John Bulava, Saul Cohen, Jozef Dudek, Robert Edwards, Eric Engelson, Justin Foley, Balint Joo, Jimmy Juge, Huey-Wen Lin, Nilmani Mathur, Colin Morningstar, Mike… 展开作者
John Bulava, Saul Cohen, Jozef Dudek, Robert Edwards, Eric Engelson, Justin Foley, Balint Joo, Jimmy Juge, Huey-Wen Lin, Nilmani Mathur, Colin Morningstar, Mike Peardon, David Richards, Sinead Ryan, Christopher Thomas, Anthony Thomas, Stephen Wallace
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Invited Poster presented at 2009 DOE Scientific Discovery through Advanced Computing (SciDAC) conference, June 14-18, 2009, San Diego, CA. To appear in Journal of Physics Conference Series
The calculation of the spectrum of QCD is key to an understanding of the strong interactions, and vital if we are to capitalize on the experimental study of the spectrum. In this paper, we describe progress towards understanding the spectrum of resonances of both mesons and baryons from lattice QCD, focusing in particular on the resonances of the $I=1/2$ nucleon states, and of charmonium mesons composed of the heavy charmed quarks.
The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable when the untwisted quark mass sweeps across zero.
An effective residual interaction for a meson-meson system is computed in lattice QCD. We describe the theoretical framework and present its application to the I=2 channel S-wave interaction of the pi pi system. Scattering phase shifts are also computed and compared to experimental results.
We investigate -- as an alternative to usual Monte Carlo Renormalization Group methods -- the feasibility of extracting QCD beta-functions directly from a lattice analysis of correlations between the action and Wilson loops. We test this correlation technique numerically in four dimensional SU(2) gauge theory, on a 16^4 lattice at beta = 2.5 and find very promising results.
We report on our simulations with Neuberger valence fermions on CLS $N_f=2$ configurations with non-perturbatively $O(a)$-improved Wilson sea quarks. We consider the matching of QCD to ChPT in the so called mixed-regime in which the sea quarks are in the $p$-regime while the valence quarks are in the $ε$-regime. From this matching, we can get information on $Σ$, $L_6$ and the combination $L_8+2L_6+2L_7$.
Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight factors and therefore potentially enable the determination of the phase diagram of QCD. Here we present results for QCD in the limit of heavy quarks and show evidence that the phase diagram can be mapped out by direct simulation. We apply adaptive step-size scaling and adaptive gauge cooling to ensure the convergence of these simulations.
Some past and ongoing explorations of the spectrum of QCD using Monte Carlo simulations on a space-time lattice are described. Glueball masses in the pure-gauge theory are reviewed, and the energies of gluonic excitations in the presence of a static quark-antiquark pair are discussed. Current efforts to compute the baryon spectrum using extended three-quark operators are also presented, emphasizing the need to use irreducible representations of the cubic point group to identify spin quantum numbers in the continuum limit.
We perform an extensive study of autocorrelation of several observables in lattice QCD with two degenerate flavours of naive Wilson fermions and unimproved Wilson gauge action using DD-HMC algorithm. We show that (1) at a given lattice spacing, autocorrelation of topological susceptibility decreases with decreasing quark mass and autocorrelations of plaquette and Wilson loop do not increase with decreasing quark mass, (2) autocorrelation of topological susceptibility substantially increases with decreasing lattice spacing but autocorrelation of topological charge density correlator shows only …
Numerical simulations with access to all possible meson quantum numbers, J^{PC}, are presented using two-flavor (up and down) quenched twisted mass lattice QCD with three different lattice spacings and four different quark masses. The connection between the quantum numbers (P and C) and the symmetries of the twisted mass action are discussed, as is the connection between J and the lattice rotation group, for the 400 operators used in this study. Curve fitting of this large data set is accomplished by using an evolutionary fitting algorithm. Results are reported for conventional and exotic quan…
We use a modified directed path algorithm to study the finite temperature chiral singularities of two color lattice QCD with staggered fermions at strong coupling. Our lattice calculations are done at a fixed finite temperature in the broken phase with a variety of different quark masses. We find that to the lowest order, the behavior of our observables, namely the condensates and the decay constants are all consistent with the predictions of the low energy effective theory of our model. We further notice that in order to see consistency, the quark masses used in our lattice calculations need …
We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility violations can be kept under control, we find a variation of the integrated autocorrelation times by a factor of about two in the quantities of interest. Trajectories longer than conventionally used are found to be superior both in the Nf=0 and Nf=2 examples considered here. We also provide evidence that they lead to faster thermalization of systems with light quar…
As a follow up to the previous talk about the beta function of SU(3) gauge theory with Nf=2 symmetric representation (clover) fermions [arXiv:0809.2885 [hep-lat]], we describe our explorations of the beta-kappa plane, away from the massless limit. Our simulations are mostly done on lattices of length L=8 and 12. We observe a phase transition from a strong coupling confined phase to a deconfined, chirally restored phase. The line of transitions avoids (so far) the location of the infrared fixed point discussed in the last talk.
