Lattice HQET with exponentially improved statistical precision

TL;DR

An alternative discretization for static quarks on the lattice retaining the O( a )-improvement properties of the Eichten–Hill action is introduced and B-meson correlation functions are computed with good statistical precision in the static approximation for x 0 >1 fm.

Abstract

We introduce an alternative discretization for static quarks on the lattice retaining the O(a) improvement properties of the Eichten-Hill action. In this formulation, statistical fluctuations are reduced by a factor which grows exponentially with Euclidean time, x_0. For the first time, B-meson correlation functions are computed with good statistical precision in the static approximation for x_0>1 fm. At lattice spacings a \approx 0.1 fm, a \approx 0.08 fm and a \approx 0.07 fm the B_s-meson decay constant is determined in static and quenched approximations. A correction due to the finite mass of the b-quark is estimated by combining these static results with a recent determination of F_Ds.

Figures (3)

• Figure 1: The step scaling function $\Sigma_{\rm A}^{\rm stat}(3.48,a/L)$ for different choices of the action $S_{\rm h}$. Results for $S_{\rm h}^{\rm EH}$ were extrapolated to $\Sigma_{\rm A}^{\rm stat}(3.48,0)$zastat:pap3 ($\bullet$). In all cases $c_{\rm A}^{\rm stat}$ from 1-loop perturbation theory is used, which is sufficient since $\Sigma_{\rm A}^{\rm stat}(3.48,a/L)$ does not depend very sensitively on this improvement coefficient. For $S_{\rm h}^{\rm A}$, $S_{\rm h}^{\rm S}$ and $S_{\rm h}^{\rm HYP}$ points have been displaced on the horizontal axis for clarity.
• Figure 2: The ratio $R_{\rm NS}$, eq. (\ref{['e_SN']}), for the correlation function $f_{\rm A}^{\rm stat}$ for a statistics of 2500 measurements. Circles refer to $S_{\rm h}^{\rm EH}$ while squares and triangles to $S_{\rm h}^{\rm S}$ and $S_{\rm h}^{\rm HYP}$, respectively. $S_{\rm h}^{\rm A}$ behaves like $S_{\rm h}^{\rm S}$. Physical units are set by using $r_{0}=0.5\,{\rm fm}$pot:r0pot:r0_SU3.
• Figure 3: Effective energies for wave functions $\Omega_1$ (open symbols) and $\Omega_2$ (filled symbols) using $S_{\rm h}^{\rm HYP}$ (circles) and $S_{\rm h}^{\rm S}$ (triangles). Results refer to a $24^3 \times 36$ lattice, $\beta=6.2$.