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Title: Gradient Flow and Scale Setting on MILC HISQ Ensembles

We report on a scale determination with gradient-flow techniques on the N f = 2 + 1 + 1 HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales p √t 0/a and w 0/a and their tree-level improvements,√t 0;imp and w 0;imp, are computed on each ensemble using Symanzik ow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We also determine the scales p t 0 = 0:1416( +8 -5) fm and w 0 = 0:1717( +12 -11) fm, where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of w 0 and √t 0 is comparable to or more precise than the best previous estimates, respectively. We also find the continuum mass-dependence of w 0 that will be useful for estimating the scales of other ensembles. Furthermore, we estimate the integrated autocorrelation length of . For long flowmore » times, the autocorrelation length of appears to be comparable to or smaller than that of the topological charge.« less
 [1] ;  [2] ;  [2] ;  [2] ;  [3] ;  [3] ;  [3] ;  [4] ;  [5] ;  [6] ;  [7] ;  [8] ;  [9]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Washington Univ., St. Louis, MO (United States)
  3. Univ. of Utah, Salt Lake City, UT (United States)
  4. Indiana Univ., Bloomington, IN (United States)
  5. American Physical Society (APS), Ridge, NY (United States)
  6. Syracuse Univ., NY (United States)
  7. Univ. of California, Santa Barbara, CA (United States)
  8. Univ. of Arizona, Tucson, AZ (United States)
  9. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 2470-0010; PRVDAQ; arXiv eprint number arXiv:1503.02769; TRN: US1601622
Grant/Contract Number:
AC02-07CH11359; FG02-91ER40628; FC02-12ER41879; FG02-91ER40661; SC0010120; FG02-13ER-41976; AC02-98CH10886
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 93; Journal Issue: 9; Journal ID: ISSN 2470-0010
American Physical Society (APS)
Research Org:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Contributing Orgs:
MILC Collaboration
Country of Publication:
United States
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1254380