Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.
Differences between vector potentials in different gauges contain no dynamics in both classical and quantum electrodynamics and chromodynamics. Consequently, once gauge invariance is established, results calculated in non-covariant gauges can be expected to agree with results obtained in covariant gauges in all Lorentz frames. We show in particular that canonical quantization in the Coulomb gauge can be used without giving up explicit gauge invariance. Quantization in the Coulomb gauge is particularly simple because it involves only the two transverse photons/gluons present in all gauges. Thes…
Quantum chromodynamics is the quantum gauge field theory that describes the strong interactions. This article reviews the basic structure, successes and challenges of quantum chromodynamics as it manifests itself at short and long distances, including the concepts of asymptotic freedom, confinement and infrared safety.
Using some assumptions about the correlation function of velocity in a turbulent flow, a cylindrically symmetric tube-like solution is obtained. It is proposed that this turbulent flow is similar to a flux tube in quantum chromodynamics. Using similar assumptions for quantum chromodynamics, a flux tube filled with a color electric field is obtained. The connection between turbulence theory and quantum chromodynamics is discussed.
Recently the new interest arised (hep-ph/0403139) to the chiral coefficients $L_{11}, L_{12}, L_{13}$ in the low-energy ChPT lagrangian describing the pseudoscalar meson coupling to gravity and/or light singlet dilatons. In 90ties we estimated these coefficients within the Chiral and Conformal Bosonization Model but published the results in the journal not easily accessible for the physics community. We put now our old paper to the E-archives.
It is shown that the Lagrangian of Quantum Chromodynamics can be modified by the adding gluon masses. On mass-shell renormalizability of the resulting theory is discussed.
This talk reviews some recent trends in perturbative quantum chromodynamics, with emphasis on higher orders in perturbation theory, resummation and power corrections.
The Odderon is the leading exchange in hadronic scattering processes at high energies in which negative charge conjugation and parity quantum numbers are transferred in the t-channel. We review the origin of the Odderon in Regge theory, its status in perturbative and nonperturbative Quantum Chromodynamics, as well as its phenomenology.
We present the analytical calculation in perturbative Quantum Chromodynamics of the (alpha_s)^3 contribution to the Ellis-Jaffe sum rule for the structure function g1 of polarized deep inelastic lepton-nucleon scattering.
The classical Lagrangian of chromodynamics, its quantization in the perturbation theory framework, and renormalization form the subject of these lectures. Symmetries of the theory are discussed. The dependence of the coupling constant $α_s$ on the renormalization scale $μ$ is considered in detail.
We survey results in lattice quantum chromodynamics from groups in the USQCD Collaboration. The main focus is on physics, but many aspects of the discussion are aimed at an audience of computational physicists.
We discuss three topics relevant to testing the Standard Model to high precision: commensurate scale relations, which relate observables to each other in pertubation theory without renormalization scale or scheme ambiguity, the relationship of compositeness to anomalous moments, and new methods for measuring the anomalous magnetic and quadrupole moments of the W and Z.
I discuss methods based on the large Nc expansion to study nonperturbative aspects of quantum chromodynamics, the theory of the strong force. I apply these methods to the analysis of weak decay processes and the nonperturbative computation of the weak matrix elements needed for a complete evaluation of these decays in the Standard Model of elementary particle physics.
The variational Hamiltonian approach to Quantum Chromodynamics in Coulomb gauge is investigated within the framework of the canonical recursive Dyson--Schwinger equations. The dressing of the quark propagator arising from the variationally determined non-perturbative kernels is expanded and renormalized at one-loop order, yielding a chiral condensate compatible with the observations.
We examine the effect of quantum longitudinal rescaling of coordinates, on the action of quantum chromodynamics (with quarks) to one loop. We use an aspherical Wilsonian integration (previously applied to the pure Yang-Mills theory and to quantum electrodynamics). Quantum fluctuations produce anomalous powers of the rescaling parameter in the coefficients of the rescaled action. Our results are valid for small rescalings only, because perturbation theory breaks down for large rescalings.
It is commonly believed that $π^0 \to 2 γ$ decay shows that there are three colours in Quantum Chromodynamics (QCD). It is shown here that this is not correct. When correct colour dependent charges of the quarks are considered then it is shown that this decay does not make any statement about the number of colours in QCD.
