The NN interaction in a quark model with quark-antiquark excitations

Quark-antiquark excitations inherent in the quark-gluon interaction have been incorporated into a quark model of the nucleon to study the effects of such excitations on the NN interaction within the framework of the resonating group method. The three-quark (3q) components of a single nucleon are augmented by ($\text{3}\text{q}\text{)(}\text{q}\text{q}$) excitations with the 24 possible spin, isospin, color combinations for the energetically lowest p-wave relative motion function. Quark exchange kernels are then calculated for the two-nucleon system described by these improved nucleon internal functions; and these exchange kernels are converted to phase-shift-equivalent effective NN potentials by the Wigner-transform WKB technique. The off-shell qq? pair-creation terms are derived from the one-gluon exchange diagrams in the Breit approximation in analogy with the derivation of the qq and qq? potentials. The parameters of the interaction are chosen to be consistent with the experimental Δ-N mass difference, the nucleon-vector-meson coupling constants, and the nucleon magnetic moments. Within these constraints, the predicted amplitudes of the ($\text{3}\text{q}\text{)(}\text{q}\text{q}$) components of the nucleon internal functions have been shown to be insensitive to the precise values of the model parameters. In particular, they pass the crucial test of being insensitive to very large changes in the magnitude of the confinement potential constant which is a necessary ingredient of the model. The qq? excitations lead to the following effects in the S-wave NN potentials: (i) The repulsive core heights of the simple 3q-3q model are greatly reduced but retain their strong essentially linear energy dependence, with numerical values very similar to those of the short-range phenomenological terms of the Paris potential. (ii) The effective potentials have acquired an attractive part in the 0.8-1.5 fm range. However, this attraction is too weak to bind the deuteron or fit the extreme low-energy S-wave phase shifts.     

Pseudobaryons

We point out the possibility of observing narrow peaks of bound states of qq with qqq?. They are expected to be produced diffractively in $\text{pp}\text{→(}\text{pp}\text{p}\text{?}{}_{\mathrm{<mtext>forward</mtext>}}\text{+}$ anything, with (pp?) forming baryonium (qq-q?q?) states.     

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.     

Quantum integrable systems related to lie algebras

Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g²v(q) of the following 5 types: v_I(q) = q^?2, v_II(q) = sinh^?2q, v_III(q) = sin^?2q, $\text{v}{}_{\mathrm{<mtext>IV</mtext>}}\text{(q) =}\text{P}\text{(q)}$, v_V(q) = q^?2 + ω²q². Here $\text{P}\text{(q)}$ is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp(q_jq_{j+ 1}) is moreover considered.This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.     

Jets in pp collisions: Radiation zeroes and the electric charges of colored quarks

Measurements involving more than one photon (e.g., γγ → hadrons, e⁺e^- → q$\text{q}$γ) can determine the electric charge of colored quarks rather than the color-averaged value measured, for example, by the R-value in e⁺e^- → hadrons. We draw attention to the fact that this measurement of the absolute quark charges can be performed in hadron collisions via the process qq → qqγ. The charge signature is dramatic due to the appearance of radiation zeroes whose position depends on the values of the electric charges. This can be exploited to perform such measurements with a detector lacking γ/π⁰ separation capability. Such experiments also study the interface of color and electromagnetic amplitudes and can further elucidate the QCD origin of jets.     

Baryonium and the four-body problem

A stochastic variational method is used to solve the Schrödinger equation for the non-relativistic $\text{qq}\text{q}\text{q}$ system. The quarks are considered as interacting with the two-body one-gluon exchange potential and a linear four-body confining potential. The mass spectrum for the non-strange baryonium states is predicted, and a preliminary estimate made for the strength of the coupling of M-baryonium states to T-baryonium. The stability of baryonium states with respect to decay into mesons is investigated.     

Photoproduction of charm and beauty

The photoproduction of charm and beauty are reexamined within QCD. In addition to the photon-gluon amalgamation mechanism, $\text{q}$q → b$\text{b}$ or c$\text{c}$ is also examined. It turns out that for beauty production at SPS photon beams, the $\text{q}$q → b$\text{b}$ mechanism is dominant over γ-g amalgamation for Buras-Gaemers gluon distributions. The possibility of experimental measurement is briefly discussed.     