We study the three nucleon force in Nf=2 dynamical clover fermion lattice QCD, utilizing the Nambu-Bethe-Salpeter wave function of the three nucleon system. Since parity-odd two nucleon potentials are not available in lattice QCD at this moment, we develop a new formulation to extract the genuine three nucleon force which requires only the information of parity-even two nucleon potentials. In order to handle the extremely expensive calculation cost, we consider a specific three-dimensional coordinate configuration for the three nucleons. We find that the linear setup is advantageous, where nuc…
QCD at non-zero chemical potential ($μ$) for quark number has a complex fermion determinant and thus standard simulation methods for lattice QCD cannot be applied. We therefore simulate this theory using the Complex-Langevin algorithm with Gauge Cooling in addition to adaptive methods, to prevent runaway behaviour. Simulations are performed at zero temperature on a $12^4$ lattice with 2 quarks which are light enough that $m_N/3$ is significantly larger than $m_π/2$. Preliminary results are qualitatively as expected. The quark-number density is close to zero for $μ< m_N/3$, beyond which it incr…
We explore the region of small sea quark masses below $m_{PS}/m_V=0.5$ in two-flavor QCD using a mean-field improved clover quark action and an RG-improved gauge action at $a \simeq 0.2$ fm on $12^3 \times 24$ and $16^3 \times 24$ lattices. We find that instability of the standard BiCGStab algorithm at small quark masses can be mostly removed by the BiCGStab(DS-$L$) algorithm, which employs $L$-th minimal residual polynomials with a dynamical selection of $L$. We also find singular spikes of $ΔH$ in the HMC algorithm at moderate values of $Δτ$. Nature of the spike is studied. We also study fin…
The canonical approach for finite density lattice QCD has a numerical instability. This instability makes it difficult to use the method reliably at the finite real chemical potential region. We studied this instability in detail and found that it is caused by the cancellation of significant digits. In order to reduce the effect of this cancellation, we adopt the multiple precision calculation for our discrete Fourier transformation (DFT) program, and we get the canonical partition function Zc(n,T) with required accuracy. From the obtained Zc(n,T), we calculate Lee--Yang zero distribution vary…
Chiral phase transition of two flavor QCD at finite quark masses is known to be crossover except near the chiral limit, but it can turn to a first order transition when adding many extra flavors. This property is used to explore the nature of the phase transition of massless two flavor QCD using lattice numerical simulations. The extra heavy flavors being incorporated in the form of the hopping parameter expansion through the reweighting, the number of the extra flavors and their masses appear only in a single parameter, defined by $h$. We determine the critical value of the parameter, at whic…
We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. By choosing strong bare gauge couplings we arrive at values for the physical lattice spacings of O(0.1 fm). Such gauge actions tend to confine the Monte Carlo history to a single topological sector. This topological stability facilitates the collection of a large set of configurations in a specific sector, which is profitable for numerical studies in the epsilon-regime. The suppression of small plaquette values is also expected to be favourable for simulati…
It has been shown that in the twisted mass formulation of Lattice QCD at maximal twist large cutoff effects are generated when the quark mass becomes of O(a Lambda_QCD^2). In general, these effects can be suppressed in two ways: either by choosing the critical quark mass in an "optimal way", or by adding the Clover term to the twisted action. We investigate the second option by performing a quenched lattice QCD simulation with twisted Clover fermions and pion masses as low as 280 MeV. We show that the Clover term is indeed efficient in reducing the large cutoff effects. In particular, the so-c…
I report on the current status of QCD phase diagram at vanishing baryon density. I focus on the QCD phase diagram with three degenerate quark flavor using Highly Improved Staggered Quarks on $N_τ=6$ lattices. No evidence of a first order phase transition in the pion mass window of $80\lesssim m_π \lesssim 230 $MeV is found. The pion mass at the critical point where the chiral first order phase transition ends is estimated to be $m^c_π \lesssim 45$ MeV.
