QCD with Four Flavors of HISQ Quarks


The MILC Collaboration is using the BG/Q, Mira, at ALCF, the Cray XE6/XK6, Blue Waters, at NCSA, Cray XC systems, Edison and Cori at NERSC to generate gauge configurations with four flavors of dynamical HISQ quarks.  We have completed our program to generate configurations with three flavors of dynamical asqtad quarks; however, physics analysis on these ensembles continues.  A table of the asqtad ensembles is available on this web site.  A more detailed description of them, as well as a summary of the physics results obtained with them was published in Reviews of Modern Physics.

Our plan is to generate ensembles with dynamical up, down, strange, and charm HISQ quarks because with them taste breaking is reduced by about a factor of three as compared with asqtad at the same lattice spacing, and the leading lattice spacing artifacts are reduced by a factor of two or more.  We shall use these configurations to extend our studies of the properties of light pseudoscalar mesons, the topological susceptibility, the hadron mass spectrum, and, in conjunction with the Fermilab Lattice Collaboration, the decays and mixings of B and D mesons, the hadronic contributions to the anomalous magnetic moment of the muon, and the axial form factor of the nucleon.  The configurations are available to members of the USQCD Collaboration as they are generated.

Table 1 below shows the current status and future plans for our program to generate gauge configurations with four flavors of Highly Improved Staggered Quarks (HISQ).  In this is work, we keep the strange and charm quark masses m_s and m_c as close as possible to their physical values. The up and down quarks are taken to be degenerate with common mass m_l=m_s/5, m_s/10 and the mass for which the Goldstone pion mass takes on its physical value, which is very close to m_l=m_s/27. The first column of the table gives the lattice spacing, the second the ratio m_l/m_s, the third the lattice dimensions and the fourth m_pi*L, where m_pi is the Goldstone pion mass and L is the spatial width of the box. The fifth column is m_pi in MeV.  Subsequent columns give the number of equilibrated configurations in February, 2015 and 2016.  We plan to generate approximately 1,000 configurations in each ensemble.

We have also generated a limited number of HISQ gauge configurations with the strange quark mass less than it physical value.  Such ensembles are very helpful in controlling the chiral extrapolation, as was demonstrated in the case of the asqtad ensembles.  The parameters of these configurations are listed in Table 2.  All of these ensembles have a lattice spacing of approximately 0.12 fm.  The first two columns of Table 2 give the ratio of the light quark masses to the physical strange quark mass m_s. (We distinguish between the masses of the two light quark because for the ensemble in the last row they are different.)  The third column gives the ratio of the simulation strange quark mass m_s’ to the physical strange quark mass, and the fourth column shows the lattice dimensions.  The fifth and sixth columns show the number of equilibrated configurations as of February, 2011 and February, 2012, respectively.

The MILC Collaboration:

Alexei Bazavov, Claude Bernard, Nathan Brown,

Carleton DeTar, Daping Du, Steven Gottlieb, Urs Heller, James Hetrick, Javad Komijani, Jack Laiho, Chris Monahan,

James Osborn, Thom Primer, Robert Sugar, Doug Toussaint, Ruth Van de Water, Ran Zhou