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arXiv2007

Chiral Random Two-Matrix Theory and QCD with imaginary chemical potential

We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to determine both low energy constants Sigma and F in the leading order chiral Lagrangian, due to their respective coupling to quark mass and chemical potential. We briefly recall the analytic formulas for all density and individual eigenvalue correlations and then illustrate them in detail in the simplest, quenched case with imaginary isospin chemical potential. Some peculiarities are pointed out for this example: i) the factorisation of density and individual eigenvalue correlation functions for large chemical potential and ii) the factorisation of the non-Gaussian weight function of bi-orthogonal polynomials into Gaussian weights with ordinary orthogonal polynomials.

hep-th↗

arXiv2007

Phase structure of twisted Eguchi-Kawai model

We study the phase structure of the four-dimensional twisted Eguchi-Kawai model using numerical simulations. This model is an effective tool for studying SU(N) gauge theory in the large-N limit and provides a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that its Z_N^4 symmetry, which is crucial for the validity of this model, can break spontaneously in the intermediate coupling region. We investigate in detail the symmetry breaking point from the weak coupling side. Our simulation results show that the continuum limit of this model cannot be taken.

hep-lat↗

arXiv2007

Spectral Properties of Quarks in the Quark-Gluon Plasma

We analyze the spectral properties of the quark propagator above the critical temperature for the deconfinement phase transition in quenched lattice QCD using clover improved Wilson fermions. The bare quark mass dependence of the quark spectral function is analyzed by varying the hopping parameter κin Landau gauge. We assume a two-pole structure for the quark spectral function, which is numerically found to work quite well for any value of κ. It is shown that in the chiral limit the quark spectral function has two collective modes that correspond to the normal and plasmino excitations, while it is dominated by a single-pole structure when the bare quark mass becomes large.

hep-lat↗

arXiv2007

Centre Vortices in SU(3)

We investigate the effectiveness of using smearing as a means to generate a preconditioning transformation for gauge fields prior to fixing to Maximal Centre Gauge. This still leaves the gauge-fixed field in the original gauge orbit. As expected, we find that this preconditioning leads to higher maxima of the gauge-fixing condition, resulting in lower numbers of P-vortices. We also find that removing vortices appears to give a loss of confinement for all cases but that the string tension as measured from vortex-only configurations drops from about 65% to as low as 26% when using the preconditioning method.

hep-lat↗

arXiv2007

Running alpha(s) from Landau-gauge gluon and ghost correlations

We estimate the running coupling constant of the strong interactions within the nonperturbative framework of lattice QCD in Landau gauge. Our calculation is based on the ghost-gluon vertex which in the particular case of Landau gauge allows for a definition of alpha(s) in a MOM scheme solely in terms of the gluon and ghost dressing functions. As a first step we investigate the zero and two-flavour case and report here on preliminary results.

hep-lat↗

arXiv2007

Finite ma Errors of the Overlap Fermion

In this talk, we shall assess the finite ma errors from the overlap fermion. We shall present results on the speed of light from the dispersion relation and hyperfine splitting between the vector and pseudoscalar mesons as a function to ma to reveal the mΛ_{QCD}a^2 and m^2a^2 errors. We conclude from this study that one should be limited to using ma less than 0.5 in order to keep the systematic ma errors below a few percent level.

hep-lat↗

arXiv2007

Theoretical progress on pi pi scattering lengths and phases

pi pi scattering at low energy is sensitive to the structure of the QCD vacuum. I review the calculations of the pi pi scattering lengths and phases, and group them in three cathegories: 1. those based on very general theoretical constraints (like dispersion relations and crossing symmetry) and phenomenology, 2. those which in addition make explicit use of chiral symmetry, 3. the first-principle ones, done with lattice QCD. I then compare these to the experimental results. Thanks to recent progress in all these and in the experimental determination of the scattering lengths we are improving substantially our knowledge of the QCD vacuum.