Relativistic heavy-ion collisions and the lattice QCD Monte-Carlo simulations are important ``experimental'' tools for investigating the properties of the medium described by QCD under extreme conditions. After briefly examining their characteristics, I pick up the study of the critical points in QCD as an example of the research subjects that these two tools play complementary roles and discuss recent topics that have been achieved with the use of each tool.
It is usual to study confinement via quantum chromodynamics (QCD) alone. The deconfinement transition of the pure gauge theory (i.e. with static quarks) is then characterized by the breaking of center symmetry. Center vortices offer an intuitive and quantitative description of the transition. Dynamical quarks explicitly break center symmetry, and the phase transition becomes a crossover. However, it may be misleading to study QCD in isolation. Quarks also carry fractional electric charge. This bestows the Standard Model with a global center symmetry that combines color center phases with an ap…
Using a correlation matrix analysis consisting of a variety of smearings, the CSSM Lattice collaboration has successfully isolated states associated with the Roper resonance and other "exotic" excited states such as the $Λ(1405)$ on the lattice at near-physical pion masses. We explore the nature of the Roper by examining the eigenvectors that arise from the variational analysis, demonstrating that the Roper state is dominated by the $χ_1$ nucleon interpolator and only poorly couples to $χ_2.$ By examining the probability distribution of the Roper on the lattice, we find a structure consistent …
QCD exhibits complex dynamics near S-wave two-body thresholds. For light mesons, we see this in the failure of quark models to explain the $f_0(500)$ and $K_0^*(700)$ masses. For charmonium, an unexpected $X(3872)$ state appears at the open charm threshold. In heavy-light systems, analogous threshold effects appear for the lowest $J^P = 0^+$ and $1^+$ states in the $D_s$ and $B_s$ systems. Here we describe how lattice QCD can be used to understand these threshold dynamics by smoothly varying the strange-quark mass when studying the heavy-light systems. Small perturbations around the physical s…
I start by giving a brief overview over new developments in the area of confinement and topology. As an example for the interrelations between topological objects, instantons at finite temperature are discussed. Then I focus on new insights into the structure of the QCD vacuum obtained through filtering methods, in particular those based on decompositions w.r.t. fermionic eigenmodes.
We studied the QCD phase transition as a function of quark mass in the $N_f=3$ QCD at vanishing baryon density. Lattice simulations have been performed using Highly Improved Staggered Quarks on $N_τ=6$ lattices with quark masses that correspond to pion masses in the region $80 \lesssim m_π \lesssim 230 $MeV. We found no evidence of the first order phase transition in the current pion mass window. The pion mass at the critical point where the first order phase transition starts is estimated to be $m^c_π\lesssim 45$ MeV.
Following our previous proposal [1], we construct a class of good "lattice cross sections" (LCSs), from which we could study partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that proposed functions for la…
We discuss in detail a method to study transverse momentum dependent parton distribution functions (TMDs) using lattice QCD. To develop the formalism and to obtain first numerical results, we directly implement a bi-local quark-quark operator connected by a straight Wilson line, allowing us to study T-even, "process-independent" TMDs. Beyond results for x-integrated TMDs and quark densities, we present a study of correlations in x and transverse momentum. Our calculations are based on domain wall valence quark propagators by the LHP collaboration calculated on top of gauge configurations provi…
Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure.
The Interacting Instanton Liquid Model is used to explore the role of instanton induced dynamics in hadron structure. To support the validity of this model in the chiral regime, the quark mass dependencies of several properties are shown to agree with chiral perturbation theory, including the density of eigenmodes of the Dirac operator and the masses of the pion and nucleon. A quark mass m* = 80 MeV emerging naturally from the model is shown to specify the mass scale above which the fermion determinant is suppressed, the zero modes become subdominant, and the density of quasi-zero modes become…
The first exploratory calculations of QCD vacuum correlation functions on a lattice are reported. Qualitative agreement with phenomenological results is obtained in channels for which experimental data are available, and these correlation functions are shown to be useful in exploring approximations based on sum rules and interacting instantons.
The low energy excitation spectrum of the critical Wilson surface is discussed between the roughening transition and the continuum limit of lattice QCD. The fine structure of the spectrum is interpreted within the framework of two-dimensional conformal field theory.