We establish that in Quantum Chromodynamics (QCD) at zero temperature, SU_{L+R}(N_F) exhibits the vector mode conjectured by Georgi and SU_{L-R}(N_F) is realized in either the Nambu-Goldstone mode or else Q_5^a is also screened from view at infinity. The Wigner-Weyl mode is ruled out unless the beta function in QCD develops an infrared stable zero.
In the high density, low temperature limit, Quantum Chromodynamics exhibits a transition to phases characterized by color superconductivity and energy gaps in the fermion spectra. We review some fundamental results obtained in this area and in particular we describe the low energy effective lagrangian describing the motion of the quasi-particles in the high density medium (High Density Effective Theory).
Using Dyson-Schwinger equations we obtain an ultraviolet asymptotics for the dynamical mass of quark in QCD. We also determine a numerical value for the πmeson decay constant f_π.
These lectures provide an overview of Quantum Chromodynamics (QCD), the SU(3) gauge theory of the strong interactions. The running of the strong coupling and the associated property of Asymptotic Freedom are analyzed. Some selected experimental tests and the present knowledge of $α_s$ and the quark masses are briefly summarized. A short description of the QCD flavour symmetries and the dynamical breaking of chiral symmetry is also given.
I make some remarks on events leading to the final formulation of quantum chromodynamics, stimulated by the ``Search and Discovery''article by Bertram Schwarzschild in the December, 2004 {\it Physics Today}. The following text and references is being submitted as a letter to the editor of {\it Physics Today}.
Using a technique devised by Bender, Milton and Savage, we derive the Dyson-Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The 't~Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field t…
We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton and ${}^3$He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to $m_π\sim 800$ MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of ${}^3$He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired prot…
The perturbative quantum chromodynamics (pQCD) has been extremely successful in the prediction and description of main properties of quark and gluon jets. There are, however, some problems of the jet calculus with the higher order corrections of the modified perturbative expansion which should be resolved to get more precise statements. Some of them are discussed here.
The Broadhurst-Kataev conjecture, that the ``discrepancy'' in the connection with the $π^0 \to γγ$ anomaly equals the beta function $β(\barα)$ times a power series in the effective coupling $\barα$, is proven to all orders of perturbative quantum chromodynamics. The use of nested short-distance expansions is justified via Weinberg's power-counting theorem.
The Faddeev two body bound state model is discussed as an example of a QCD inspired model thought by some to exhibit dimensional transmutation. This simple model is solved exactly and the growth of a specified dimensional energy scale is shown to be an illusion.
We show by explicit construction of an alternative theory for the strong interactions that it cannot be distinguished from QCD by any of the usual precision tests except on extending these theories to the full electroweak theory, by the Z- particle width.
We suggest the idea, supported by concrete calculations within chiral models, that the critical endpoint of the phase diagram of Quantum Chromodynamics with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, $μ_5$, conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, $μ$, to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping o…
In this report, I discuss the current state of the problem of the axial anomaly in quantum electrodynamics (QED) and quantum chromodynamics (QCD) and how the axial anomaly is related to the structure of the vacuum in QCD. In QCD, the vacuum average of the axial anomaly is proportional to a new quantum number n, the winding number. The axial anomaly condition implies that there are zero modes of the Dirac equation for a massless quark and that there is spontaneous breaking of chiral symmetry in QCD, which leads to the formation of a quark condensate. The axial anomaly can be represented in the …
The possible connection between High-T$_c$ superconductivity and quantum chromodynamics is considered that is based on two interacting Ginzburg-Landau equations. For High-T$_c$ superconductivity these two equations describe Cooper electrons interacting with different kind of quasi particles (phonons, magnons, excitons and so on). The interaction term describes a possible interaction between different kind of quasi particles. For quantum chromodynamics the equations describe two kinds of gauge condensates. The condensates describe a gauge potential from a subalgebra of the SU(3) gauge group and…
We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in Quantum Chromodynamics (QCD). We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results, that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.
A six-quark state with the benzene-like structure is proposed and studied based on color string model. The calculation with the quadratic confinement show that such structure has the lowest energy among the various hidden color six-quark structures proposed so far. Its possible effect on $NN$ scattering is discussed.
It is argued that exotic mesons consisting of two quarks and two antiquarks are not ruled out in quantum chromodynamics with a large number $N$ of colors, as generally thought. They can come in two varieties: short-lived tetraquarks with decay rates proportional to $N$, which would be unobservable if $N$ were sufficiently large, and long-lived tetraquarks with decay rates proportional to 1/N. The $f_0(500)$ and $f_0(980)$ may be examples of these two varieties of exotic mesons.
