QCD Action Research Articles

Heavy quarks on anisotropic lattices: The charmonium spectrum

We present results for the mass spectrum of $c{\bar c}$ mesons simulated on anisotropic lattices where the temporal spacing $a_t$ is only half of the spatial spacing $a_s$. The lattice QCD action is the Wilson gauge action plus the clover-improved Wilson fermion action. The two clover coefficients on an anisotropic lattice are estimated using mean links in Landau gauge. The bare velocity of light $\nu_t$ has been tuned to keep the anisotropic, heavy-quark Wilson action relativistic. Local meson operators and three box sources are used in obtaining clear statistics for the lowest lying and first excited charmonium states of $^1S_0$, $^3S_1$, $^1P_1$, $^3P_0$ and $^3P_1$. The continuum limit is discussed by extrapolating from quenched simulations at four lattice spacings in the range 0.1 - 0.3 fm. Results are compared with the observed values in nature and other lattice approaches. Finite volume effects and dispersion relations are checked.

Testing imaginary vs. real chemical potential in finite-temperature QCD

One suggestion for determining the properties of QCD at finite temperatures and densities is to carry out lattice simulations with an imaginary chemical potential whereby no sign problem arises, and to convert the results to real physical observables only afterwards. We test the practical feasibility of such an approach for a particular class of physical observables, spatial correlation lengths in the quark–gluon plasma phase. Simulations with imaginary chemical potential followed by analytic continuation are compared with simulations with real chemical potential, which are possible by using a dimensionally reduced effective action for hot QCD (in practice we consider QCD with two massless quark flavours). We find that for imaginary chemical potential the system undergoes a phase transition at | μ/ T|≈ π/3, and thus observables are analytic only in a limited range. However, utilising this range, relevant information can be obtained for the real chemical potential case.

Lattice QCD and chiral mesons

The standard QCD action is improved by the addition of irrelevant operators built with chiral composites. An effective Lagrangian is derived in terms of auxiliary fields, which has the form of the phenomenological chiral Lagrangians. Our improved QCD action appears promising for numerical simulations as the pion physics is explicitely accounted for by the auxiliary fields.

Chiral symmetry in lattice QCD

A chiral invariant effective action for lattice QCD is proposed. Its connection to the multifermion model is established. A possibility of using this action for computer simulations is discussed.

Wong’s equations and the smallxeffective action in QCD

We propose a new form for the small x effective action in QCD. This form of the effective action is motivated by Wong's equations for classical, colored particles in non-Abelian background fields. We show that the BFKL equation, which sums leading logarithms in x, is efficiently reproduced with this form of the action. We argue that this form of the action may be particularly useful in computing next-to- leading-order results in QCD at small x.

DUAL MEISSNER EFFECT IN THE INFRARED REGION OF QCD WITH QUARKS

Motivated by the suggestion of 't Hooft and Mandelstam that magnetic monopoles must play a crucial role in the ir region of QCD and that of Nambu that dual Meissner effect as a mechanism of confinement, QCD in this region is described by the magnetic symmetry of Cho. The standard SU(3) QCD action with quarks is considered which now contains the monopole configurations. A dual action is constructed and mass term for the dual Abelian field is generated by gauge mixing mechanism. The effective dual action thus obtained exhibits dual Meissner effect.

The extended chiral quark model confronts QCD

We discuss the truncation of low energy effective action of QCD below the chiral symmetry breaking (CSB) scale, including all operators of dimensionality less or equal to 6 which can be built with quark and chiral fields. We perform its bosonization in the scalar, pseudoscalar, vector and axial-vector channels in the large- N c and leading-log approximation. Constraints on the coefficients of the effective lagrangian are derived from the requirement of Chiral Symmetry Restoration (CSR) at energies above the CSB scale in the scalar-pseudoscalar and vector-axial-vector channels, from matching to QCD at intermediate scales, and by fitting some hadronic observables. In this truncation two types of pseudoscalar states (massless pions and massive II-mesons), as well as a scalar, vector and axial-vector one arise as a consequence of dynamical chiral symmetry breaking. Their masses and coupling constants as well as a number of chiral structural constants are derived. A reasonable fit of all parameters supports a relatively heavy scalar meson (quarkonium) with the mass ∼ 1 GeV and a small value of axial pion-quark coupling constant g A ≅ 0.55.