Monte Carlo studies of QCD at finite density suffer from the sign problem, which becomes easily uncontrollable as the chemical potential $μ$ is increased even for a moderate lattice size. In this work we make an attempt to approach the high density low temperature region by the complex Langevin method (CLM) using four-flavor staggered fermions with reasonably small quark mass on a $8^3 \times 16$ lattice. Unlike the previous work on a $4^3 \times 8$ lattice, the criterion for correct convergence is satisfied within a wide range of $μ$ without using the deformation technique. In particular, the…
We present a summary of our results for the light hadron spectrum in quenched lattice QCD and preliminary ones in two-flavor full QCD. For the quenched hadron spectrum we find that the mass formulae predicted by quenched chiral perturbation theory(QChPT) give a good description of our results. Employing the QChPT mass formulae for chiral extrapolations we conclude that the mass spectrum in the continuum limit deviates unambiguously and systematically from experiment. For our two-flavor full QCD results we focus on the dynamical quark effects on the light hadron spectrum.
Results from a comprehensive new analysis on the excitation spectrum of the QCD string are presented. A rapid onset of string formation is observed in the spectrum on a length scale of 2 fm, with Dirichlet boundary conditions. The crossover from the short distance spectrum towards string excitations and an observed fine structure in the 1--3 fm range are related to effective string theory. The deficiencies of the Nambu-Goto bosonic string model in describing the observed spectrum are briefly discussed.
Various holographic approaches to QCD in five dimensions are explored using input both from the putative non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure QCD. A part of the higher alpha' corrections are resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS_5 with lo…
In this work we outline a program for lattice QCD that would provide a first step toward understanding the strong and weak interactions of strange baryons. The study of hypernuclear physics has provided a significant amount of information regarding the structure and weak decays of light nuclei containing one or two Lambda's, and Sigma's. From a theoretical standpoint, little is known about the hyperon-nucleon interaction, which is required input for systematic calculations of hypernuclear structure. Furthermore, the long-standing discrepancies in the P-wave amplitudes for nonleptonic hyperon d…
The low energy mass spectrum of QCD in the large $N_C$ limit is computed. The low-lying states in the meson spectrum are explicitly evaluated up to the fourth order in the strong coupling perturbative expansion. The 't Hooft limit is smooth and the meson masses are in very good agreement with the experimental values.
We investigate the QCD phase diagram for small values of baryon and strange quark chemical potentials from simulations at non-zero isospin chemical potential. Simulations at pure isospin chemical potential are not hindered by the sign problem and pion condensation can be observed for sufficiently large isospin chemical potentials. We study how the related phase boundary evolves with baryonic and strange chemical potentials via reweighting in quark chemical potentials and discuss our results. Furthermore, we propose and implement an alternative method to approach nonzero baryon (and strange qua…
We present the report of the LatKMI collaboration on the lattice QCD simulation for the cases of 4 and 8 flavors. The Nf=8 in particular is interesting from the model-building point of view: The typical walking technicolor model with the large anomalous dimension is the so-called one-family model (Farhi-Susskind model). Thus we explore the walking behavior in LQCD with 8 HISQ quarks by comparing with the 4-flavor case (in which the chiral symmetry is spontaneously broken). We report preliminary results on the spectrum, analyzed through the chiral perturbation theory and the finite-size hypersc…
Beam energy scan programs in heavy-ion collisions aim to explore the QCD phase structure at high baryon density. Sensitive observables are applied to probe the signatures of the QCD phase transition and critical point in heavy-ion collisions at RHIC and SPS. Intriguing structures, such as dip, peak and oscillation, have been observed in the energy dependence of various observables. In this paper, an overview is given and corresponding physics implications will be discussed for the experimental highlights from the beam energy scan programs at the STAR, PHENIX and NA61/SHINE experiments. Further…
Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.
The non-perturbative quark-gluon interaction depends significantly on the value of the quark mass. In particular, in the light quark mass regime, correlations are strongly influenced by dynamics associated to chiral symmetry breaking. We use the Interacting Instanton Liquid Model (IILM) as a tool to investigate the microscopic dynamical mechanisms which underly the dependence on the quark mass and drive the transition into the chiral regime of QCD. To ensure the validity of the model, we first verify that the dependence on the quark mass for several observables calculated in the IILM agrees we…
Quantum Chromodynamics (QCD) is generally assumed to be the fundamental theory underlying nuclear physics. In recent years there is progress towards investigating the nucleon structure from first principles of QCD. Although this structure is best revealed in Deep Inelastic Scattering, a consistent analysis has to be performed in a fully non-perturbative scheme. The only known method for this purpose are lattice simulations. We first sketch the ideas of Monte Carlo simulations in lattice gauge theory. Then we comment in particular on the issues of chiral symmetry and operator mixing. Finally we…
We present the QCD hadron spectrum for the cases of both quenched and two-flavor dynamical domain wall fermions. We compare the results obtained using the Wilson gauge action and a renormalization group improved gauge action. Finite volume effects and the dependence on the finite extent of the fifth dimension are discussed.
