Hybrids: Mixed states of quarks and gluons

We calculate the spectrum of the four ground state hybrid $\text{(}\text{q}\text{qg}\text{)}$ nonets, J^PC = (0, 1, 2)^?+, 1^??, using the MIT bag model to first order in cavity perturbation theory. Quark and gluon self-energies are included by a fit to the s-wave mesons and baryons and to the glueball candidate i(1440). We find a large gluon self-energy which substantially increases our predictions of the glueball and hybrid masses. We discuss the phenomenology of hybrids, including a suggestion that the A₃ (1670) and a second peak at 1850 MeV in the fπ channel may be mixtures of the isovector $\text{q}\text{q}$ d-wave state with the $\text{q}\text{qg}$ s-wave.     

QCD predictions for four-jet final states in e+e− annihilation

We have calculated the four-jet production processes $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→q}\text{q}\text{gg}$ and $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→q}\text{q}\text{q}\text{q}$ to lowest-order QCD perturbation theory. We find that (q$\text{q}$q$\text{q}$) production is small compared to the dominant process $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→q}\text{q}\text{gg}$ which can in part be traced to the fact that the latter process is more singular as the 2- and 3-jet phase-space limits are approached. We present differential 4-jet acoplanarity distributions and compare them with non-perturbative acoplanarity distributions at maximum PETRA and PEP energies. Leading log cross-section formulae are derived for various cut-off procedures and are compared to the results of our numerical integrations. We also present results on associated heavy quark production in e⁺e^? annihilation.     

Triality,exotics and the dynamical basis of the quark model

A non-relativistic three-triplet model with a simple two-body interaction is shown to bind only q$\text{q}$ and qqq states. Three triplets and unobserved charmed states are crucial in preventing binding of 4q$\text{q}$ and 2 q$\text{q}$ systems. They provide repulsive channels to make the q$\text{q}$ and 3q systems behave like “neutral atoms” with canceling attractive and repulsive forces between them and additional quarks. The ratio of q$\text{q}$ and qq interactions is just right to bind the q$\text{q}$ and 3q systems properly while leaving the qq system with the mass of a quark.     

The S-wave QQqq states in the adiabatic approximation

The static potential energy for an S-wave $\text{Q}\text{Q}\text{q}\text{q}$ system is discussed in an adiabatic (Born-Oppenheimer) approximation. Both spherical bag and arbitrary bag are considered. We concentrate on those $\text{Q}\text{Q}\text{q}\text{q}$ states in which both ($\text{Q}\text{Q}$) and ($\text{q}\text{q}$) are colour singlets. Their energy level, wave function, and possible experimental observation are studied.     

Non-leading corrections to the Drell-Yan cross section at small transverse momentum

The production of Drell-Yan lepton pairs at small transverse momentum is analyzed to second order in QCD perturbation theory. By calculating exactly all terms involving powers of the large logarithm ln $\text{(}\text{Q}{}^2\text{q}{}_{\mathrm{<mtext>T</mtext>}}{}^2$), we are able to confront the predictions of “soft gluon” cross sections in which these logarithms are summed to all orders. Our results confirm the factorization properties of these cross sections, and yield new information on previously undetermined coefficients.     

New meson configurations in the bag model (II). Mixing effects

We evaluate transitions and mixings between ordinary mesons, glueballs, multiquark states, and unconventional quark-antiquark-gluon configurations (hybrid states). Hybrid states mix largely with $\text{q}\text{q}$, glueballs contain some component of $\text{q}\text{q}\text{g}$ (but nearly none of $\text{q}\text{q}$), whereas the multiquarks are nearly disconnected. Based on a naive perturbative estimate, we expect hybrid states to be large and lowest glueballs to form narrow resonances.     

On the diffraction of neutrons by magnetic spiral structures

A beam of neutrons of wave vector K incident on a magnetic spiral structure with propagation vector q gives rise to two diffracted beams. These are peaked at $\text{K·q}\text{q}\text{～±}\text{q}\text{2}$, and their intensity varies with the direction of K with the same functional form as is derived in the dynamical theory of X-ray diffraction. In real cases the two lines are broad enough to overlap significantly, giving rise to intrinsic double diffraction effects in a multi-domain crystal. These have been observed experimentally in holmium.     

Quark dynamics and pion-nucleon coupling

In the framework of nonperturbative QCD phenomenology we discuss: (1) The elementary process for the creation of color-singlet q$\text{q}$-pairs inside a hadron. (2) The interaction of the q$\text{q}$-pair with the surrounding quark-gluon medium. An important consequence of these discussions is that meson emission takes place preferentially, if the primary q$\text{q}$-pair is created in the surface region of the hadron. For the case of pseudoscalar coupling we employ PCAC to obtain the coupling of the q$\text{q}$-pair to the pion. The resulting form and coupling strength of the πNN vertex is consistent with the phenomenological OPEP.     

