Number Of Quark Flavors Research Articles

Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature

In the ε-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random matrix ensemble has been proposed, where a constant, deterministic matrix is added to the Dirac operator. Its eigenvalue correlation functions can be written as the determinant of a kernel that depends on temperature. Due to recent progress in this specific class of random matrix ensembles, featuring a deterministic, additive shift, we can determine the limiting kernel and correlation functions in this class, which is the class of polynomial ensembles. We prove the equivalence between this new determinantal representation of the microscopic eigenvalue correlation functions and existing results in terms of determinants of different sizes, for an arbitrary number of quark flavours, with and without temperature, and extend them to non-zero topology. These results all agree and are thus universal when measured in units of the temperature dependent chiral condensate, as long as we stay below the chiral phase transition.

Complex poles and spectral functions of Landau gauge QCD and QCD-like theories

In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group $SU(3)$ and various numbers of quark flavors $N_F$ within the asymptotic free region. Both the gluon and quark propagators at the best-fit parameters for $N_F=2$ QCD have one pair of complex conjugate poles, while the number of complex poles in the gluon propagator varies between zero and four depending on the number of quark flavors and quark mass. Moreover, as a general feature, we argue that the gluon spectral function of this model with nonzero quark mass is negative in the infrared limit. In sharp contrast to gluons, the quark and ghost propagators are insensitive to the number of quark flavors within the current approximations adopted in this paper. These results suggest that details of the confinement mechanism may depend on the number of quark flavors and quark mass.

Cyclic Mario worlds \u2014 color-decomposition for one-loop QCD

We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons.

Investigating the quark flavor dependence of the chiral magnetic effect with a multiphase transport model

Because the properties of the QCD phase transition and the chiral magnetic effect (CME) depend on the number of quark flavors ($N_{f}$) and quark mass, relativistic heavy-ion collisions provide a natural environment to investigate the flavor features if quark deconfinement occurs. We introduce an initial two-flavor or three-flavor dipole charge separation into a multiphase transport (AMPT) model to investigate the flavor dependence of the CME. By taking advantage of the recent ALICE data of charge azimuthal correlations with identified hadrons, we attempt to disentangle two-flavor and three-flavor CME scenarios in Pb+Pb collisions at 2.76 TeV. We find that the experimental data show a certain potential to distinguish the two scenarios, therefore we further suggest to collect more data to clarify the possible flavor dependence in future experiments.

Domain wall fermion QCD with the exact one flavor algorithm

Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$, where $\mathscr{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$ --- in particular, no square root is necessary --- enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors --- such as the strange or charm --- computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $\Delta I = 1/2$ $K \rightarrow \pi \pi$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $\mathscr{D}$, and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to re-use the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2+1 flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.

Holograms of a dynamical top quark

We present holographic descriptions of dynamical electroweak symmetry breaking models that incorporate the top mass generation mechanism. The models allow computation of the spectrum in the presence of large anomalous dimensions due to walking and strong Nambu--Jona-Lasinio interactions. Technicolor and QCD dynamics are described by the bottom-up Dynamic AdS/QCD model for arbitrary gauge groups and numbers of quark flavors. An assumption about the running of the anomalous dimension of the quark bilinear operator is input, and the model then predicts the spectrum and decay constants for the mesons. We add Nambu--Jona-Lasinio interactions responsible for flavor physics from extended technicolor, top-color, etc., using Witten's multitrace prescription. We show the key behaviors of a top condensation model can be reproduced. We study generation of the top mass in (walking) one doublet and one family technicolor models and with strong extended technicolor interactions. The models clearly reveal the tensions between the large top mass and precision data for $\ensuremath{\delta}\ensuremath{\rho}$. The necessary tunings needed to generate a model compatible with precision constraints are simply demonstrated.

QCD fixed points: Banks–Zaks scenario or dynamical gluon mass generation?

Fixed points in QCD can appear when the number of quark flavors [Formula: see text] is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass (DGM) generation does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their [Formula: see text] functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large [Formula: see text], we verify that between [Formula: see text] and [Formula: see text] both cases exhibit fixed points at similar coupling constant values [Formula: see text]. We argue that the states of minimum vacuum energy, as a function of the coupling constant up to [Formula: see text] and for several [Formula: see text] values, are related to the dynamical gluon mass generation mechanism.

