QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.We wish to thank Dr. Lech Mankiewicz for very helpful discussions. This work was supported by DFG (G. Hess program).     

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.     

Modified action for light quarks in the instanton vacuum

The procedure of averaging in an instanton medium in quarks with any number of flavors is discussed. It is shown that the effect of the instanton medium is equivalent to an interaction of light quarks with dynamically generated mass (four-quark interaction N _f = 2) and massless bosonic spinor fields (ghosts). The fact that the instanton liquid is dilute makes it possible to use perturbation theory. The article is published in the original.     

Some new symmetric relations of quark masses and prediction of fourth-generation quark masses

In this study, we discover a mass space defined by generalized Koide relations, named here as k-relations, and achieve some new symmetric relations. These relations can be further used to predict the fourth-generation quark masses in terms of dilation magnitude and angular rotation ratios in the general mass space. Thus far, no theory has been proposed that can constrain the number of generations of quarks; this theory naturally limits the number of generations of quarks.     

Two-Quark Condensate Changes with Quark Current Mass

Using the Schwinger-Dyson equation and perturbation theory, we calculate the two-quark condensates for the light quarks u, d, strange quark s and a heavy quark c with their current masses respectively. The results show that the two-quark condensate will decrease when the quark mass increases, which hints the chiral symmetry may be restored for the heavy quarks.     

Wave functions and mass spectrum for a system of two relativistic spinor quarks coupled by a chromodynamical interaction

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.     

Distribution of charmed constituent quarks in hadrons

By using a statistical approach within noncovariant perturbation theory, the distributions of light and charmed quarks in hadrons are derived with allowance for the charmed-quark mass. The parameters of the model are extracted from a comparison with NA3 data on the hadroproduction of J/ψ particles. A reanalysis of EMC data on charm production in muon-nucleon scattering is performed. In relation to the conventional source of charmed quarks from photon-gluon fusion, the EMC data are found to suggest the presence of an additional contribution from deep-inelastic scattering on charmed quarks at large x. The resulting admixture of Fock states that contain charmed quarks in the decomposition of the proton wave function is about 1%. The approach presented for the excitation of Fock states involving charmed quarks can also be applied to states featuring beauty quarks, as well as to the hadronic component of the virtual photon (resolved photon component).     

Generations of massless composite quarks and leptons

We present a QCD-like composite model in which quarks, leptons and technifermions are three-body systems made out of three kinds of massless elementary fermions t, c and w, each carrying technicolor, color and weak gauge interactions, respectively. Discrete symmetries, remnants of the U(1)_A of the original lagrangian, are responsible for the masslessness of all the quarks and leptons and give the precise meaning of the generations. The model exhibits three generations for both quarks and leptons. Small but non-zero masses of the quarks and leptons are produced by the technicolor condensate of the composite technifermions, which thereby leads to the non-trivial Cabibbo mixing. Proton decays are all forbidden at the mass scale of the QCD-like theory.     

Colour dielectric model of the proton

A model of the proton with its constituent quarks bound in a colour polarizable medium with dielectric constant varying as (a/r−b ²) from a fixed centre, is presented. The Dirac equation modified by the colour polarization is solved and the analytic expression for the wavefunction of the quarks obtained shows that quarks with higher energy lie closer to the fixed centre. The energy spectrum is equispaced without any continuum. A semiclassical approximation scheme yields closed orbits for quarks which have smaller size for higher energies and no orbits with size bigger than a certain maximum, thereby rendering the quarks permanently confined. The wavefunctions of the three quarks constituting the proton are used to calculate physical parameters of the proton such as its mass, charge radius and weak coupling constant which with suitable choice of the constantsa andb appearing in the dielectric constant agree fairly well with experimental results.     

Nucleon axial charge in full lattice QCD

The nucleon axial charge is calculated as a function of the pion mass in full QCD. Using domain wall valence quarks and improved staggered sea quarks, we present the first calculation with pion masses as light as 354 MeV and volumes as large as (3.5 fm)3. We show that finite volume effects are small for our volumes and that a constrained fit based on finite volume chiral perturbation theory agrees with experiment within 7% statistical errors.     

