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arXiv2007

Universal properties of large N phase transitions in Wilson loops

Numerical studies support the conjecture that in continuum planar QCD the eigenvalue density of a Wilson loop operator undergoes a transition as the loop is dilated while keeping the loop shape fixed. A second part of the conjecture is that the transition obeys large N universality and that this universality class is the same in 2, 3 and 4 Euclidean space-time dimensions. The focus of the talk will be on clarifying precisely what the conjecture is claiming.

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arXiv2007

Higgs mechanism in five-dimensional gauge theories

Lattice simulations of five-dimensional gauge theories on an orbifold revealed that there is spontaneous symmetry breaking. Some of the extra-dimensional components of the gauge field play the role of a Higgs field and some of the four-dimensional components become massive gauge bosons. The effect is confirmed by computing the Coleman-Weinberg potential with a cutoff. We compare the results of this computation with the lattice data.

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arXiv2007

Neutral mesons and disconnected diagrams in Twisted Mass QCD

We evaluate properties of neutral mesons in Nf=2 dynamical simulations of TMQCD at maximal twist. The pion is explored - establishing the size of the isospin splitting (an order a^2 effect). We investigate the eta' (the Nf=2 flavour singlet pseudoscalar meson) and neutral rho and scalar mesons. We show that disconnected diagrams can be evaluated very efficiently in TMQCD using variance reduction methods.

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arXiv2007

Dynamical Chirally Improved Quarks: First Results for Hadron Masses

We present first results for a study with two mass-degenerate dynamical Chirally Improved (CI) fermions on lattices of spatial extent 2.4 fm. The CI Dirac operator obeys the Ginsparg-Wilson condition in good approximation. The pion mass we use is still large O(470 MeV) for the 16**3*32 lattices with lattice spacing of 0.15 fm. The hadron masses are obtained with the variational technique and the results compared with earlier quenched calculations with similar lattice parameters. We find indications for the isovector, scalar meson a0(980) near the experimental value, in contradistinction to quenched results which always produced a mass value compatible with the first excitation a0(1450).

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arXiv2008

Coulomb gauge studies of SU(3) Yang-Mills theory on the lattice

We study the infrared behaviour of lattice SU(3) Yang-Mills theory in Coulomb gauge in terms of the ghost propagator, the Coulomb potential and the transversal and the time-time component of the equal-time gluon propagator. In particular, we focus on the Gribov problem and its impact on the observables. We observe that the simulated annealing method is advantageous for fixing the Coulomb gauge in large volumes. We study finite size and discretization effects. While finite size effects can be controlled by the cone cut, and the ghost propagator and the Coulomb potential become scaling functions with the cylinder cut, the equal-time gluon propagator does not show scaling in the considered range of the inverse coupling constant. The ghost propagator is infrared enhanced. The Coulomb potential is now extended to considerably lower momenta and shows a more complicated infrared regime. The Coulomb string tension satisfies Zwanziger's inequality, but its estimate can be considered only preliminary because of the systematic Gribov effect that is particularly strong for the Coulomb potential.

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arXiv2007

Worldline Approach to Chiral Fermions

We propose to apply ``worldline numerics'' to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of the worldlines, which is central to the numerical treatment, preserves chiral symmetry exactly. Numerical results for a kink configuration as a scalar background field are shown and compared with analytical results. The case of finite fermion chemical potential is also briefly discussed.

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arXiv2007

Precision Lattice Calculation of D and Ds decay constants

We present a determination of the decay constants of the $D$ and $D_s$ mesons from lattice QCD, each with a total error of about 2%, approximately a factor of three better than previous calculations. We have been able to achieve this through the use of a highly improved discretization of QCD for charm quarks, coupled to gauge configurations generated by the MILC collaboration that include the full effect of sea u, d, and s quarks. We have results for a range of u/d masses down to m_s/5 and three values of the lattice spacing, which allow us to perform accurate continuum and chiral extrapolations. We fix the charm quark mass to give the experimental value of the η_c mass, and then a stringent test of our approach is the fact that we obtain correct (and accurate) values for the mass of the D and D_s mesons. We compare f_D and f_{D_s} with f_K and f_π, and using experiment determine corresponding CKM elements with good precision.

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arXiv2007

Spectral properties of the non-hermitian Wilson-Dirac operator in the Schroedinger functional

We report on some preparatory investigations for the simulation of the QCD Schroedinger functional with a non-hermitian polynomial hybrid Monte Carlo algorithm. The complex spectrum of the non-hermitean free operator with SF boundary condititons is computed semianalytically. Then it is shown how one can obtain relevant information on the boundary of the spectral domain also in the presence of nontrivial gaugefields by monitoring the behavior of polynomials in the Wilson operator applied on random vectors.

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arXiv2007

Using evolutionary algorithms to extract field theory mass spectra

The spectrum of masses from a lattice QCD simulation may be found by fitting exponential functions to correlators of operators possessing the quantum numbers of the particles of interest. The ability of evolutionary algorithms to find globally optimized solutions containing a variable number of states across multiple data sets is exploited to provide a promising solution to the problem of finding these fits.

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arXiv2007

Improvement of the pion spectrum with HYP-smeared staggered fermions

We extend our previous study of taste-symmetry breaking using HYP-smeared staggered fermions in two ways. First, we improve the statistics of a comparison of unimproved and HYP-smeared staggered fermions on quenched lattices with $a\approx 0.1 $fm. This allows us to obtain a signal for all pion tastes, rather than just a subset, and thus to make a complete comparison. In addition, it allows us to differentiate between wall and local sources. Second, we compare HYP-smeared valence quarks to asqtad valence quarks on 2+1 flavor unquenched MILC lattices. We find that taste breaking is substantially reduced by HYP-smearing, bringing the size of this discretization effect (which is the dominant such effect with staggered fermions) down to the size expected generically for any fermion type.