Polyakov loop fluctuations and deconfinement in the limit of heavy quarks

We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows, and the first-order transition ends in a critical end point. The nature of the critical end point is examined by studying the longitudinal and transverse fluctuations of the Polyakov loop, quantified by the corresponding susceptibilities. The longitudinal susceptibility is enhanced in the critical region, while the transverse susceptibility shows a monotonic behavior across the transition point. We investigate the dependence of the critical end point on the number of quark flavors at vanishing and finite quark density and relate these results to lattice findings.

The Equation of State for Non-ideal Quark Gluon Plasma

The mass spectra of quarkonium systems at T= 0 are analyzed by solving the nonrelativistic radial wave equation using the internal energy potential. The QGP matter is studied through the dissociations of quarkonium states. A modified form of the internal energy potential function is used to determine the EoS at different number of quark flavors by using Mayer's cluster expansion theory and phenomenological thermodynamic model. The thermodynamic model gives a good agreement with the lattice results rather than Mayer’s cluster expansion theory. One can conclude that, the Mayer’s cluster expansion theory may be more suitable to study a weakly coupled plasma while, the QGP may be considered as a strongly interacting plasma.

QCD topology at finite temperature: Statistical mechanics of self-dual dyons

Topological phenomena in gauge theories have long been recognized as the driving force for chiral symmetry breaking and confinement. These phenomena can be conveniently investigated in the semiclassical picture, in which the topological charge is entirely carried by (anti-)self-dual gauge configurations. In such an approach, it has been shown that near the critical temperature, the nonzero expectation value of the Polyakov loop (holonomy) triggers the ``Higgsing'' of the color group, generating the splitting of instantons into ${N}_{c}$ self-dual dyons. A number of lattice simulations have provided some evidence for such dyons, and traced their relation with specific observables, such as the Dirac eigenvalue spectrum. In this work, we formulate a model, based on one-loop partition function and including Coulomb interaction, screening and fermion zero modes. We then perform the first numerical Monte Carlo simulations of a statistical ensemble of self-dual dyons, as a function of their density, quark mass and the number of flavors. We study different dyonic two-point correlation functions and we compute the Dirac spectrum, as a function of the ensemble diluteness and the number of quark flavors.

Conformality in many-flavour lattice QCD at strong coupling

Abstract It is widely believed that chiral symmetry is spontaneously broken at zero temperature in the strong coupling limit of staggered fermions, for any number of colors and flavors. Using Monte Carlo simulations, we show that this conventional wisdom, based on a mean-field analysis, is wrong. For sufficiently many fundamental flavors, chiral symmetry is restored via a bulk, first-order transition. This chirally symmetric phase appears to be analytically connected with the expected conformal window of many-flavor continuum QCD. We perform simulations in the chirally symmetric phase at zero quark mass for various system sizes L, and measure the torelon mass, the Dirac spectrum and the hadron spectrum. All masses go to zero with 1/L. L is hence the only infrared length scale. Thus, the strong-coupling chirally restored phase appears as a convenient laboratory to study IR-conformality. Finally, we present a conjecture for the phase diagram of lattice QCD as a function of the bare coupling and the number of quark flavors.

Holographic equations of state and astrophysical compact objects

We solve the Tolman-Oppenheimer-Volkoff equation using an equation of state (EoS) calculated in holographic QCD. The aim is to use compact astrophysical objects like neutron stars as an indicator to test holographic equations of state. We first try an EoS from a dense D4/D8/D8 model. In this case, however, we could not find a stable compact star, a star satisfying pressure-zero condition with a radius R, p(R) = 0, within a reasonable value of the radius. This means that the EoS from the D4/D8/D8 model may not support any stable compact stars or may support one whose radius is very large. This might be due to a deficit of attractive force from a scalar field or two-pion exchange in the D4/D8/D8 model. Then, we consider D4/D6 type models with different number of quark flavors, N f = 1, 2, 3. Though the mass and radius of a holographic star is larger than those of normal neutron stars, the D4/D6 type EoS renders a stable compact star.