Exact summation of outer rainbow self-energy graphs in λφ2ϕ2 theory

We use momentum space techniques to sum the complete class of outer rainbow graphs contributing to the IPI two-point function in λφ²?² theory. The results are exact to all orders of λ and for all values of q². By working in momentum space, we avoid the ambiguities which arose in the configuration space treatment of earlier work. It is shown that the renormalized integral equation can be reduced to a Volterra equation with $\text{non}\text{-}\text{L}{}^2$ kernel. The solution is found to agree with the asymptotic results of our configuration space treatment. Properties of the solution such as uniqueness, cut-off dependence, relation to perturbation theory and anomalous ultraviolet behaviour are discussed.     

Event shapes in e+e− annihilation

We present a complete set of rotationally invariant observables (H_l) which characterizes the ‘shapes’ of final states in e⁺e^? annihilation. They are infrared stable when calculated in QCD perturbation theory. We compare the ‘shapes’ of final states from the processes $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{q}\text{q}\text{,}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{q}\text{q}\text{(}\text{G}\text{)}$ and from the three-gluon decays of heavy vector mesons. We also consider the production and decay of heavy quarks and leptons. Using a realistic model for the development of hadron jets, we find that for c.m. energies above about 10 GeV, these processes may be clearly distinguished by their distributions in the H_l. We indicate how our analysis may be extended to deep inelastic lepton-hadron interactions and hadron-hadron collisions involving large transverse momenta.     

Large q expansions for q-state gauge-matter Potts models in lagrangian form

We consider the lagrangian form of a q-state generalization of Ising gauge theories with matter fields in d = 3 and 4 dimensions. The theory is exactly soluble in the limit q → ∞ and corrections are easily calculable in power series in $\text{1}\text{q}{}^{\mathrm{<mtext>1</mtext><mtext>d</mtext>}}$. Extrapolating the series for the free energies and latent heats by the method of Padé approximants, we have constructed the phase diagrams for all values of q. Our results agree well with known results for pure spin systems and, for the case q = 2, with Ising Monte Carlo data.     

Phase transition in the three-dimensional chiral field

The essentially nonlinear chiral field in three dimensional space time non-renormalizable in the usual perturbation expansion is studied. We consider systematic $\text{1}\text{N}$ expansion for this model. In the framework of the latter a phase transition takes place: above the critical point the theory is in the O(N) symmetric phase, below it the O(N) symmetry breaks. The $\text{1}\text{N}$ renormalized expansion for both phases is described and the connection between the non-renormalizability of the conventional perturbation theory and the non-analytic dependence on the coupling constant is established.     

On quark molecules

The nonrelativistic quark model with three triplets and an octet of coloured gluons is examined. The interaction energy corresponding to certain quark molecules is calculated. It is shown that systems of $\text{qq}\text{qq}$ and $\text{qqqq}\text{q}$ are more strongly bound than $\text{q}\text{q}$ and qqq. Thus in order for the model to be valid there must exist exotic particles.     

Quantum maps

We quantize area-preserving maps M of the phase plane q, p by devising a unitary operator $\text{U}$ transforming states | φ_n〉 into | φ_n+1〉. The result is a system with one degree of freedom q on which to study the quantum implications of generic classical motion, including stochasticity. We derive exact expressions for the equation iterating wavefunctions ψ_n(q), the propagator for Wigner functions W_n(q,p), the eigenstates of the discrete analog of the quantum harmonic oscillator, and general complex Gaussian wave packets iterated by a $\text{U}$ derived from a linear M. For | ψ_n〉 associated with curves $\text{L}$_n in q, p, we derive a semiclassical theory for evolving states and stationary states, analogous to the familiar WKB method. This theory breaks down when $\text{L}$_n gets so complicated as to develop convolutions of area ? or smaller. Such complication is generic; its principal morphotologies are“whorls” and “tendrils,” associated respectively with elliptic and hyperbolic fixed points of M. Under $\text{U}$, ψ_n(q) eventually transforms into a new sort of wave that no longer perceives the details of $\text{L}$_n. For all regimes, however, the smoothed | ψ_n(q)|² appears semiclassically appears to be given accurately by the smoothed projection of $\text{L}$_n onto the q axis, both smoothings being over a de Broglie wavelength. The classical, quantum, and semiclassical theory is illustrated by computations on the discrete quartic oscillator map. We display for the first time stochastic wavefunctions, dominated by dense clusters of caustics and characterized by multiple scales of oscillation.     

Perturbation theory with instantons

We develop “perturbation theory” rules for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the “dilute gas” approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form where b is the coefficient in the expansion of the β function: β = bg³ + 3. .     

Perturbation theory in terms of superfields

A perturbation theory in terms of superfields has been developed for a class of super-symmetric Lagrangians which contain massless spin zero boson and $\text{spin}\text{-}\text{1}\text{2}$ Majorana spinor fields.