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Lattice gauge theory with staggered fermions: how, where, and why (not)

Andreas S. Kronfeld

TL;DR

The paper addresses the nonperturbative validity of rooting the 4-taste staggered fermion determinant to one flavor per species, a practical technique in 2+1 flavor lattice QCD. It develops a theoretical framework (Gedanken algorithm, replica trick, RS$\chi$PT, and Symanzik effective theory) to understand how phantoms arise and cancel, and how unitarity violations at finite lattice spacing are controlled in the continuum limit. It robustly refutes key criticisms by analyzing limit-ordering, topology, anomalies, and 't Hooft vertices, and explains why rooted staggered fermions can produce correct continuum physics with careful treatment. The work also discusses new developments (HISQ and gauge-action improvements) that reduce taste-breaking and radiative corrections, underscoring the practical viability and evolving reliability of rooted staggered fermions for LHC-era phenomenology.

Abstract

Many results from lattice QCD of broad importance to particle and nuclear physics are obtained with 2+1 flavors of staggered sea quarks. In the continuum limit, staggered fermions yield four species, called tastes. To reduce the number of tastes to one (per flavor), the simulation employs the fourth root of the four-taste staggered fermion determinant. This talk surveys evidence in favor of this procedure, refutes recent criticisms, and reviews recent algorithmic and technical improvements. Physics results are covered in other plenary talks.

Lattice gauge theory with staggered fermions: how, where, and why (not)

TL;DR

The paper addresses the nonperturbative validity of rooting the 4-taste staggered fermion determinant to one flavor per species, a practical technique in 2+1 flavor lattice QCD. It develops a theoretical framework (Gedanken algorithm, replica trick, RSPT, and Symanzik effective theory) to understand how phantoms arise and cancel, and how unitarity violations at finite lattice spacing are controlled in the continuum limit. It robustly refutes key criticisms by analyzing limit-ordering, topology, anomalies, and 't Hooft vertices, and explains why rooted staggered fermions can produce correct continuum physics with careful treatment. The work also discusses new developments (HISQ and gauge-action improvements) that reduce taste-breaking and radiative corrections, underscoring the practical viability and evolving reliability of rooted staggered fermions for LHC-era phenomenology.

Abstract

Many results from lattice QCD of broad importance to particle and nuclear physics are obtained with 2+1 flavors of staggered sea quarks. In the continuum limit, staggered fermions yield four species, called tastes. To reduce the number of tastes to one (per flavor), the simulation employs the fourth root of the four-taste staggered fermion determinant. This talk surveys evidence in favor of this procedure, refutes recent criticisms, and reviews recent algorithmic and technical improvements. Physics results are covered in other plenary talks.

Paper Structure

This paper contains 18 sections, 48 equations, 1 figure.

Table of Contents

  1. Why this paper?
  2. The lattice community in the LHC era
  3. Staggered fermions without rooting
  4. Rooting with full SU(4) taste symmetry
  5. Rooting with staggered fermions
  6. Explicit refutation of Refs. Creutz:2006ysCreutz:2006wvCreutz:2007ygCreutz:2007nvCreutz:2007rk
  7. Order of limits
  8. Mutilated quark-mass dependence
  9. Cancellation of non-unitary contributions
  10. Rank of chiral symmetry
  11. Anomalies
  12. Topology
  13. 't Hooft vertices
  14. Summary
  15. New developments
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Pseudoscalar spectrum for 2 flavors of staggered fermion, so 8 species in all. The isovector multiplets (with $I_3=+1$, $0$, $-1$) each consist of sixteen states, split by lattice artifacts of order $\Lambda^4a^2$ into submultiplets with 1, 4, 6, 4, and 1 states (for, respectively, irreps of taste $I$, $V$, $T$, $A$, and $P$). The isosinglet multiplet is similar, except that the taste-singlet $I$ splits from the others by continuum-QCD effects (as usual). This $\eta'$-like state suffers from noisy correlators, and numerical data are consistent with this picture without being definitive Gregory:2007ev.