Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks

TL;DR

This work surveys a decade of nonperturbative QCD simulations employing 2+1 flavor improved staggered quarks (asqtad) by the MILC collaboration, detailing the lattice formulations, algorithmic advances, and the public MILC ensembles used to perform controlled continuum and chiral extrapolations. It covers the theoretical framework around staggered fermions, including SChPT and rooting, and documents extensive physics results: light-hadron spectroscopy, light pseudoscalar properties, heavy-light meson masses and decays, semileptonic form factors, and fundamental constants such as α_s and m_c. The report also discusses extensions to mixed-action and heavy-quark frameworks (Fermilab, NRQCD, and HISQ), plus broad applications to B- and D-physics, quarkonium, and hadronic contributions to muon g−2, demonstrating strong agreement with experimental data and providing precise determinations of CKM elements and low-energy constants. Looking forward, the paper anticipates improvements from superfine/ultrafine ensembles, electromagnetic/isospin-breaking corrections, and further heavy-quark action refinements, with HISQ poised to further reduce discretization errors and taste violations. Overall, the MILC program has markedly advanced lattice QCD precision and its role in phenomenology and tests of the Standard Model, setting the stage for future refinements and broader applications.

Abstract

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms and the rapid increase in computing power available to lattice gauge theorists. In this article we describe simulations of full QCD using the improved staggered quark formalism, ``asqtad'' fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about 3 times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. We review the improved staggered formalism, emphasizing both advantages and drawbacks. In particular, we review the procedure for removing unwanted staggered species in the continuum limit. We then describe the asqtad lattice ensembles created by the MILC Collaboration. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. We review physics results obtained with them, and discuss the impact of these results on phenomenology. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constant of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths and more. We conclude with a brief look at highly promising future prospects.

Figures (42)

• Figure 1: Comparison of the ratio of lattice QCD and experimental values for several observables, where the lattice QCD calculations are done in the quenched approximation (left) and with $2+1$ flavors of asqtad sea quarks (right). This is an updated version of a figure from Davies:2003ik.
• Figure 2: Lüscher-Weisz action Wilson loops: a) standard plaquette, b) $2\times1$ rectangle and c) $1\times1\times1$ parallelogram
• Figure 3: Illustration of taste violations for staggered fermion actions with various link fattenings. The valence quark masses were adjusted to give the same $m_{\pi_5}/m_\rho = 0.55$ for all fermion actions. The results are for quenched gauge field configurations with a Symanzik improved gauge action using $\beta= 7.30$. The staggered fermion actions are standard, or one-link (OL), "fat3+Naik" (OFN) , "fat5" and "asqtad". The pions are labeled by the taste structure, with the taste singlet the heaviest, and the taste pseudoscalar ($\pi_5$), the pseudo-Goldstone boson, the lightest. For more comparisons see Orginos:1999kg.
• Figure 4: The pressure (left) per fermion degree of freedom for free Kogut-Susskind, Naik, Wilson and "p4" Heller:1999xz fermions as a function of $N_T = 1/(aT)$. The continuum value is shown as the horizontal solid line. Figure from Bernard:2004je; an earlier version appeared in Bernard:1997mz. The 'speed of light squared', (right), calculated from the pion dispersion relation, for Naik and K-S pions. Figure from Bernard:1997mz.
• Figure 5: Rho masses (left) and nucleon masses (right) in units of $r_1 \approx 0.32$ fm, in a slight update from Bernard:1999xx. Octagons are unimproved staggered fermions with Wilson gauge action, diamonds are unimproved staggered fermions with Symanzik improved gauge action, crosses are Naik fermions and squares are asqtad fermions, both with Symanzik improved gauge action. For comparison we also show tadpole clover improved Wilson fermions with Wilson gauge action Bowler:1999ae (fancy squares) and with Symanzik improved gauge action Collins:1996zc (fancy diamonds).