Non-perturbatively Determined Relativistic Heavy Quark Action

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 $ma$ where $\vec{p}$ is the heavy quark's spatial momenta.

46 pages, 6 figures

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• Flavor Physics in the Quark Sector
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• B- and D-meson decay constants from three-flavor lattice QCD
• ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ form factors, differential branching fraction, and angular observables from lattice QCD with relativistic $b$ quarks
• Charmed-Baryon Spectroscopy from Lattice QCD with N_f=2+1+1 Flavors
• Singly and Doubly Charmed J=1/2 Baryon Spectrum from Lattice QCD
• Relativistic Heavy Quark Effective Action
• Quarkonium mass splittings in three-flavor lattice QCD
• Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy
• $B_s\to K\ell \nu$ decay from lattice QCD
• Search for $\bar{b}\bar{b}us$ and $\bar{b}\bar{c}ud$ tetraquark bound states using lattice QCD
• Probing nucleon strange and charm distributions with lattice QCD
• Approaches to inclusive semileptonic $B_{(s)}$-meson decays from Lattice QCD
• Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice
• The B*Bpi coupling using relativistic heavy quarks
• Precision for B-meson matrix elements
• Exclusive semileptonic $B_s\to K\ell \nu$ decays on the lattice
• An exploratory study of heavy domain wall fermions on the lattice
• Heavy flavor physics from lattice QCD
• $B\to \rho \ell \bar{\nu }$ resonance form factors from $B\to \pi \pi \ell \bar{\nu }$ in lattice QCD
• A fully non-perturbative charm-quark tuning using machine learning
• Bottom-Hadron Mass Splittings from Static-Quark Action on 2+1-Flavor Lattices
• Symanzik Improvement with Dynamical Charm: A 3+1 Scheme for Wilson Quarks
• Calculating B-meson decay constants using domain-wall light quarks and nonperturbatively tuned relativistic b-quarks
• Form factors for semi-leptonic $B$ decays
• Standard Model parameters and heavy quarks on the lattice
• Lattice renormalisation of O(a) improved heavy-light operators
• B-Bbar Mixing and Matching with Fermilab Heavy Quarks
• On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD
• An Improved Action for Heavy Quarks
• The Beauty of Lattice Perturbation Theory: The Role of Lattice Perturbation Theory in B Physics
• Binding energy of the $T_{bb}$ tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions