Isgur-Wise functions for confined light quarks in a colour electric potential

We explore the influence on the Isgur-Wise function of the colour electric potential between heavy and light quarks in mesons. It is shown that in bag models, its inclusion tends to restore light quark flavour symmetry relative to the MIT bag predictions, and that relative to this model it flattens the Isgur-Wise function. Results compare very well with observations.Work supported in part (M.S.) by the KBN grant no. 20-38-09101. We also thank the Norwegian Research Council for a travel grant     

Excited states of confined quarks

Low lying excitations of colored quarks and gluons are studied in the bag theory. The baryons and mesons considered have one quark in a P-wave excited state and the remainder in the ground state. They correspond to 1/2⁻ and 3/2⁻ baryons and to 0⁺ and 1⁺ mesons. Gluon hyperfine interactions are included to lowest order. SU(3) is broken by the strange quark mass. All parameters of the model were determined previously by fitting the masses of the light hadrons. The calculated masses of these states are generally found to be lighter than the observed states. Our spectrum contains states which do not occur in models of quark confinement with only two body forces but which should be present in the physical spectrum of any baglike confinement model.     

Excited states of confined quarks. II

We continue an analysis of the low lying excitations of colored quarks and gluons in the bag theory. These states correspond to members of an SU(6) L = 1 [56] and [70]. A study of the small oscillations of the surface of bags reveals the presence of a translation mode, an L = 1 [56]. Physical states must be constructed which are orthogonal to it. The spectrum of these states is too low but in qualitative agreement with observation. The lowest excited states form a [70]. In addition, L = 1 [56]'s should also be present, elevated in energy with respect to the [70]. We discuss ways of improving our results and the relation of our model to other calculations of baryonic spectra and mixing angles.     

Self energy of heavy quarks in confined QCD

We calculate the self energy of a heavy quark in order α _s of QCD confined to a spherical cavity. Only the radius-(and position-) dependent terms which cannot be renormalized away are taken into account. Besides the leadingO(M ⁰) contribution which acts as a confining potential we determine theO (1/M ²) corrections which contain orbital terms and contributions to theLS potential. This calculation completes the determination of the Breit-Fermi Hamiltonian for a confinedQ \(\bar Q\) system whose interaction parts have been discussed previously. We give some preliminary estimates of the resultant spin dependent level splittings in charmonium.     

Constituent models for quarks and leptons

Constituent models predicting several families of quarks and leptons are presented. They satisfy 't Hooft's anomaly conditions and a “principle of exclusion” introduced here. Some mechanisms for breaking GSW symmetry and generating masses for quarks and leptons consistent with the GIM mechanism are also given.     

D0-branes as light-front confined quarks

We argue that different aspects of light-front QCD at the confined phase can be recovered by the matrix quantum mechanics of D0-branes. The relevant matrix quantum mechanics is obtained from dimensional reduction of pure Yang–Mills theory to dimension 0+1. The aspects of QCD dynamics which are studied in correspondence with D0-branes are: (1) phenomenological inter-quark potentials, (2) the whiteness of hadrons and (3) scattering amplitudes. In addition, some other issues such as the large-N behavior, the gravity–gauge theory relation and also a possible justification for involving “non-commutative coordinates” in the study of QCD bound states are discussed. Received: 12 January 2001 / Published online: 6 April 2001     

Electromagnetic self-energy of quarks confined to a sphere

We calculate the electromagnetic energy shift, δω, of a massless fermion confined to a sphere. We find δω > 0, in agreement with our previous result for a slab, and in disagreement with the sign needed to obtain the right value of the neutron-proton mass difference in a model in which the hadron consists of confined massless quarks. We consider the effect of a bare mass for the confined quarks, and show that it is then possible for δω to be negative.     

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.     

Current algebra of quarks confined to a cavity

Equal-time commutators of fields with charges are calculated in a cavity approximation to the MIT bag model, with N flavours of non-interacting quarks confined to a rigid spherical cavity and SU(N) symmetry arbitrarily broken by mass terms. It is proved that inside the cavity the algebra is identical with that of free field theory, whilst on the boundary quark fields commute with axial charges. Vector divergences and sigma commutators belong to a $\text{(N,}\text{N}\text{) + (}\text{N}\text{, N)}$ multiplet of chiral SU(N) × SU(N). Axial divergences contain additional surface terms which do not contribute to sigma commutators. A non-strange quark mass in the range 20–44 MeV is required to give a value 30–70 MeV for the nucleon matrix element of the sigma commutator relevant to pion-nucleon scattering.     

Spectral functions of quarks in quark matter

We present a simple albeit self-consistent approach to the spectral function of light quarks in infinite quark matter. Relations between correlation functions and collision rates are used to calculate the spectral function in an iterative procedure. The quark interactions are described by the SU(2) Nambu-Jona-Lasinio model. Calculations were performed in the chirally restored phase at zero temperature.Received: 30 September 2002, Published online: 22 October 2003PACS: 24.85. + p Quarks, gluons, and QCD in nuclei and nuclear processes - 12.39.Fe Chiral Lagrangians - 12.39.Ki Relativistic quark model     

Vertex functions for d-wave mesons in the light-front approach

While the light-front quark model (LFQM) is employed to calculate hadronic transition matrix elements, the vertex functions must be pre-determined. In this work we derive the vertex functions for all d-wave states in this model. Especially, since both ³ D ₁ and ³ S ₁ are 1⁻⁻ mesons, the Lorentz structures of their vertex functions are the same. Thus when one needs to study the processes where ³ D ₁ is involved, all the corresponding formulas for ³ S ₁ states can be directly applied; only the coefficient of the vertex function should be replaced by that for ³ D ₁. The results would be useful for studying the newly observed resonances, which are supposed to be d-wave mesons, and furthermore possible 2S–1D mixing in ψ′ with the LFQM.     

Oscillator potential from a bootstrap model of confined quarks

For a particular choice of the Bethe-Salpeter kernel and the confined quark propagator, we obtain a self consistent tent solution for the $\text{q}\text{q}$ scattering amplitude. The potential associated with this scattering turns out to be a harmonic oscillator potential.     

Vertex models on Feynman diagrams

We discuss the statistical mechanics of vertex models on both generic (“thin”) and planar (“fat”) random graphs. Such models can be formulated as the N → 1 and N → ∞ limits of N × N complex matrix models, respectively. From the graph theoretic perspective one is using matrix model and field theory inspired methods to count various classes of directed graphs. For the thin random graphs we use saddle point methods to solve the models in the thermodynamic, large number of vertices limit and note that, as in the case of the eight-vertex model on the square lattice, various other models such as the Ising model appear as particular limits. The generic solution of the fat graph model is rather more elusive, but we show that for several choices of the couplings the models can be reduced to eigenvalue integrals and their critical behaviour deduced.     

Can quarks always be confined by a linear potential?

It is demonstrated on the basis of the Dirac equation that quarks cannot be confined by a vector gluon potential of the form(r/r ₀)^a or[ln(r/r ₀]^a, a>0, if the quark-gluon interaction conserves parity. In order to confine quarks with the parity-conserving interaction, the effective gluon potential must be a pseudovector or a scalar. These are shown in a simple Yang-Mills field with theSU(2) group.     

Loop calculations in confined QCD II. The self energy of massive quarks

We present an explicit numerical evaluation of the self energy of confined massive quarks for the ground state of the MIT bag model. The calculation is performed in the Coulomb gauge, using a technique developed in part I.     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.