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We investigate mesons containing charm quarks on fine lattices with a^{-1} \sim 5 GeV. The quenched approximation is employed using the Wilson gauge action at β= 6.6 and nonperturbatively O(a) improved Wilson quarks. We present results for decay constants using various interpolating fields and give preliminary results for form factors of semileptonic decays of D_s mesons to light pseudoscalar mesons.
The possibility is explored to relate confinement to properties of gauge invariant field strength correlators.
We consider a chirally invariant lattice Higgs-Yukawa model based on the Neuberger overlap operator. As a first step towards the eventual determination of Higgs mass bounds we present the phase structure of the model analytically in the large Nf-limit in the physically interesting region of the Yukawa coupling constant. We confront the analytically obtained phase diagram with corresponding HMC-simulations and find an excellent agreement at large values of Nf. In the opposite case the large Nf computation still gives a good qualitative description of the phase diagram. We also present first and very preliminary results on the Higgs upper bound at one selected cut-off of the theory.
We present a calculation of the form factor for B -> D* l nu using a 2+1 improved staggered action for the light quarks (on the MILC configurations), and the Fermilab action for the heavy quarks. The form factor is computed at zero recoil using a new double ratio method which yields the form factor more directly than previous approaches.
We discuss the current status of our calculation of the physics of pi and K mesons using three dynamical flavors of improved staggered quarks. This year, we have a new ensemble with a lattice spacing of 0.06 fm and a light sea mass of 0.2 m_s, as well as significant increases in statistics at several coarser lattice spacings and/or heavier sea masses. Results for decay constants, quark masses, low energy constants, condensates, and V_{us} are presented.
We present a preliminary calculation of B_K using domain-wall valence quarks and 2+1 flavors of improved staggered sea quarks. Both the size of the residual quark mass, which measures the amount of chiral symmetry breaking, and of the mixed meson splitting Delta_mix, a measure of taste-symmetry breaking, show that discretization effects are under control in our mixed action lattice simulations. We show preliminary data for pseudoscalar meson masses, decay constants and B_K. We discuss general issues associated with the chiral extrapolation of lattice data, and, as an example, present a preliminary chiral and continuum extrapolation of f_pi. The quality of our data shows that the good chiral properties of domain-wall quarks, in combination with the light sea quark masses and multiple lattice spacings available with the MILC staggered configurations, will allow for a precise determination of B_K.
For N>4 there is a first order bulk transition that cleanly separates the strong and weak coupling regimes of SU(N) lattice gauge theories with the plaquette action. We find that in this case the calculated string tension can be readily fitted throughout the weak coupling region by a standard 3-loop perturbative expression modified by lattice spacing corrections of the expected form. While our fits demand the presence of the latter, they are not constraining enough to tell us which of the various bare coupling schemes is a `good' one, in the sense that terms in the beta-function beyond 3-loops are indeed negligible (in the relevant range of scales). To resolve this ambiguity we work in SU(3), using the Schrodinger Functional coupling scheme as a benchmark, and find that the Parisi mean-field improved coupling scheme matches it very well. Using the latter scheme, we have fitted the values of the string tension that have been calculated for SU(3) to SU(8), to obtain Lambda_MSbar/sqrt(sigma) = 0.503(2)(40) + 0.33(3)(3)/N**2, where the first error is statistical and the second is our estimate of the systematic error from all sources.
Employing functional approaches the infrared behaviour of Landau gauge QCD vertex functions is investigated. Results for the ghost-gluon, three-gluon and quark-gluon vertex functions are presented. As can be analytically shown a linear rising potential between heavy quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities implies the existence of scalar Dirac amplitudes of the full vertex and the quark propagator. These amplitudes can only be present when chiral symmetry is broken, either explicitly or dynamically. The corresponding relations thus constitute a novel mechanism that directly links chiral symmetry breaking with confinement.
The QCD phase diagram at finite temperature and density is a topic of considerable interest. Although much progress has been made in recent years, some open questions remain. Even at zero density, the order of the transition for two light flavors of fermions has not yet been conclusively established. While considerable evidence exists in favor of a second-order transition for massless quarks and a crossover for massive quarks, some recent results with two flavors of staggered fermions suggest a transition of first order. Since lattice simulations are performed in finite simulation volumes, actual phase transitions cannot be observed directly. Thus, finite-size scaling is a very useful tool in the analysis of lattice data. By comparing the scaling behavior of observables to the expected scaling properties, values of critical exponents can be confirmed and the order as well as the universality class of a transition can be established. In the comparison to lattice QCD results, the critical exponents and the universal scaling functions have been obtained mainly by means of lattice simulations of O(N) spin models, and results are usually restricted to the critical temperature or the point at which the susceptibilities peak. We propose to use a non-perturbative Renormalization Group method for this purpose. We have calculated the critical finite-size scaling behavior and the universal scaling functions for the three-dimensional O(4)-model for a wide range of temperatures and values of the symmetry breaking parameter. Our results are suitable for a comparison to lattice QCD results for the chiral susceptibility and the order parameter and can be used to check the consistency of the finite-size scaling behavior with that of the O(N) universality class.
