Free Quarks Research Articles

Finite density QCD with a canonical approach

We present a canonical method where the properties of QCD are directly obtained as a function of the baryon density rho, rather than the chemical potential mu. We apply this method to the determination of the phase diagram of four-flavor QCD. For a pion mass m_pi \sim 350 MeV, the first-order transition between the hadronic and the plasma phase gives rise to a co-existence region in the T-rho plane, which we study in detail, including the associated interface tension. We obtain accurate results for systems containing up to 30 baryons and quark chemical potentials mu up to 2 T. Our T-mu phase diagram agrees with the literature when mu/T \lesssim 1. At larger chemical potential, we observe a ``bending down'' of the phase boundary. We compare the free energy in the confined and deconfined phase with predictions from a hadron resonance gas and from a free massless quark gas respectively.

Meson correlation functions in a QCD plasma

The temporal pseudoscalar meson correlation function in a QCD plasma is investigated in a range of temperatures exceeding T c and yet of experimental interest. Only the flavour-singlet channel is considered and the imaginary time formalism is employed for the finite temperature calculations. The behaviour of the meson spectral function and of the temporal correlator is first studied in the HTL approximation, where one replaces the free thermal quark propagators with the HTL resummed ones. This procedure satisfactory describes the soft fermionic modes, but its application to the propagation of hard quarks is not reliable. An improved version of the so-called NLA scheme, which allows a better treatment of the hard fermionic modes, is then proposed. The impact of the improved NLA on the pseudoscalar temporal correlator is investigated.

QUARK–GLUON PLASMA IN A BAG MODEL WITH A SOFT SURFACE

We analyze the implications of quantum hadrodynamics (QHD) and quantum chromodynamics (QCD) to model, respectively, two distinct phases of nuclear matter, a baryon–meson phase and a quark–gluon phase. We develop an equation of state (EoS) in the framework of a quark–meson coupling model for the hadron–meson phase using a new version of the fuzzy bag model with scalar–isoscalar, vector–isoscalar and vector–isovector meson–quark couplings and leptonic degrees of freedom as well as the constrains from chemical equilibrium, baryon number and electric charge conservation. We model the EoS for the QGP phase for asymptotically free massless quarks and gluons using the MIT approach and a temperature and baryon chemical potential dependent bag constant, B(T,μ), which allows an isentropic equilibrium phase transition from a QGP to a hadron gas as determined by thermodynamics. Our predictions yield the EoS and static global properties of neutron stars and protoneutron stars at low and moderate values of temperature. Our results are slightly modified in comparison to predictions based on the standard MIT bag model with a constant bag pressure B.

A general solution for the quark propagator in two-dimensional covariant gauge QCD

We have investigated a closed set of equations for the quark propagator, which has been obtained earlier within a new, nonperturbative approach to two-dimensional covariant gauge QCD. It is shown that this theory implies quark confinement (the quark propagator has no poles, indeed), as well as dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidden). The above-mentioned set of equations can be exactly solved in the chiral limit. We develop an analytical formalism, the so-called chiral perturbation theory at the fundamental quark level, which allows one to find solution for the quark propagator in powers of the light quark masses. Each correction satisfies the differential equation, which can be formally solved. We develop also an analytical formalism which allows one to find solution for the quark propagator in the inverse powers of the heavy quark masses. It coincides with the free heavy quark propagator up to terms of order 1/mQ3, where mQ is the heavy quark mass. So this solution automatically possesses the heavy quark flavor symmetry up to terms of order 1/mQ. At the same time, we have found a general solution for the heavy quark propagator, which by no means can be reduced to the free one.

Strongly Coupled Plasmas in High-Energy Physics

One of the main activities in high-energy and nuclear physics is the search for the so-called quark-gluon plasma, a new state of matter which should have existed a few microseconds after the Big Bang. A quark-gluon plasma consists of free color charges, i.e. quarks and gluons, interacting by the strong (instead of electromagnetic) force. Theoretical considerations predict that the critical temperature for the phase transition from nuclear matter to a quark-gluon plasma is about 150 - 200 MeV. In the laboratory such a temperature can be reached in a so-called relativistic heavy-ion collision in accelerator experiments. Using the color charge instead of the electric charge, the Coulomb coupling parameter of such a system is of the order 10 - 30. Hence the quark-gluon plasma is a strongly coupled, relativistic plasma, in which also quantum effects are important. In the present work the experimental and theoretical status of the quark-gluon plasma physics will be reviewed, emphasizing the similarities and differences with usual plasma physics. Furthermore, the mixed phase consisting of free quarks and gluons together with hadrons (e.g. pions) will be discussed, which can be regarded as a complex plasma due to the finite extent of the hadrons.