We explore the QCD phase diagram at finite density with four-flavor staggered fermions using the complex Langevin method, which is a promising approach to overcome the sign problem. In our previous work on an $8^3 \times 16$ lattice at $β= 5.7$ with the quark mass $m = 0.01$, we have found that the baryon number density has a clear plateau as a function of the chemical potential. In this study, we use a $16^3 \times 32$ lattice to reduce finite volume effects and find that the plateau structure survives. Moreover, the number of quarks in the plateau region turns out to be 24, which is exactly …
Various suggestions exist for incorporating the strange quark into twisted mass QCD. One option for quenched simulations is to employ two twisted doublets, (u,d) and (c,s), with separate twist angles. Working in the isospin limit, preliminary results for the quenched spectrum of strange hadrons are presented, with both twist angles tuned to pi/2. Splittings within the mass multiplets provide some insight into the symmetry breaking effects of twisted mass lattice QCD.
The distribution of the low-lying QCD Dirac spectrum is analyzed by means of partial quenched chiral perturbation theory. We identify an energy scale below which the valence quark mass dependence of the QCD partition function is given by chiral Random Matrix Theory. This is the the domain where the low-energy QCD partition function is dominated by the fluctuations of the mass term of the Goldstone bosons. In mesoscopic physics this domain is known the ergodic domain and the corresponding energy scale is the Thouless energy.
A brief review is given of the lattice QCD calculation of the hadron spectrum. The status of current attempts toward inclusion of dynamical up, down and strange quarks is summarized focusing on our own work. Recent work on the possible existence of pentaquark states are assessed. We touch upon the PACS-CS Project for building our next machine for lattice QCD, and conclude with a near-term physics and machine prospects.
We present results of simulations of the quenched quarkonium spectrum at two values of the lattice spacing and for quark masses around $m_c$ using the tadpole improved clover action. Attention is focussed on the lowest lying S and P states, and the triplet fine structure is obtained for the first time using a relativistic action.
We present results from an analysis of the light spectrum and the decay constants f_π and f_V^{-1} in Full QCD with n_f=2 Wilson fermions at a coupling of beta=5.6 on a 16^3x32 lattice.
We report on the first large-scale study of two flavor QCD with domain wall fermions (DWF). Simulation has been carried out at three dynamical quark mass values about 1/2, 3/4, and 1 $m_{strange}$ on $16^3\times 32$ volume with $L_s=12$ and $a^{-1}\approx 1.7$ GeV. After discussing the details of the simulation, we report on the light hadron spectrum and decay constants.
This paper is a continuation of ArXiv:0707.1324 where improved holographic theories for QCD were set up and explored. Here, the IR confining geometries are classified and analyzed. They all end in a "good" (repulsive) singularity in the IR. The glueball spectra are gaped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Mesons dynamics is implemented via space fi…
Using the Sigma model to explore the lowest order pseudo-scalar spectrum with SU(3) breaking, this talk considers an additional exact "taste" symmetry to mimic species doubling. Rooting replicas of a valid approach such as Wilson fermions reproduces the desired physical spectrum. In contrast, extra symmetries of the rooted staggered approach leave spurious states and a flavor dependent taste multiplicity.
We study glueball and gluelump spectra calculated after abelian projection in both quenched and $N_f=2$ full QCD. The abelian projection is made after MA gauge fixing. We demonstrate that both spectra can be recovered despite the problem with positivity. We suggest the interpretation of some of the gluelump states in the language of the abelian projected theory.
We analyze the eigenvalue statistics of the staggered Dirac operator above $T_{c}$ in QCD with 2+1 flavors of dynamical quarks. We use physical quark masses in our simulations. We compare the eigenvalue statistics from several parts of the Dirac spectrum with the predictions of Random Matrix Theory for this universality class and with Poisson statistics. We show that at the low end of the spectrum the eigenmodes are localized and obey Poisson statistics. Above a boundary region the eigenmodes become delocalized and obey Random Matrix statistics. Thus the QCD Dirac spectrum with physical dynami…