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects (such as gluon recombination) is a reaction-diffusion process. In these lectures, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for…
These lectures provide an overview of Quantum Chromodynamics (QCD), the $SU(3)_C$ gauge theory of the strong interactions. After briefly reviewing the empirical considerations which lead to the introduction of {\it colour}, the QCD Lagrangian is discussed. The running of the strong coupling and the associated property of {\it Asymptotic Freedom} are analyzed. Some selected experimental tests and the present knowledge of $α_s$ are summarized. A short description of the QCD flavour symmetries and the {\it dynamical breaking of chiral symmetry} is also given.
We show that two dimensional QCD can, to a good approximation, describe the hadronic structure functions measured in Deep Inelastic Scattering. We transform this theory into a new form, Quantum HadronDynamics (QHD), whose semi-classical approximation is closer to nature. The Baryon is then a topological soliton, and its structure function can be predicted by a variational principle. This prediction can be tested by comparison with measurements of neutrino scattering cross-sections.
We calculate the renormalization group flows of all perturbatively renormalizable interactions in the three-dimensional Ginzburg-Landau potential for the chiral phase transition of three-flavor quantum chromodynamics. On the contrary to the common belief we find a fixed point in the system that is able to describe a second-order phase transition in the infrared. This shows that long-standing assumptions on the transition order might be false. If the transition is indeed of second-order, our results may hint that the axial $U(1)$ symmetry restores at the transition temperature.
We have investigated $B_c$ spectroscopy with the use of a quantum-chromodynamic potential model which was recently used by us for the light-heavy quarkonia. We give our predictions for the energy levels and the $E$1 transition widths. We also find, rather surprisingly, that although $B_c$ is not a light-heavy system, the heavy quark effective theory with the inclusion of the $m_b^{-1}$ and $m_b^{-1}\ln m_b$ corrections is as successful for $B_c$ as it is for $B$ and $B_s$.
We exactely calculate the inclusive transverse momentum (kt) distributions and the 2-particle momentum correlations in high energy hadronic jets at the Modified Leading Logarithmic Approximation (MLLA) of QCD (Quantum Chromodynamics). We first obtain the exact solution of the evolution equations at "small x", which we calculate at the so called "limiting spectrum". We then go beyond this approximation by performing the steepest descent evaluation, which allows to generalize the preceeding results. Our predictions are in good agreement with the data (LEP, Tevatron) and improve those which have …
We construct the effective potential for the dimension two composite operator 1/2 A^{a 2}_μin QCD with massless quarks in the Landau gauge for an arbitrary colour group at two loops. For SU(3) we show that an estimate for the effective gluon mass decreases as N_f increases.
Dispersion relations for the scattering of hadrons are considered within the framework of Quantum Chromodynamics. It is argued that the original methods of proof remain applicable. The setting and the spectral conditions are provided by an appropriate use of the BRST cohomology. Confinement arguments are used in order to exclude quarks and gluons from the physical subspace. Local, BRST-invariant hadron fields are considered as leading terms in operator product expansions for products of fundamental fields. The hadronic amplitudes have neither ordinary nor anomalous thresholds which are directl…
I review the basics of perturbative QCD, including infrared divergences and safety, collinear and $k_T$ factorization theorems, and various evolution equations and resummation techniques for single- and double-logarithmic corrections. I then elaborate its applications to studies of jet substructures and hadronic two-body heavy-quark decays.
In this thesis, we study the novel dynamic critical phenomena induced by superfluidity and the chiral magnetic effect in Quantum Chromodynamics (QCD), respectively. In particular, we find the new dynamic universality class of the high-density QCD critical point between the nuclear and quark superfluid phases beyond the conventional Hohnenberg and Halperin's classification. We also consider the second-order chiral phase transition under an external magnetic field and find that the inclusion of the chiral magnetic effect changes the dynamic universality class from the model E into model A within…
The non-divergent diagrams describing two-gluon exchange and annihilation between quarks and antiquarks are calculated in the Feynman gauge, based on quantum chromodynamics in a spherical cavity. Using the experimental $N$, $Δ$, $Ω$, and $ρ$ masses to fit the free parameters of the M.I.T.\ bag model, the predicted states agree very well with the observed low-lying hadrons. As expected, the two-gluon annihilation graphs lift the degeneracy of the $π$ and $η$, while the $ρ$ and $ω$ remain degenerate. Diagonalizing the $η- η'$ subspace Hamiltonian yields a very good value for the mass of the $η$ …
By the use of an effective superpotential in supersymmetric quantum chromodynamics (SQCD) with N_f flavors and N_c colors of quarks for N_f>=N_c+2, the influence of soft supersymmetry (SUSY) breakings is examined to clarify dynamics of chiral symmetry breakings near the SUSY limit. In case that SQCD triggers spontaneous chiral symmetry breakings, it is possible to show that our superpotential dynamically favors the successive formation of condensates, leaving either SU(N_f-N_c) or SU(N_f-N_c+1) unbroken as a chiral nonabelian symmetry.