LANDAU GHOSTS AND ANTI-GHOSTS IN CONDENSED MATTER AND HIGH DENSITY HADRONIC MATTER

It is observed that the "ghost" (originally discovered by Landau in quantum electro-dynamics) and its counterparts in other theories are indeed ubiquitous as they occur in a one-loop approximation to any conventional (unbroken) gauge theory. The mechanism is first exposed in its generality via the Dyson equation and a simple but explicit example in condensed matter is provided through the static Clausius–Mossotti equation and its dynamic counterpart, the Lorenz–Lorentz equation. The physical phase transition phenomenon associated with it is found to be super-radiance. We verify quantitatively that water (and many other polar liquids) are indeed super-radiant at room temperature. In quantum chromo-dynamics on the other hand, we encounter, thanks to asymptotic freedom, an "anti-ghost" which is closely associated with color confinement. Thus, in QCD, free quarks and glue exist in a super-radiant phase and hadronic matter exists in the normal one.

Infrared behavior of the running coupling constant and bound states in QCD

The perturbative expression of the running strong coupling constant \alpha_{\rm s}(Q^{2}) has an unphysical singularity for Q^{2} = \Lambda^{2}_{\rm QCD}. Various modification have been proposed for the infrared region. The effect of some of such proposals on the quark-antiquark spectrum is tested on a Bethe-Salpeter (second order) formalism which was successfully applied in previous papers to an overall evaluation of the spectrum in the light-light, light-heavy and heavy-heavy sectors (the only serious discrepancy with data being for the light pseudoscalar meson masses). In this paper only the {\rm c} \bar{\rm c}, {\rm b} \bar{\rm b} and {\rm q} \bar{\rm q} (q = u or d) cases are considered and fine structure is neglected. It is found that in the {\rm b} \bar{\rm b} and {\rm c} \bar{\rm c} cases the results are little sensitive to the specific choice. In the light-light case the Dokshitzer et al. prescription is again essentially equivalent to the truncation prescription used in the previous calculation and it is consistent with the same a priori fixing of the quark light masses on the typical current values m_{\rm u} = m_{\rm d} = 10 MeV (only the pion mass resulting completely out of scale of about 500 MeV). With the Shirkov-Solovtsov prescription, on the contrary, a reasonable agreement with the data is obtained only at the price of using a phenomenological momentum dependent effective mass for the quark. The use of such an effective mass should amount to a correction of the free quark propagator. It is remarkable that this has also the effect of bringing the pion mass in the correct range.

Dynamical symmetry breaking, confinement with flat-bottom potential

In this Letter, we calculate the dressed quark propagator with the flat bottom potential in the framework of the rainbow Schwinger–Dyson equation. Then based on the nonperturbative dressed quark propagator, we calculate the π decay constant and the quark condensate. The π decay constant is an important parameter in describing the interplay between dynamical symmetry breaking and confinement, while the quark condensate is an order parameter for dynamical chiral symmetry breaking. To implement confinement, we prove that the dressed quark propagator has no poles on the real timelike p 2 axial, the absence of Kallen–Lehmann spectral representation obviously precludes the existence of free quarks.

Λ0polarization as a probe for production of deconfined matter in ultrarelativistic heavy-ion collisions

We study the polarization change of Lambda^0's produced in ultra-relativistic heavy-ion collisions with respect to the polarization observed in proton-proton collisions as a signal for the formation of a Quark-Gluon Plasma (QGP). Assuming that, when the density of participants in the collision is larger than the critical density for QGP formation, the Lambda^0 production mechanism changes from recombination type processes to the coalescence of free valence quarks, we find that the Lambda^0 polarization depends on the relative contribution of each process to the total number of Lambda^0's produced in the collision. To describe the polarization of Lambda^0's in nuclear collisions for densities below the critical density for the QGP formation, we use the DeGrand-Miettinen model corrected for the effects introduced by multiple scattering of the produced Lambda^0 within the nuclear environment.

Global duality in heavy flavor decays in the ’t Hooft model

We average the decay width of a heavy meson in the 't Hooft model over the heavy quark mass M with a smooth weight function. The averaging has support over a few resonance spacings. We use the previously determined heavy meson decay width which differs from the free quark width by a $1/M$ correction. In contrast, we find that the averaged meson and quark widths differ by a ${1/M}^{2}$ correction. We speculate on the relevance of our results to the phenomenologically relevant case of (3+1)-dimensional QCD.

Dressed Quark Propagator at Finite Temperature in the Schwinger-Dyson Approach with the Rainbow Approximation: Exact Numerical Solutions and Their Physical Implication

The Schwinger-Dyson equation for the quark in the rainbow approximation at finite temperature (T) is solved numerically without introducing any ansatz for the dressed quark propagator. The dymanical quark mass-function and the wave-function renormalization are found to have non-trivial dependence on three-momentum, Matsubara-frequency and temperature. The critical temperature of the chiral phase transition (T_c) and the T-dependence of the quark condensate are highly affected by the wave-function renormalization. We found that T_c \simeq 155 MeV which is consistent with the result of the finite temperature lattice QCD simulation. It is also found that the system is not a gas of free quarks but a highly interacting system of quarks and gluons even in the chirally symmetric phase.

