papers
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Finally, in [ref] a more conventional non-perturbative tuning of the 4-parameter action with $r_t=1$ and $r_s=ν$, and of the 3-parameter action where additionally $c_E=c_B$ has been performed.
A fully non-perturbative charm-quark tuning using machine learning · Charm-quark action · 0.92
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References [ref] aim at a reduction of the quadratic and higher, $n≥2$, terms by tree-level and one-loop perturbation theory.
Symanzik Improvement with Dynamical Charm: A 3+1 Scheme for Wilson Quarks · Introduction · 0.84
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Several different approaches have been suggested for determining the parameters $m_Q$, $ν$, $c_B$, and $c_E$ [ref] .
Charmed bottom baryon spectroscopy from lattice QCD · Charm quark action · 0.97
Discussion
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