We review some outstanding puzzles and experimental anomalies in hadron physics that appear to challenge conventional wisdom and, in some cases, the foundations of QCD. We also discuss possible solutions and propose new tests and experiments that could illuminate the underlying physics and novel phenomenological features of QCD. In some cases, new perspectives for QCD physics have emerged.
We give a selection of results on spectrum and decay constants of light and heavy-light hadrons. Effective field theories relevant for their lattice calculation, namely non-relativistic QCD (NRQCD) for heavy quarks on the lattice and Chiral Perturbation Theory for light quarks, are briefly discussed.
Starting from a rewiev of DGLAP and BFKL evolution equations for small-x processes, a sistematic study is performed in order to understand the limits of both the formulations and to improve them in a unique framework, which aims to cover the whole range of applicability of perturbative QCD and which describes the transition mechanism from perturbative to non-perturbative physics in the region where unitarity contributions are expected not to be important.
These lectures on QCD stress the theoretical elements that underlie a wide range of phenomenological studies, particularly gauge invariance, renormalization, factorization and infrared safety. The three parts cover the basics of QCD, QCD at tree level, and higher order corrections.
This study proposes that the longstanding problems of quantum chromodynamics (QCD) as an SU(3)_C gauge theory, the confinement mechanism and Θvacuum, can be resolved by dynamical spontaneous symmetry breaking (DSSB) through the condensation of singlet gluons and quantum nucleardynamics (QND) as an SU(2)_N \times U(1)_Z gauge theory is produced. The confinement mechanism is the result of massive gluons and the Yukawa potential provides hadron formation. The evidences for the breaking of discrete symmetries (C, P, T, CP) during DSSB appear explicitly: baryons and mesons without their parity part…
Recent results on the QCD phase diagram are reviewed. We begin with a detailed introduction of lattice techniques. Then results at vanishing chemical potential are presented. The order of the phase transition, the transition temperature and the equation of state are discussed. At non-vanishing chemical potential we study the mu-T phase line, the critical point as well as the equation of state.
It is analyzed the effects of a hot and magnetized medium on the axion mass, self-coupling and topological susceptibility when in presence of an anisotropic external magnetic field along the $z$-direction, within the Nambu--Jona-Lasinio effective model for quantum chromodynamics. The effects of both Magnetic Catalysis and Inverse Magnetic Catalysis are explicitly taken into account through appropriate matching of parameters with those from lattice Monte-Carlo numerical simulations. It is also analyzed the dependence of the results with respect to different model parametrizations in the context…
The exact QCD is one of the cornerstones of particle physics. Hence it would appear that there should exist no physical situation where a broken version of QCD may have any relevance. However, here I shall show that a spontaneously broken version of QCD may have been significant in an early universe scenario. How this can be made compatible with the exact QCD shall be pointed out. This gives rise to a new cosmological dark matter object (called "rungion").
The low-energy physics of quantum chromodynamics (QCD) and ferromagnets is dominated by Goldstone bosons. While the effective theory of QCD - chiral perturbation theory - is well established in the particle physics community, the systematic studies of ferromagnetic systems within the effective Lagrangian framework are not well-known. We analyze the low-temperature properties of ferromagnets in one, two and three space dimensions up to three-loop order in the effective expansion, i.e., beyond the accuracy of any previous results obtained with conventional condensed matter methods. In particular…
A major contribution to the quest of constructing quantum dynamics of non-Abelian fieds is due to V.N. Gribov. Perturbative approach to the colour confinement, both in gluodynamics and the real world, was long considered heretic but is gaining ground. We discuss Gribov's approach to the confinement problem, centered around the role played by light quarks - the supercritical light quark confinement scenario. We also review some recent developments that are motivated, directly or indirectly, by his ideas.