STRANGE STAR IN THE PRESENCE OF A STRONG MAGNETIC FIELD

We study the effect of a strong magnetic field on interacting quark matter and apply the same to strange star. We find that interacting strange matter is less stable than noninteracting strange matter in the presence of a strong magnetic field. We then calculate strange star structure parameters such as mass and radius and find that the strange star is less compact for interacting quark matter than for free quark matter in presence of strong magnetic field. The maximum masses of strange stars are found to be within the recent observational limit.

Production processes as a tool to study parametrizations of quark confinement

We introduce diquarks as separable correlations in the two-quark Green's function to facilitate the description of baryons as relativistic three-quark bound states. These states then emerge as solutions of Bethe-Salpeter equations for quarks and diquarks that interact via quark exchange. When solving these equations we consider various dressing functions for the free quark and diquark propagators that prohibit the existence of corresponding asymptotic states and thus effectively parametrize confinement. We study the implications of qualitatively different dressing functions on the model predictions for the masses of the octet baryons as well as the electromagnetic and strong form factors of the nucleon. For different dressing functions we in particular compare the predictions for kaon photoproduction, $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}K\ensuremath{\Lambda},$ and associated strangeness production, $p\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{pK}\ensuremath{\Lambda},$ with experimental data. This leads to conclusions on the permissibility of different dressing functions.

Contractor renormalization group and the Haldane conjecture

The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}1/2$ and $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}1$ HAF.

Meson screening masses at high temperature in quenched QCD with improved Wilson Quarks

We report on a lattice investigation of improved quenched Wilson fermions above and below the confinement-deconfinement phase transition. Results on meson screening masses as well as spatial wave functions are presented. Moreover, the meson dispersion relation is studied. Below the critical temperature we do not observe any significant temperature effect while above $T_c$ the data are consistent with a leading free quark behavior.

The discovery of quarks

AbstractIn the period following World War II, there was a rapid development of particle physics. With the construction of synchrotrons and the development of detector technology, many new particles were discovered and the systematics of their interactions investigated. The invention of the bubble chamber played an especially important role in uncovering the rich array of hadrons that were discovered in this period.In 1961 Murray Gell‐Mann [1] and Yuval Ne'eman [2] independently introduced a classification scheme, based on SU(3) symmetry, which placed hadrons into families on the basis of spin and parity. Like the periodic table for the elements, this scheme was predictive as well as descriptive, and various hadrons, such as the Ω—, were predicted within this framework and were later discovered.In 1964 Gell‐Mann [3] and George Zweig [4] independently proposed quarks as the building blocks of hadrons as a way of generating the SU(3) classification scheme. When the quark model was first proposed, it postulated three types of quarks: up (u), down (d), and strange (s), with charges 2/3, —1/3, and —1/3 respectively. Each of these was hypothesized to be a spin1/2 particle. In this model the nucleon (and all other baryons) is made up of three quarks, and each meson consists of a quark and an antiquark. For example, as the proton and neutron both have ero strangeness, they are (u,u,d) and (d,d,u) systems respectively.Though the quark model provided the best available tool for understanding the properties of the hadrons that had been discovered at the time, the model was thought by many to be merely a mathematical representation of some deeper dynamics, but one of heuristic value. Among the reasons for this assessment were the following:free quarks had not been found though they had been sought in numerous accelerator and cosmic ray investigations and in searches in the terrestrial environment; there was a deep suspicion about the validity of their fractional charge assignments; and some of the baryon states constructed on the basis of the quark model violated the Pauli exclusion principle. Despite these difficulties there were a small number of theorists who continued to apply the model to explain a wide range of hadronic phenomena.The theory of hadron structure that was most widely accepted at the time was the bootstrap model, an approach based on S‐Matrix theory. This model, sometimes referred to as “nuclear democracy,” was based on the idea that there were no fundamental particles and that all hadrons are made up of one another. This picture was consistent with the low momentum transfer scattering seen in hadron‐hadron interactions and with the observed “soft” electromagnetic form factors of the proton and neutron; however, it could not provide the comprehensive description of multiplet structures that was given by the quark model.Inelastic electron‐nucleon scattering results, and later those from neutrino‐scattering, played a pivotal role in resolving this dilemma by firmly establishing the quark model. These experiments demonstrated that the proton and neutron are composite structures made up of point‐like spin 1/2 constituents, with fractional charges consistent with those of quarks.More detailed descriptions of the deep inelastic program and its results are given in the written versions of the 1990 Nobel Lectures in Physics of Richard Taylor [5], Henry Kendall [6], and the author [7].

