Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics

TL;DR

The paper tackles taste-exchange and discretization errors in staggered-quark lattice QCD by introducing the HISQ action, which suppresses one-loop taste-exchange and eliminates tree-level ${a^2}$ and $(am)^4$ errors to leading order in $v/c$. It develops HISQ through refined link smearing, reunitarization, and a tunable Naik term parameterized by $\epsilon$, and validates the approach with light-quark and charm simulations. The results show taste-exchange is reduced by about a factor of 3–4 relative to ASQTAD for relevant observables, with residual effects below ${\sim}1\%$ at lattice spacings around $a\lesssim 0.1$ fm; charm simulations achieve near-perfect relativistic dispersion with $c^2(p)\approx1$ and a $\psi$–$\eta_c$ splitting near ${111(5)\,\rm MeV}$ on MILC configurations. Together, these findings position HISQ as the most accurate relativistic discretization for charm on current lattices and enable high-precision $D$-physics and charmonium studies with fully dynamical quarks.

Abstract

We use perturbative Symanzik improvement to create a new staggered-quark action (HISQ) that has greatly reduced one-loop taste-exchange errors, no tree-level order a^2 errors, and no tree-level order (am)^4 errors to leading order in the quark's velocity v/c. We demonstrate with simulations that the resulting action has taste-exchange interactions that are at least 3--4 times smaller than the widely used ASQTAD action. We show how to estimate errors due to taste exchange by comparing ASQTAD and HISQ simulations, and demonstrate with simulations that such errors are no more than 1% when HISQ is used for light quarks at lattice spacings of 1/10 fm or less. The suppression of (am)^4 errors also makes HISQ the most accurate discretization currently available for simulating c quarks. We demonstrate this in a new analysis of the psi-eta_c mass splitting using the HISQ action on lattices where a m_c=0.43 and 0.66, with full-QCD gluon configurations (from MILC). We obtain a result of~111(5) MeV which compares well with experiment. We discuss applications of this formalism to D physics and present our first high-precision results for D_s mesons.

Figures (8)

• Figure 1: The leading tree-level taste-exchange interaction, which involves the exchange of a gluon with momentum $\zeta\pi/a$ where each $\zeta_\mu$ is 0 or 1 but $\zeta^2\ne0$.
• Figure 2: Infrared contributions from (naive lattice) quark vacuum polarization corresponding to a pion vacuum polarization loop in a simulation of one flavor. The sums are over all infrared sectors, where quarks have momenta near $p_\mu=\zeta_\mu\pi/a$ for one of the sixteen $\zeta$s consisting of just 0s and 1s. The factors of $1/16$ are from the $1/16$ rule (Eq. (\ref{['sixteenth-rule']})) and cancel the sums. Gluons, to all orders, are implicit in these diagrams.
• Figure 3: The only one-loop diagrams that result in $q\overline{q}\to q\overline{q}$ taste exchange for ASQTAD quarks. Diagrams with additional external quark lines are suppressed by additional powers of $a^2$.
• Figure 4: The speed of light squared, $c^2({\bf p})$, computed for an $\eta_c$ meson using the ASQTAD action with ${\bf p}=(p_\mathrm{min},p_\mathrm{min},0)$ and different Naik-term renormalizations $\epsilon$, where $p_\mathrm{min}$ is the smallest lattice momentum possible (approximately 500 MeV here). The correct value, $\epsilon=0.19(5)$, occurs at the intersection of the interpolating line with the line $c^2=1$, as shown. Here $am_c=.38$.
• Figure 5: The speed of light squared, $c^2({\bf p}^2)$, for $\eta_c$ mesons at different momenta on a lattice where $am_c\approx0.66$ for the HISQ action with $\epsilon= -0.21$. A comparison with other results from Table \ref{['c2-table']} suggests that choosing $\epsilon=-0.22$ would move all points down onto the line $c^2=1$ to within errors.