6262185
Lattice QCD with Eight Degenerate Quark Flavors
We report on simulations of QCD with many flavors of degenerate quarks, the DBW2 gauge action and naive staggered fermions, using the rational hybrid Monte Carlo algorithm. We primarily focus on eight degenerate quark flavors where a variety of values of the coupling constant and quark mass have been used in the simulations. The scaling behavior of the hadron spectrum and the string tension of the heavy quark potential is studied, to probe whether the zero temperature, continuum limit of the theory breaks chiral symmetry.
118449163
Lattice QCD with 12 Quark Flavors: A Careful Scrutiny
With a substantial amount of simulations, we have explored the system across a wide range of lattice scales. We have located a lattice artifact, first order bulk transition, have studied its properties, and found that the flavor-singlet scalar meson mass vanishes at the critical endpoint. We will discuss the lattice phase diagrams and the continuum limits for both a spontaneous chiral symmetry breaking phase and an infrared conformal phase, and compare results with other groups.
118389195
Scalar correlators near the 3-flavor thermal critical point
We investigate screening masses at both sides of the first order finite temperature transition with 3 quark flavors using the nonperturbatively improved clover fermion action and the Iwasaki gauge action. We have developed the method of hierarchical truncations with stochastic probing to accelerate the noise estimator for evaluating quark loops at every spatial lattice slices. At parameter values we study, the flavor singlet scalar meson has a screening mass about half of the pion screening mass. It becomes lighter as the system approaches the critical endpoint.
117928601
Critical end point of Nf=3 QCD at finite temperature and density
Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, JapanWe investigate the phase structure of 3-ﬂavor QCD in the presence of ﬁnite quark chemical po-tential aµ=0.1 by using the Wilson-Clover fermion action. Especially, wefocus on locating thecritical end point that characterizes the phase structure. We do this by the kurtosis intersectionmethod for the quark condensate. For Wilson-type fermions,the correspondence between bareparameters and physical parameters is indirect. Hence we present a strategy to transfer the bareparameter phase structure to the physical one.32nd International Symposium on Lattice Field Theory LATTICE 2014June 23 - 28, 2014New York, USA
117675037
Finite size scaling for 4-flavor QCD with finite chemical potential
We present a finite size scaling study for 3 and 4-flavor QCD with nonzero quark chemical potential by the grand canonical approach. We employ the Wilson-clover fermions and adopt the phase reweighting method where the phase factor is computed exactly. In 4-flavor study, we show the finite size scaling study for the moments of various physical quantities, which demonstrates a typical behavior of the 1st order phase transition as well as the crossover or weak 1st order phase transition. For 3-flavor theory, we study the critical end point in the bare parameter space spanned by the hopping parameter, the gauge coupling and the chemical potential.
118336670
Lattice QCD with 12 Degenerate Quark Flavors
We report on new data from additional zero temperature simulations of QCD with 12 flavors. This is a continuation of previous studies using the DBW2 gauge action and naive staggered fermions. With the use of the force gradient integrator and a multiple-quark-mass preconditioned HMC, we have done simulations with input quark masses from mq = 0:003 to mq = 0:008. We have observed a metastable, first order, bulk transition that occurs at small input quark masses. As the quark mass increases, this first order bulk transition ends at a second order critical point, and, for still heavier quark masses, becomes the cross-over we have previously reported. We present measurements of hadron masses, decay constants and other low energy observables in the small quark mass region on the weak coupling side of the bulk transition. Our results show that the behavior of the system is still consistent with spontaneously broken chiral symmetry. We also discuss a preliminary investigation into the behavior of the bulk transition itself. We have found that, as the system approaches the second order critical end point, the scalar singlet meson becomes lighter. Thus it appears that the critical endpoint corresponds to a continuum limit theory only involving scalars and, following known triviality arguments, this is likely a free field theory. The presence of this critical endpoint could influence scaling of lattice observables in the conventional continuum limit.
119144040
RG flows, cycles, and c-theorem folklore
Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow-function is multi-valued in the couplings. Exact general results for renormalization group (RG) flows are important as they may provide physical insight for strongly coupled systems. The c-theorem for 2D systems [1] and the a-theorem for 4D systems [2, 3] are two such results that have been established for very broad classes of models [4]. The c-theorem shows the existence of a monotonically decreasing function of the length scale, c (L), which interpolates between 2D Virasoro central charges of theories at conformal fixed points, and thereby provides an intuitively correct count of system degrees of freedom — fewer in the infrared than in the ultraviolet. The a-theorem establishes similar monotonic flow for the induced coefficient of the Euler density, a (L), for a 4D theory in a curved spacetime background. It is a common conclusion — a “folk theorem”— based on these monotonically evolving “observables” that the underlying couplings can not have RG trajectories which are limit cycles or undergo more exotic (e.g. chaotic) oscillations (e.g. see 2nd bullet item under §6 in [5]). The point of this note is to explain and illustrate with just one coupling, as simply as possible, why this conclusion is unwarranted. (Somewhat similar criticism of the monotonic folklore has been proffered in other contexts, involving degenerate Morse function counterexamples for models with vorticity in the flow of several couplings [6].) In principle, we believe cyclic or perhaps even chaotic coupling trajectories are not ruled out by either the cor a-theorems, nor are they necessarily excluded by other monotonic “potential flow-functions.” To illustrate our reasoning, we begin with a very simple example based on a mechanical analogy. While this example does indeed exhibit both monotonic flow and a cycling trajectory, it has the peculiar feature — insofar as intuitively counting degrees of freedom is concerned — that the monotonic flow is unbounded both above and below. Nevertheless, we recall there is a field theory model that produces just such behavior [8]. We then exhibit another example where the monotonic flow is bounded below and the coupling trajectory is not only cyclic but, in fact, chaotic. The essential ideas, expressed for a single coupling x (t), where t = lnL, are given by general statements for a locally gradient RG flow, dx (t) dt = β (x (t)) = − (x (t)) dx (t) , (1) dC (x (t)) dt = dx dt dC dx = β dC dx = − (
115167324
Multi-operator brackets acting thrice
We generalize an identity first found by Bremner for Nambu 3-brackets. For odd N-brackets built from associative operator products, we show that for any fixed A, when totally antisymmetrized over all the Bs.