Mean link versus average plaquette tadpoles in lattice NRQCD

We compare mean-link and average plaquette tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. Simulations are done for the three quarkonium systems $c\bar c$, $b\bar c$, and $b\bar b$. The hyperfine splittings are computed both at leading and at next-to-leading order in the relativistic expansion. Results are obtained at a large number of lattice spacings. A number of features emerge, all of which favor tadpole renormalization using mean links. This includes much better scaling of the hyperfine splittings in the three quarkonium systems. We also find that relativistic corrections to the spin splittings are smaller with mean-link tadpoles, particularly for the $c\bar c$ and $b\bar c$ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about one in lattice units (with the bare quark masses turning out to be much larger with mean-link tadpoles).Comment: LATTICE(heavyqk) 3 pages, 2 figure

Update: Accurate Determinations of alpha_s from Realistic Lattice QCD

We use lattice QCD simulations, with MILC configurations (including vacuum polarization from u, d, and s quarks), to update our previous determinations of the QCD coupling constant. Our new analysis uses results from 6 different lattice spacings and 12 different combinations of sea-quark masses to significantly reduce our previous errors. We also correct for finite-lattice-spacing errors in the scale setting, and for nonperturbative chiral corrections to the 22 short-distance quantities from which we extract the coupling. Our final result is alpha_V(7.5GeV,nf=3) = 0.2120(28), which is equivalent to alpha_msbar(M_Z,n_f=5)= 0.1183(8). We compare this with our previous result, which differs by one standard deviation.Comment: 12 pages, 2 figures, 4 table

B Physics on the Lattice: Present and Future

Recent experimental measurements and lattice QCD calculations are now reaching the precision (and accuracy) needed to over-constrain the CKM parameters $\bar\rho$ and $\bar\eta$. In this brief review, I discuss the current status of lattice QCD calculations needed to connect the experimental measurements of $B$ meson properties to quark flavor-changing parameters. Special attention is given to $B\to\pi\ell\nu$, which is becoming a competitive way to determine $|V_{ub}|$, and to $B^0-\bar{B^0}$ mixings, which now include reliable extrapolation to the physical light quark mass. The combination of the recent measurement of the $B_s$ mass difference and current lattice calculations dramatically reduces the uncertainty in $|V_{td}|$. I present an outlook for reducing dominant lattice QCD uncertainties entering CKM fits, and I remark on lattice calculations for other decay channels.Comment: Invited brief review for Mod. Phys. Lett. A. 15 pages. v2: typos corrected, references adde

Unquenched Charmonium with NRQCD - Lattice 2000

We present results from a series of NRQCD simulations of the charmonium system, both in the quenched approximation and with n_f = 2 dynamical quarks. The spectra show evidence for quenching effects of ~10% in the S- and P-hyperfine splittings. We compare this with other systematic effects. Improving the NRQCD evolution equation altered the S-hyperfine by as much as 20 MeV, and we estimate radiative corrections may be as large as 40%.Comment: Lattice 2000 (Heavy Quark Physics

Direct determination of the strange and light quark condensates from full lattice QCD

We determine the strange quark condensate from lattice QCD for the first time and compare its value to that of the light quark and chiral condensates. The results come from a direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution, derived here, to convert the non-normal-ordered mψ̅ ψ to the MS̅ scheme at a fixed scale. This is then a well-defined physical “nonperturbative” condensate that can be used in the operator product expansion of current-current correlators. The perturbative subtraction is calculated through O(αs) and estimates of higher order terms are included through fitting results at multiple lattice spacing values. The gluon field configurations used are “second generation” ensembles from the MILC collaboration that include 2+1+1 flavors of sea quarks implemented with the highly improved staggered quark action and including u/d sea quarks down to physical masses. Our results are ⟨s̅ s⟩MS̅ (2  GeV)=-(290(15)  MeV)3, ⟨l̅ l⟩MS̅ (2  GeV)=-(283(2)  MeV)3, where l is a light quark with mass equal to the average of the u and d quarks. The strange to light quark condensate ratio is 1.08(16). The light quark condensate is significantly larger than the chiral condensate in line with expectations from chiral analyses. We discuss the implications of these results for other calculations

The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory

The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.Comment: 9pp (REVTEX manuscript). Postscript figures appende

Unstable Modes in Three-Dimensional SU(2) Gauge Theory

We investigate SU(2) gauge theory in a constant chromomagnetic field in three dimensions both in the continuum and on the lattice. Using a variational method to stabilize the unstable modes, we evaluate the vacuum energy density in the one-loop approximation. We compare our theoretical results with the outcomes of the numerical simulations.Comment: 24 pages, REVTEX 3.0, 3 Postscript figures included. (the whole postscript file (text+figures) is available on request from [email protected]

Unquenching effects on the coefficients of the L\"uscher-Weisz action

The effects of unquenching on the perturbative improvement coefficients in the Symanzik action are computed within the framework of L\"uscher-Weisz on-shell improvement. We find that the effects of quark loops are surprisingly large, and their omission may well explain the scaling violations observed in some unquenched studies.Comment: 7 pages, 5 figures, uses revtex4; version to appear in Phys.Rev.

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

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^\msbar_s(2 {GeV}) = 87(0)(4)(4)(0) MeV, and \hat m^\msbar(2 {GeV}) = 3.2(0)(2)(2)(0) MeV, where \hat m = \sfrac12 (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^\msbar_u(2 {GeV}) = 1.9(0)(1)(1)(2) MeV and m^\msbar_d(2 {GeV}) = 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