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

References in corpus (1)

• Relativistic Heavy Quark Effective Action

Cited by in corpus (5)

• Relativistic Heavy Quark Effective Action
• Bottom-Hadron Mass Splittings from Static-Quark Action on 2+1-Flavor Lattices
• Standard Model parameters and heavy quarks on the lattice
• Lattice renormalisation of O(a) improved heavy-light operators
• An Improved Action for Heavy Quarks