hep-ph↗

arXiv2007

Moving NRQCD and B to K* gamma

The formulation of NRQCD discretized in a reference frame boosted relative to the B rest frame will enable calculation of B form factors over a larger range of momentum transfer. We have initiated a program to calculate form factors describing the rare decay B to K* gamma. We discuss the strategy and challenges of the project. As a first step in the numerical calculations, we present first results for bottomonium quantities using the O(Lambda_{QCD}^2/m^2, v_{NR}^4) moving NRQCD action.

hep-lat↗

arXiv2007

The High Density Region of QCD from an Effective Model

We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov-type loops as the main dynamical variables representing the fermionic matter. This model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the simulated Monte Carlo ensemble with the true one. We review the main features of the model and present results concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the Polykov loop susceptibility, which may be used to characterize the various phases expected at high baryonic density. In this way, we obtain information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints about the behaviour of non-zero density QCD.

hep-lat↗

arXiv2007

The 2+1 flavor topological susceptibility from the asqtad action at 0.06 fm

We report new data for the topological susceptibility computed on 2+1 flavor dynamical configurations with lattice spacing 0.06 fm, generated with the asqtad action. The topological susceptibility is computed by HYP smearing and compared with rooted staggered chiral perturbation theory as the pion mass goes to zero. At 0.06 fm, the raw data is already quite close to the continuum extrapolated values obtained from coarser lattices. These results provide a further test of the asqtad action with rooted staggered flavors.

hep-lat↗

arXiv2007

New Higgs physics from the lattice

We report the first results from our comprehensive lattice tool set to explore non-perturbative aspects of Higgs physics in the Standard Model. We demonstrate in Higgs-Yukawa models that Higgs mass lower bounds and upper bounds can be determined in lattice simulations when triviality requires the necessity of a finite cutoff to maintain non-zero interactions. The vacuum instability problem is investigated and the lattice approach is compared with the traditional renormalization group procedure which sets similar goals to correlate lower and upper Higgs mass bounds with the scale of new physics. A novel feature of our lattice simulations is the use of Ginsparg-Wilson fermions to represent the effects of Top quark loops in Higgs dynamics. The need for chiral lattice fermions is discussed and the approach is extended to full Top-Higgs-QCD dynamics. We also report results from our large $N_F$ analysis of Top-Higgs Yukawa models to gain analytic insight and to verify our new lattice tool set which is deployed in the simulations. The role of non-perturbative lattice studies to investigate heavy Higgs particle scenarios is illustrated in extensions of the Standard Model.

hep-lat↗

arXiv2007

The Landau gauge gluon propagator: Gribov problem and finite-size effects

The SU(2) gluon propagator in Landau gauge is studied on the lattice. Our gauge fixing procedure employs simulated annealing and Z(2)-flips. It finds higher maxima of the gauge functional compared with those obtained with the standard overrelaxation and leads to systematic deviations of the gluon propagator in the infrared region. In particular, finite-size effects for lattice sizes from (1.7 fm)^4 up to (6.5 fm)^4 become weak. The propagator shows a plateau at p \approx 300 MeV.

hep-lat↗

arXiv2007

Glueballs and mesons in the superfluid phase of two-color QCD

QCD with two colors undergoes a transition to a superfluid phase with diquark condensate when the quark chemical potential equals half the pion mass. We investigate the gluonic aspects of the transition by inspecting the behavior of the glueball correlators evaluated via a multi-step smearing procedure for several values of chemical potential ranging between zero and the saturation threshold. The results are based on an analysis of 0++ glueball correlators, on a sample of 40000 independent configurations on each parameter set. The amplitudes of the correlators peak for μ= m_π/2,indicating that the superfluid phase transition affects the gluonic sector as well. The mass of the fundamental state decreases in the superfluid phase, and the amplitude of the propagators drops, suggesting a reduction of the gluon condensate, in agreement with model calculations. The analysis of the smearing dependence of the results helps disentangling the role of long and short distance phenomena at the superfluid transition.