Quark masses

Because of the observed similarity between leptons and quarks, any lepton mass formula can be applied with proper modification to estimate the quark masses. In this work such an application of Rosen's (1978) lepton mass formula is attempted.     

Semileptonic decays of heavy quarks in quantum chromodynamics

We investigate the semileptonic decays of heavy quarks in the leading non-trivial order in quantum chromodynamics. Effects of gluon corrections and the initial quark Fermi motion on the semileptonic rates and decay distributions are calculated. The resulting lepton energy spectrum for the charm semileptonic decay is compared with data to extract the mass of the charm quark. This is combined with the semileptonic branching ratio to predict the charm-quark lifetime. We find the lepton energy spectrum very stable with respect to gluon corrections. Expected spectra from the semileptonic decays of bottom and top quarks are presented. We also study the semileptonic decay process Q → q?v_? + G, involving the emission of a single hard non-collinear gluon. This process should be observable with a branching ratio of a few percent in the decays of top (and heavier) quarks.     

Speculations on quark observation

Results of non-perturbative calculations in several models of relativistic quantum field theory lead to the concept of a stable particle whose mass is not well defined. Assuming that quarks are such particles, we propose several possible methods of quark observation.     

Test of the heavy quark–light diquark approximation for baryons with a heavy quark

We check a commonly used approximation in which a baryon with a heavy quark is described as a heavy quark–light diquark system. The heavy quark influences the diquark internal motion reducing the average distance between the two light quarks. Besides, we show how the average distance between the heavy quark and any of the light quarks, and that between the heavy quark and the center of mass of the light diquark, are smaller than the distance between the two light quarks, which seems to contradict the heavy quark–light diquark picture. This latter result is in agreement with expectations from QCD sum rules and lattice QCD calculations. Our results also show that the diquark approximations produces larger masses than the ones obtained in a full calculation.     

Quark deconfinement at high temperature and thick vortices

First we describe Mack's effectiveZ(2) theory of quark confinement in theSU(2) lattice gauge theory at zero temperature. Then we show how quarks get liberated above a critical temperature, which has a numerical value somewhat below the glueball mass (in natural units).     

Defining the mass spectrum of mesons while taking into account the relativistic character of interactions

Taking into account the relativistic and nonlocal character of interactions, the mass spectrum of mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only by taking into account the nonperturbative and the nonlocal character of interactions. There is certainly a dependence of the constituent mass of constituent particles on the mass of a free state. When quarks are light, the difference in current and valent masses of quarks is greater than in valent masses of quarks; when quarks are heavy, the difference in theses masses is insignificant. One alternative version of the account of nonlocality is suggested for a definition of the properties of hadrons at large distances. The dependence of constituent mass on the radius of confinement is studied.     

Light quarks and instantons

Instantons and anti-instantons can profoundly influence the structure of a non-Abelian gauge theory involving N flavors of massless quarks. Interactions of the quarks with these pseudoparticles can spontaneously generate a quark mass, break the theory's SU(N) × SU(N) chiral symmetry and bind quark-antiquark pairs to form N² ? 1 Goldstone bosons. If the spontaneously generated quark mass is small, multipseudoparticle configurations can be treated in a dilute gas approximation.     

Heavy quarks in polarized structure functions

Quark mass effects are included in the calculation of polarized structure functions. In particular, the validity of fixed order perturbation theory and of massless evolution is studied in the framework of heavy quarks structure functions. The polarized version of the ACOT and MRRS interpolating schemes for the evolution of massive quarks distributions is also developed and studied. The different behaviours of the various approaches in x and Q² are shown.     

Relations between the masses of the superpartners of leptons and quarks,the goldstino coupling and the neutral currents

The mass² splittings between leptons and quarks and their spin-0 partners under supersymmetry are related to the goldstino couplings. The bosonic partner of the goldstino cannot be the photon itself. But it should be, in part, a linear combination of the various neutral gauge bosons. As a result, mass relations constrain the neutral current structure of the theory. They require the existence of at least two neutral gauge bosons in addition to the photon and suggest the possibility of a universal mass² splitting between leptons and quarks and their spin-0 partners.