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arXiv2007

The Glue Content of the Pion

We perform a quenched computation of the glue momentum fraction in the pion. Different discretizations of the gluonic energy-momentum tensor are studied on the lattice for that purpose. We discuss some implications based on the momentum sum rule. Finally we point out promising applications of the techniques developed here.

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arXiv2007

HMC algorithm for two-flavour lattice QCD: Schwarz-preconditioning with a one-dimensional domain decomposition

We study a variant of the Schwarz-preconditioned HMC algorithm. In contrast to the original proposal of Lüscher, we apply the domain decomposition in one lattice direction only. This is sufficient to reduce the condition number of the fermion matrix restricted to the domains compared with the full fermion matrix. For the same linear extension of the domain, less links reside on the boundaries of the domains. Therefore it becomes e.g. practical to iterate the decomposition. We perform numerical tests for two degenerate flavours of Wilson fermions. The standard Wilson gauge action at $β=5.6$ is used. The performance of our implementation is compared with other recent studies using various types of preconditioning.

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arXiv2007

The vector and axial vector current in Wilson ChPT

We construct the vector and axial vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. Our construction is slightly different compared to ChPT in continuum QCD, where the currents are essentially the (partially) conserved currents associated with the chiral symmetries. In WChPT, due to explicit chiral symmetry breaking at non-zero lattice spacing, there appear O(a) terms in the expressions for the currents which do not stem from the effective action. In addition, the finite renormalization of the currents needs to be taken into account in order to properly match the currents of the effective theory. As an illustration we compute f_pi to one loop with the renormalized axial vector current for a particular renormalization condition. It turns out that for this particular condition some of the O(a) corrections are taken care of by the renormalization.

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arXiv2007

Pseudo-scalar meson form factors with maximally twisted Wilson fermions at Nf = 2

We present preliminary results for various electroweak form factors of pseudo-scalar mesons using the tree-level improved Symanzik gauge action and the maximally twisted mass fermionic action with Nf = 2 dynamical flavors. Our results, obtained for both light and heavy quark masses at a single lattice spacing (a ~ 0.09 fm) and at a single lattice volume (V * T = 24**3 * 48), exhibit a quite remarkable statistical precision thanks to the use of all-to-all quark propagators computed with a stochastic method. Moreover very low values of the four-momentum transfer are achieved by making use of twisted boundary conditions on the valence quark fields. The mass dependence of the pion charge radius is analyzed using Chiral Perturbation Theory, obtaining clear evidence of relevant two-loop contributions. The universal Isgur-Wise function is computed from heavy-to-heavy electromagnetic transitions and its slope in the case of $u(d)$ spectator quarks is found to be rho(IW)**2 = 0.77 +/- 0.28, where the error is statistical only.

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arXiv2007

A survey of large N continuum phase transitions

The main focus of this talk is the physics of large N QCD on a continuum torus. A cascade of phase transitions associated with the breaking of U(1) symmetries will be discussed. The continuum Wilson loop as a function of its area will be discussed along with its universality properties and the associated double scaling limit. Some recent progress in twisted Eguchi-Kawai is presented. Gauge field topology and $θ$ vacuua are also discussed in the context of large N gauge theories. Phase transitions in 2D large N principal chiral models are compared with similar transitions in large $N$ gauge theories. Finally, connections to some topics in string theory and gravity are briefly described.

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arXiv2007

High density effective theory on the lattice

Long-range interactions in finite density QCD necessitate a non-perturbative approach in order to reliably map out the key features and spectrum of the QCD phase diagram. However, the complex nature of the fermion determinant in this sector prohibits the use of established Monte Carlo techniques that utilize importance sampling. Whilst significant progress has been made in the low density, high temperature region, this remains a considerable challenge at mid to high density. At large chemical potential, QCD can be approximated using high density effective theory which is free from the sign problem at leading order. We investigate the implementation of this theory on the lattice in conjunction with existing re-weighting techniques.

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arXiv2007

A test of first order scaling in Nf=2 QCD

We complete our analysis of Nf=2 QCD based on the lattice staggered fermion formulation. Using a series of Monte Carlo simulations at fixed (amq*Ls^yh) one is able to test the universality class with given critical exponent yh. This strategy has been used to test the O(4) universality class and it has been presented at the previous Lattice conferences. No agreement was found with simulations in the mass range amq=[0.01335,0.15] using lattices with Ls=16 up to 32 and Lt=4. With the same strategy, we now investigate the possibility of a first order transition using a new set of Monte Carlo data corresponding to yh=3 in the same mass and volume range as the one used for O(4). A substantial agreement is observed both in the specific heat scaling and in the scaling of the chiral condensate, while the chiral susceptibilities still presents visible deviation from scaling in the mass range explored.

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arXiv2007

Study of constant mode in charmonium correlators at finite temperature

Recent studies on the spectral function of charmonium in lattice QCD suggest survival of $J/ψ$ state in the deconfinement phase till relatively high temperature. Based on the studies, different scenarios of $J/ψ$ suppression are discussed to understand experimental results in the Heavy Ion Collision experiments. The scenarios require the information on the dissociation temperatures of $χ_c$ and $ψ'$ as well as that of $J/ψ$. In order to investigate these states in finite temperature lattice QCD, we have to consider an effect of a characteristic constant mode in the correlators. As a result of the study on the constant mode, we find that most drastic change in charmonium correlators for $χ_c$ states just above the deconfinement transition are caused by the constant mode. It may indicate the survival of $χ_c$ states after the deconfinement transition until, at least, $1.4T_c$.

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