We present results on the mass of the nucleon and the $Δ$ using two dynamical degenerate twisted mass quarks. The evaluation is performed at four quark masses corresponding to a pion mass in the range of 690-300 MeV on lattices of size 2.1 fm and 2.7 fm. We check for cutoff effects by evaluating these baryon masses on lattices of spatial size 2.1 fm with lattice spacings $a(β=3.9)=0.0855(6)$ fm and $a(β=4.05)=0.0666(6)$ fm, determined from the pion sector and find them to be within our statistical errors. Lattice results are extrapolated to the physical limit using continuum chiral perturbation theory. The nucleon mass at the physical point provides a determination of the lattice spacing. Using heavy baryon chiral perturbation theory at ${\cal O}(p^3)$ we find $a(β=3.9)=0.0879(12)$ fm, with a systematic error due to the chiral extrapolation estimated to be about the same as the statistical error. This value of the lattice spacing is in good agreement with the value determined from the pion sector. We check for isospin breaking in the $Δ$-system. We find that $Δ^{++,-}$ and $Δ^{+,0}$ are almost degenerate pointing to small flavor violating effects.
We explain how the strategy of solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume can be implemented to include dynamical fermions. As a primary application, some elements of an HQET computation of the mass of the b-quark beyond the leading order with N_f=2 are outlined. In particular, the matching of HQET and QCD requires relativistic QCD simulations in a volume with L ~ 0.5 fm, which will serve to quantitatively determine the heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. As a preparation for the latter, we report on our determination of the renormalization constants and improvement coefficients relating the renormalized current and subtracted bare quark mass in the relevant weak coupling region. The calculation of these coefficients employs a constant physics condition in the Schroedinger functional scheme, where the box size L is fixed by working at a prescribed value of the renormalized coupling.
We discuss some large effects of dynamical fermions. One is a cutoff effect, others concern the contribution of multi-pion states to correlation functions and are expected to survive the continuum limit. We then turn to the preparation for simulations at small lattice spacings which we are planning down to around a=0.04fm in order to understand the size of O(a^2)-effects of the standard O(a)-improved theory. The dependence of the lattice spacing on the bare coupling is determined through the Schr"odinger functional renormalized coupling.
Experimentally the charmonium hyperfine splitting is $M_{J/ψ}-M_{η_c}=117$ MeV and current lattice results are generally below this value. The difference could be due to the effects of the disconnected flavor singlet diagrams which have not been included in these calculations. Previous attempts to determine the disconnected flavor singlet corrections have led just to rough estimates in the range of $\pm 20$ MeV. We present preliminary results for these corrections calculated on fine ($a\approx 0.09$ fm) Asqtad 2+1 flavor lattices provided by the MILC Collaboration.
We present preliminary results for the charm quark mass $m_c$ and the $D$ and $D_s$ mesons decay constants $f_D$ and $f_{D_s}$ from a lattice QCD calculation with ${\rm N_f}$ = 2 dynamical fermions. We use the twisted mass fermionic action defined at maximal twist so that physical quantities are automatically ${\cal O}(a)$ improved. Two lattice spacings are considered. The charm quark mass has been renormalised in the RI-MOM scheme. After a matching to the $\msb$ scheme, we obtain from the simulation at a fine lattice ($a \sim 0.09$ fm) $m_c^{\msb}(m_c) = 1.481 \pm 0.022 \pm 0.092$ GeV, $f_D = 205 \pm 13 \pm 17$ MeV, $f_{D_s} = 271 \pm 6 \pm 6$ MeV and from the simulation at the finer lattice ($a \sim 0.07$ fm) $m_c^{\msb}(m_c) = 1.474 \pm 0.041 \pm 0.132$ GeV, $f_D = 230 \pm 31 \pm 8$ MeV and $f_{D_s} = 264 \pm 5 \pm 8$ MeV. We chose three renormalisation conditions to determine $m_c$: the spread between the final results contributes to the systematic error. At both lattice spacings, particularly at the finer one, the error on $m_c$ is dominated by present uncertainty on the renormalisation constant $Z_P$, which should be reduced before performing a reliable continuum limit.
We present results for the mass spectrum of charm and bottom heavy baryons, using MILC coarse lattice configurations with 2+1 flavors. Clover heavy quark propagators with the Fermilab interpretation and improved staggered light quark propagators are used to construct two point functions with local operators for different flavor and spin states.
The Landau-gauge gluon propagator is computed for the SU(3) gauge theory on lattices up to a size of $32^3 \times 200$. We use the standard Wilson action at $β= 6.0$ and compare our results with previous computations using large asymmetric and symmetric lattices. In particular, we focus on the impact of the lattice geometry and momentum cuts to achieve compatibility between data from symmetric and asymmetric lattices for a large range of momenta.
We present results of a perturbative matching calculation performed at one-loop for heavy-light currents. We use the Fermilab action for the heavy quarks, the Asqtad action for the light quarks, and an improved gluon action. We also present results for heavy-heavy currents with Fermilab heavy quarks and improved glue.
We present some up-to-date results on QCD phase transition in a chromomagnetic constant background field and in an abelian monopole background field. Our results indicate that the QCD critical temperature is not modified by a monopole background field, whilst it is modified by a constant chromomagnetic field. We improve our earlier estimate of the QCD critical parameters in a chromomagnetic background field by performing lattice simulations with weaker fields.