Dielectric correction to the chiral magnetic effect

We derive an electric current density $j_{em}$ in the presence of a magnetic field $B$ and a chiral chemical potential $\mu_5$. We show that $j_{em}$ has not only the anomaly-induced term $\propto \mu_5 B$ (i.e. Chiral Magnetic Effect) but also a non-anomalous correction which comes from interaction effects and expressed in terms of the susceptibility. We find the correction characteristically dependent on the number of quark flavors. The numerically estimated correction turns out to be a minor effect on heavy-ion collisions but can be tested by the lattice QCD simulation.

Is the number of light flavors in QCD great?

At a qualitative level, it is well known that QCD featuring a large number of quark flavors must differ drastically from actual QCD. However, it is possible to consider the large-Nf limit (where Nf is the number of light flavors in QCD) such that the basic dynamics of the system remains unchanged. This is the region of chiral perturbation theory, where the limit Nf → ∞ is simultaneously the limit of a large number of colors, Nc. Features are indicated that make it possible, in such a situation, to compare analytically the same quantity in a simplified model of actual QCD and in the large-Nf limit, and methods are proposed for calculating these features. Calculations in the limit Nf → ∞ are of no use in assessing quantities of the theory at small N f.

Chiral symmetry restoration in linear sigma models with different numbers of quark flavors

Chiral symmetry restoration at nonzero temperature is studied in the framework of the O(4) linear sigma model and the U(N_f)_r x U(N_f)_l linear sigma model with N_f=2,3, and 4 quark flavors. We investigate the temperature dependence of the masses of the scalar and pseudoscalar mesons, and the non-strange, strange, and charm condensates within the Hartree approximation as derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses of the non-strange and strange mesons at nonzero temperature depend sensitively on the particular symmetry of the model and the number of light quark flavors N_f. On the other hand, due to the large charm quark mass, neither do charmed mesons significantly affect the properties of the other mesons, nor do their masses change appreciably in the temperature range around the chiral symmetry restoration temperature. In the chiral limit, the transition temperatures for chiral symmetry restoration are surprisingly close to those found in lattice QCD.

Zero temperature phase structure of multi-flavor QCD

To study continuum limit of lattice QCD with many light quark flavors, we investigate the zero temperature phase structures of multi-flavor QCD. Currently a series of exploratory simulations are being performed with the number of quark flavors, N f = 6, 8, and 10 on a set of lattice volumes for various quark masses. Here, we report on the current status of our simulation on a 8 4 lattice.

Finite temperature behavior of the 3D Polyakov model with massless quarks

The (2+1)D Georgi-Glashow (or Polyakov) model with the additional fundamental massless quarks is explored at finite temperature. In the case of vanishing Yukawa coupling, it is demonstrated that the interaction of a monopole and an antimonopole in the molecule via quark zero modes leads to the decrease of the Berezinsky-Kosterlitz-Thouless critical temperature when the number of quark flavors is equal to one. If the number of flavors becomes larger, monopoles are shown to exist only in the molecular phase at any temperatures exceeding a certain exponentially small one. This means that for such a number of flavors and at such temperatures, no fundamental matter can be confined by means of the monopole mechanism.

Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, eta, and mass renormalization critical exponents at O(1/N_f^2) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MSbar results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N_f^2). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for eta in arbitrary covariant gauge is given.

The flavour and quark mass dependence of thermodynamic quantities in lattice QCD

The dependence of thermodynamic properties of QCD on the number of quark flavours is investigated. Lattice results for the equation of state are presented for 2, 2+1 and 3 quark flavours. The simulations have been performed with the improved p4-staggered fermion and a Symanzik improved gluon action on lattices of size 16 3 × 4 and 16 4.

On two-color QCD with baryon chemical potential

We study SU(2) color QCD with even number of quark flavors. First, using QCD inequalities we show that at finite baryon chemical potential μ, condensation must occur in the channel with scalar diquark quantum numbers. This breaks the U(1) symmetry generated by baryon charge (baryon superconductivity). Then we derive the effective Lagrangian describing low lying meson and baryon excitations using extended local chiral symmetry of the theory. This enables us to determine the leading term in the dependence of the masses on μ exactly.