Tue·Nov 15, 2005Tuesday·November 15, 2005

1. 01*

   Ground state energy of spin-1/2 fermions in the unitary limit

   Dean Lee (North Carolina State University)🇺🇸

   We present lattice results for the ground state energy of a spin-1/2 fermion system in the unitary limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground state energy for a system of 6, 10, 14, 18, and 22 particles, with equal numbers of up and down spins in a periodic cube. We estimate that in the limit of large number of particles, the ground state energy is 0.25(3) times the ground state energy of the free Fermi system.

   ↳ cond-mat.stat-mechhep-latnucl-thPRB(2006)·53 citations
2. 02*

   High-precision determination of the light-quark masses from realistic lattice QCD

   Quentin Mason🇬🇧 · Howard D. Trottier🇨🇦 · Ron Horgan🇬🇧 · Christine T. H. Davies🇬🇧 · G. Peter Lepage🇺🇸

   Three-flavor lattice QCD simulations and two-loop perturbation theory are used to make the most precise determination to date of the strange-, up-, and down-quark masses, $m_s$, $m_u$, and $m_d$, respectively. Perturbative matching is required in order to connect the lattice-regularized bare- quark masses to the masses as defined in the \msbar scheme, and this is done here for the first time at next-to-next-to leading (or two-loop) order. The bare-quark masses required as input come from simulations by the MILC collaboration of a highly-efficient formalism (using so-called ``staggered'' quarks), with three flavors of light quarks in the Dirac sea; these simulations were previously analyzed in a joint study by the HPQCD and MILC collaborations, using degenerate $u$ and $d$ quarks, with masses as low as $m_s/8$, and two values of the lattice spacing, with chiral extrapolation/interpolation to the physical masses. With the new perturbation theory presented here, the resulting \msbar\ masses are $m_s^{\text{msbar}}(2GeV)=87(0)(4)(4)(0)$ MeV, and ${\hat{m}}^{\text{msbar}}(2GeV)=3.2(0)(2)(2)(0)$ MeV, where $\hat{m}=\text{sfrac}12(m_u+m_d)$ is the average of the $u$ and $d$ masses. The respective uncertainties are from statistics, simulation systematics, perturbation theory, and electromagnetic/isospin effects. The perturbative errors are about a factor of two smaller than in an earlier study using only one-loop perturbation theory. Using a recent determination of the ratio $m_u/m_d=0.43(0)(1)(0)(8)$ due to the MILC collaboration, these results also imply $m_u^{\text{msbar}}(2GeV)=1.9(0)(1)(1)(2)$ MeV and $m_d^{\text{msbar}}(2GeV)=4.4(0)(2)(2)(2)$ MeV. A technique for estimating the next order in the perturbative expansion is also presented, which uses input from simulations at more than one lattice spacing.

   ↳ hep-phhep-latPRD(2006)·101 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.