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-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

Strange baryoniums: Their spectrum,decay and production

Using a quark-gluon model we study exhaustively the states with $\text{qq}\text{q}\text{q}$, where at least one q is a strange quark. The spectrum is extremely rich, but a few trajectories are singled out by their distinctive decay pattern and production mechanism. States of unusual colour content, formed from a diquark in colour-6 and an antidiquark in $\text{6}\text{-}\text{colour}$, are weakly coupled to $\text{B}\text{B}$ or two-meson channels through decay. Instead they prefer to cascade by emitting a π or a K if possible. Narrow $\text{Λ}\text{N}$ states among these are expected to be seen in Kp interactions. States with S = 2 will occur with $\text{K}{}^{\mathrm{?}}\text{Λ}\text{p}\text{or K}{}^{\mathrm{+?}}\text{gL}\text{p}$ final states, but not for example $\text{π}\text{Λ}\text{Λ}$. Some of these can be produced diffractively, with cross sections in the region of 1 μb. Those that require quantum-number exchange for production are expected to have considerably lower cross sections. Some can occur as cascade decay products.     

Effects of screening on quark-antiquark cross sections in quark-gluon plasma

Lowest-order cross sections for qq? production and annihilation can be approximately corrected for higher-order QCD effects by using a corrective K-factor. For energies where quark masses cannot be ignored, the K-factor is dominated by the wave function distortion arising from the initialor final-state interaction between the quark and the antiquark. We evaluate this K-factor for qq? production and annihilation in a quark-gluon plasma by taking into account the effects of Debye screening through a color-Yukawa potential. We present the corrective K-factor as a function of dimensionless parameters which may find applications in other systems involving attractive or repulsive Yukawa interactions. Prominent peaks of the K-factor occur for an attractive q-q? color-Yukawa interaction with Debye screening lengths of 0.835 and 3.23 times the Bohr radius, corresponding to two lowest s-wave qq? bound states moving into the continuum to become qq? resonances as the Debye screening length decreases. These resonances, especially the cc? and the bb? resonances, may be utilized to study the quark-gluon plasma by examining the systematics of the temperature dependence of heavy-quark pair production just above the threshold.     

Quantization of linear maps on a torus-fresnel diffraction by a periodic grating

Quantization on a phase space q, p in the form of a torus (or periodized plane) with dimensions Δq, Δp requires the Planck's constant take one of the values h = ΔqΔp/N, where N is an integer. Corresponding to a linear classical map T of points q, p is a unitary operator U mapping quantum states that are periodic in q and p; the construction of U involves techniques from number theory. U has eigenvalues exp(iα). The ‘eigenangles’ α must be multiples of $\text{2π}\text{n(N)}$, where n(N) is the lowest common multiple of the lengths of the classical ‘cycles’ mapped under T by those rational points in q, p which are multiples of $\text{Δq}\text{N}$ and $\text{Δp}\text{N}$ (i.e. n(N) is the ‘period of T mod N′), at least for odd N. If T is hyperbolic, n is a very erratic function of N, and the classical limit N → ∞ is very different from the ‘Bohr-Sommerfeld’ behaviour for parabolic maps. The degeneracy structure of the eigenangle spectrum is related to the distribution of cycle lengths. Computation of the quantal Wigner function shows that eigenstates of U do not correspond to individual cycles.     

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.     

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.     

Variational principle for t-dependent classical Hamiltonian systems

For a non-conservative, classical system described by Lagrangian L(q?, q_i, t), the functional $\text{Z = ?}{}^{\mathrm{T}}{}_0\text{L}\text{d}\text{t + KT}$, where K is constant, is stationary with respect to variations in q_i(t) and T, given suitable boundary conditions. In the conservative case, for systems with a single periodic coordinate, this variational procedure reduces to that given by Luttinger and Thomas.     

Bound states in the colored-quark model

The saturation problem in the three-triplet quark model, discussed previously by Nambu and by Lipkin, is investigated. We prove that in a simple version of the model, the only bound states of any color representation and any numbers of quarks and antiquarks are the $\text{q}\text{q}$ (meson), qqq (baryon), and a heavier diquark state.