Counting and entangling Planck's quanta with atoms in a box

In the period following World War II, there was a rapid development of particle physics. With the construction of synchrotrons and the development of detector technology, many new particles were discovered and the systematics of their interactions investigated. The invention of the bubble chamber played an especially important role in uncovering the rich array of hadrons that were discovered in this period. In 1961 Murray Gell-Mann [1] and Yuval Ne'eman [2] independently introduced a classification scheme, based on SU(3) symmetry, which placed hadrons into families on the basis of spin and parity. Like the periodic table for the elements, this scheme was predictive as well as descriptive, and various hadrons, such as the Ω—, were predicted within this framework and were later discovered. In 1964 Gell-Mann [3] and George Zweig [4] independently proposed quarks as the building blocks of hadrons as a way of generating the SU(3) classification scheme. When the quark model was first proposed, it postulated three types of quarks: up (u), down (d), and strange (s), with charges 2/3, —1/3, and —1/3 respectively. Each of these was hypothesized to be a spin1/2 particle. In this model the nucleon (and all other baryons) is made up of three quarks, and each meson consists of a quark and an antiquark. For example, as the proton and neutron both have ero strangeness, they are (u,u,d) and (d,d,u) systems respectively. Though the quark model provided the best available tool for understanding the properties of the hadrons that had been discovered at the time, the model was thought by many to be merely a mathematical representation of some deeper dynamics, but one of heuristic value. Among the reasons for this assessment were the following:free quarks had not been found though they had been sought in numerous accelerator and cosmic ray investigations and in searches in the terrestrial environment; there was a deep suspicion about the validity of their fractional charge assignments; and some of the baryon states constructed on the basis of the quark model violated the Pauli exclusion principle. Despite these difficulties there were a small number of theorists who continued to apply the model to explain a wide range of hadronic phenomena. The theory of hadron structure that was most widely accepted at the time was the bootstrap model, an approach based on S-Matrix theory. This model, sometimes referred to as “nuclear democracy,” was based on the idea that there were no fundamental particles and that all hadrons are made up of one another. This picture was consistent with the low momentum transfer scattering seen in hadron-hadron interactions and with the observed “soft” electromagnetic form factors of the proton and neutron; however, it could not provide the comprehensive description of multiplet structures that was given by the quark model. Inelastic electron-nucleon scattering results, and later those from neutrino-scattering, played a pivotal role in resolving this dilemma by firmly establishing the quark model. These experiments demonstrated that the proton and neutron are composite structures made up of point-like spin 1/2 constituents, with fractional charges consistent with those of quarks. More detailed descriptions of the deep inelastic program and its results are given in the written versions of the 1990 Nobel Lectures in Physics of Richard Taylor [5], Henry Kendall [6], and the author [7].

Neutrino propagation in color superconducting quark matter

We calculate the neutrino mean free path in color superconducting quark matter, and employ it to study the cooling of matter via neutrino diffusion in the superconducting phase as compared to a free quark phase. The cooling process slows when quark matter undergoes a second order phase transition to a superconducting phase at the critical temperature ${T}_{c}.$ Cooling subsequently accelerates as the temperature decreases below ${T}_{c}.$ This will directly impact the early evolution of a newly born neutron star, should its core contain quark matter. Consequently, there may be observable changes in the early neutrino emission which would provide evidence for superconductivity in hot and dense matter.

Is the electric charge conserved in brane world?

We discuss whether electric charge conservation may not hold in four-dimensional world in models with infinite extra dimensions, i.e., whether escape of charged particles from our brane is consistent with effectively four-dimensional electrodynamics on the brane. We introduce a setup with photon localized on the brane and show that charge leakage into extra dimension is allowed within this setup. The electric field induced on the brane by escaping charge does not obey four-dimensional Maxwell's equations; this field gradually disappears in a causal way. We also speculate on the possibility of the escape of colored particles and formation of colorless free quark states on the brane.

Hamiltonian lattice quantum chromodynamics at finite chemical potential

At sufficiently high temperature and density, quantum chromodynamics (QCD) is expected to undergo a phase transition from the confined phase to the quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo method works well for QCD at finite temperature, however, it breaks down at finite chemical potential. We develop a Hamiltonian approach to lattice QCD at finite chemical potential and solve it in the case of free quarks and in the strong coupling limit. At zero temperature, we calculate the vacuum energy, chiral condensate, quark number density and its susceptibility, as well as mass of the pseudoscalar, vector mesons and nucleon. We find that the chiral phase transition is of first order, and the critical chemical potential is $\mu_C =m_{dyn}^{(0)}$ (dynamical quark mass at $\mu=0$). This is consistent with $\mu_C \approx M_N^{(0)}/3$ (where $M_N^{(0)}$ is the nucleon mass at $\mu=0$).