Structure of the exact effective action and quark confinement in MSSM QCD

An expression for the exact (beyond perturbation theory) effective action in N=1 supersymmetric gauge theories where all particles, with the exception of gauge bosons, are massive is proposed. By analyzing the form of this expression, it is shown that, in supersymmetric theories, instanton effects can lead to quark confinement. On the basis of first principles, the characteristic scale of confinement is calculated within MSSM QCD, and the result is found to be consistent with experimental data. The proposed explanation differs drastically with the dual Higgs mechanism.

Monopoles and gluon fields in QCD in the maximally abelian gauge

We study monopoles and gluon fields in QCD in the maximally abelian (MA) gauge in the context of the dual superconductor picture for confinement. In the abelian gauge, unit charge magnetic monopoles appear, but multi-charge monopoles do not in general cases. The appearance of the monopole is studied in relation to the SU(Nc) singular gauge transformation. The relevant role of off-diagonal gluons is found for the appearance of monopoles in the abelian gauge in QCD. We study the gluon-field properties around the monopole in the MA gauge in terms of the action density using lattice QCD. The monopole provides infinitely large field fluctuations in the abelian sector. In the MA gauge, off-diagonal gluons are strongly suppressed but largely remain around the monopole, which indicates the effective size and the structure of monopoles. We find large cancellation between the abelian part and the off-diagonal part of the action density around the monopole in the MA gauge. Owing to this cancellation, the monopole can appear in QCD without large cost to the QCD action. Finally, we generalize the framework of the abelian projection, i.e. the extraction of the abelian gauge manifold from QCD, by introducing the `gluonic Higgs field' φD[Aμ(x)] defined from the SU(Nc) covariant derivative D̂μ. By way of φD[Aμ(x)], the maximally abelian projection can be performed in a gauge-covariant manner without the notion of gauge fixing in principle.

Heavy-light decay constants from clover heavy quark action in QCD with two flavors of dynamical quarks

We present results on an analysis of the decay constants f Bd and f Bs with two flavours of sea quark. The calculation has been carried out on 3 different bare gauge couplings and 4 sea quark masses at each gauge coupling, with m π / m ϱ ranging from 0.8 to 0.6. We employ the Fermilab formalism to perform calculations with heavy quarks whose mass is in the range of the b-quark. A detailed comparison with a quenched calculation using the same action is made to elucidate the effects due to the sea quarks.

Heavy-light decay constants from clover heavy quark action in QCD with two flavors of dynamical quarks

Heavy-light decay constants from clover heavy quark action in QCD with two flavors of dynamical quarks

Chiral Lagrangians and the QCD string

We propose a method to derive the low-energy effective action of QCD assuming that the long-distance properties of strong interactions can be described by a string theory. We bypass the usual problems related to the existence of the tachyon and absence of the adequate Adler zero by using a sigma model approach where excitations above the correct (chirally non-invariant) QCD vacuum are included. Two-dimensional conformal invariance then implies the vanishing of the O(p 4) effective lagrangian coefficients. We interpret this result and discuss ways to go beyond this limit.

The three flavour chiral phase transition with an improved quark and gluon action in lattice QCD

The finite-temperature chiral phase transition is investigated for three flavours of staggered quarks on a lattice of temporal extent N τ = 4. In the simulation we use an improved fermion action which reduces rotational symmetry breaking of the quark propagator (p4-action), include fat-links to improve the flavour symmetry and use the tree level improved (1,2) gluon action. We study the nature of the phase transition for quark masses of ma = 0.025, ma = 0.05 and ma = 0.1 on lattices with spatial sizes of 8 3 and 16 3.

Non-perturbative improvement of the anisotropic Wilson QCD action

We describe the first steps in the extension of the Symanzik O( a) improvement program for Wilson-type quark actions to anisotropic lattices, with a temporal lattice spacing smaller than the spatial one. This provides a fully relativistic and computationally efficient framework for the study of heavy quarks. We illustrate our method with accurate results for the quenched charmonium spectrum.