hep-lat↗

arXiv2007

Structure and properties of the vacuum of the Twisted Eguchi-Kawai model

We investigate numerically the phase structure of the Twisted Eguchi-Kawai (TEK) model in four dimensions. In the numerical simulations of the zero temperature TEK model (using a symmetric twist) we observe the existence of new phases that break its centre symmetry at intermediate lattice couplings and for large SU(N) gauge groups. This effect can be explained by the contribution of diagonal configurations with collapsed eigenvalues, which are particular cases of ``generalised fluxons''. We also investigate finite temperature versions of the TEK model using anisotropic lattice couplings, where in particular we find van Baal fluxons contributing at large anisotropies.

hep-lat↗

arXiv2007

Kaon Weak Matrix Elements in 2+1 flavor DWF QCD

$K \to π$ and $K \to 0$ weak matrix elements of $ΔS = 1$ operators have been measured in 2+1 flavor domain wall fermion (DWF) QCD on (3 fm)$^3$ lattices with $a^{-1} = 1.73(3)$ GeV. As is well known, using these matrix elements and chiral perturbation theory allows a determination of the $K \to ππ$ matrix elements that enter in the quantitative value for the $ΔI = 1/2$ rule and $ε^\prime/ε$. Two light dynamical sea quark masses have been used, along with six valence quark masses, with the lightest valence quark mass $\approx 1/10$ the physical strange quark mass. We report our results for lattice matrix elements in the $SU(3)_L \times SU(3)_R$ (27,1), (8,1), and (8,8) representations, paying particular attention to the statistical errors achieved after measurements on 75 configurations. We also report on our calculation of the non-perturbative renormalization coefficients for these $ΔS=1$ weak operators, using the Rome-Southampton method.

hep-lat↗

arXiv2007

Light hadron spectrum with 2+1 flavor dynamical $O(a)$-improved Wilson quarks

We present preliminary results for the light harden spectrum in $N_f=2+1$ lattice QCD obtained with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Simulations are carried out at $β=1.90$ on a $32^3 \times 64$ lattice using the PACS-CS computer. We employ Lüscher's domain-decomposed HMC algorithm to reduce the up-down quark masses toward the physical value. The pseudoscalar meson masses range from 730 MeV down to 210 MeV. We compare the light harden spectrum extrapolated to the physical point with the experimental values.

hep-lat↗

arXiv2007

Application of chiral perturbation theory to 2+1 flavor lattice QCD with O(a)-improved Wilson quarks

We apply chiral perturbation theory to the pseudoscalar meson mass and decay constant data obtained in the PACS-CS Project toward 2+1 flavor lattice QCD simulations with the O(a)-improved Wilson quarks. We examine the existence of chiral logarithms in the quark mass range from m_{ud}=47 MeV down to 6 MeV on a (2.8 fm)^3 box with the lattice spacing a=0.09 fm. Several low energy constants are determined. We also discuss the magnitude of finite size effects based on chiral perturbation theory.

hep-lat↗

arXiv2007

Meson correlators in the epsilon-regime of two-flavor lattice QCD

We calculate the meson correlators in the $ε$-regime of two-flavor QCD. On a $16^3\times 32$ lattice with $a\sim 0.11$ fm, the lattice simulations are performed with the dynamical overlap fermions. We reduce the sea quark mass down to $\sim$ 3 MeV and the valence quark masses are taken in the range 1-4 MeV. The meson correlators in various channels are compared with the predictions of (partially quenched) chiral perturbation theory (ChPT). Including the NLO order of the $ε$-expansion, we extract the leading-order low energy constants of ChPT, the pion decay constant $F$ and the chiral condensate $Σ$, as $F=87.3(5.5)$ MeV and $Σ^{\bar{\mathrm{MS}}}=[237.8(4.0){MeV}]^3$.

hep-lat↗