Chiral-Symmetry Breaking and Confinement in the Heavy-Light $\boldmath {q}\unboldmath \bar {\boldmath {q}\unboldmath $ System

The effective quark Lagrangian is derived from the QCD action by means of averaging over the vacuum fields. In the limit of large N_c and keeping for simplicity the lowest order gluonic correlator one obtains nonlinear equations for the quark propagator, exhibiting scalar confinement. Connection to the quark zero mode density is discussed.

The extended chiral quark model and QCD

We consider the low energy effective action of QCD below the chiral symmetry breaking scale, including, in Wilson's spirit, all operators of dimensionality less or equal to 6 ehich can be built with quark and chiral fields. The effect of gluon interactions is contained in a number of coupling constants, whose running is studied. The resulting model is an extension of both the chiral quark model and the Nambu-Jona-Lasinio one. Constraints on the coefficients of the effective Lagrangian are derived from the requirement of chiral symmetry restoration at energies above the chiral symmetry breaking scale, from matching to QCD at intermediate scales, and by fitting some hadronic observables. In this model two types of pseudoscalar states (massless pions and massive II-mesons), as well as one scalar one arise as a consequence of dynamical chiral symmetry breaking. Their masses and coupling constants are studied. We also predict a number of low energy structural constants. We find out that QCD favors a low energy effective theory which is largely dominated by the simplest chiral quark model, whereas higher dimensional operators (such as those of the Nambu-Jona-Lasinio type) can be assumed to be small.

Nexus solitons in the center vortex picture of QCD

It is very plausible that confinement in QCD comes from linking of Wilson loops to finite-thickness vortices with magnetic fluxes corresponding to the center of the gauge group. The vortices are solitons of a gauge-invariant QCD action representing the generation of gluon mass. There are a number of other solitonic states of this action. We discuss here what we call nexus solitons, in which for gauge group SU(N), up to N vortices meet a a center, or nexus, provided that the total flux of the vortices adds to zero (mod N). There are fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by the flux condition; and fully non-Abelian, resembling a deformed sphaleron. Analytic solutions are available for the quasi-Abelian case, and we discuss variational estimates of the action of the fully non-Abelian nexus solitons in SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge in four dimensions). Their presence does not change the fundamentals of confinement in the center-vortex picture, but they may lead to a modified picture of the QCD vacuum.

Lattice QCD without tuning, mixing and current renormalization

The classically perfect action of QCD requires no tuning to get the pion massless in the broken phase: the critical bare mass m q c is zero. Neither the vector nor the flavour non-singlet axial vector currents need renormalization. Further, there is no mixing between 4-fermion operators in different chiral representations. The order parameter of chiral symmetry requires, however, a subtraction which is given here explicitly. These results are based on the fact that the fixed point action satisfies the Ginsparg-Wilson remnant chiral symmetry condition. On chiral symmetry related questions any other local solution of this condition will produce similar results.

Effective action for high energy QCD and next-to-leading corrections to the BFKL pomeron

Using the effective action for gluon-Reggeon interactions local in the rapidity space the next-to-leading corrections to the QCD pomeron are discussed.

Scaling study of the two-flavor chiral phase transition with the Kogut-Susskind quark action in lattice QCD

We report on a study of the two-flavor finite-temperature chiral phase transition employing the Kogut-Susskind quark action and the plaquette gluon action in lattice QCD for a lattice with ${N}_{t}=4$ temporal size. Hybrid $R$ simulations of ${10}^{4}$ trajectories are made at quark masses of ${m}_{q}=0.075,0.0375,0.02,0.01$ in lattice units for the spatial sizes ${8}^{3}{,12}^{3}$, and ${16}^{3}$. The spatial size dependence of various susceptibilities confirm the previous conclusion of the absence of a phase transition down to ${m}_{q}=0.02$. At ${m}_{q}=0.01$ an increase of susceptibilities is observed up to the largest volume ${16}^{3}$ explored in the present work. We argue, however, that this increase is likely to be due to an artifact of too small a lattice size and it cannot be taken to be the evidence for a first-order transition. Analysis of critical exponents estimated from the quark mass dependence of susceptibilities shows that they satisfy hyperscaling consistent with a second-order transition located at ${m}_{q}=0$. The exponents obtained from larger lattice, however, deviate significantly from both those of O(2), which is the exact symmetry group of the Kogut-Susskind action at finite lattice spacing, and those of O(4) expected from an effective $\ensuremath{\sigma}$ model analysis in the continuum limit.