Qq Interaction Research Articles

Angular correlation between proton and neutron rotors

A brief review is given on the controversy and its solution about the fact that the angular momentum vector of protons and that of neutrons in well-deformed nuclei at low total angular momenta have a strong correlation that they are oriented in opposite directions. In a simple two-rotor model in 2-dimensional space, this fact is explained as originating from the quantum mechanical uncertainty relation between the angle and the angular momentum for the relative rotation of the two rotors. As the second topic, a more realistic model consisting of two triaxial rotors in 3-dimensional space coupled with a QQ interaction is employed to investigate a possible shears-band-like collective rotation predicted by T. Otsuka, in which the angle at which the angular momentum of protons and that of neutrons intersect changes continuously from 180° at spin zero toward 0° at high spins within the same rotational band. The probability distributions of the angle between the two angular momenta and the angle between the longest principal axes of two rotors are calculated to examine the participation of the scissors mode in the evolution of the ground rotational band versus spin.

Diquarks and antiquarks in exotics: A ménage à trois and a ménage à quatre

Abstract A menage a trois is very different from an ordinary family. Similarly, exotic hadrons with both qq and q q ¯ pairs have important color-space correlations that are completely absent in ordinary mesons and baryons. The presence of both types of pairs requires attention to the basic QCD physics that the q q ¯ interaction is much stronger than the qq interaction. This new physics in multiquark systems produces color structures totally different from those of normal hadrons, for example the ud system is utterly unlike the ud diquark in the uds Λ baryon. The color-space correlations produce unusual experimental properties in tetraquarks with heavy quark pairs which may be relevant for newly discovered mesons like the X ( 3872 ) resonance. Tetraquark masses can be below the two-meson threshold for sufficiently high quark masses. A simple model calculation shows the b q b ¯ u ¯ and b q c ¯ q ¯ tetraquarks below the B B ¯ and B D ¯ thresholds. Some of these states have exotic electric charge and their decays might have striking signatures involving monoenergetic photons and/or pions.

Heavy qq Interaction at Finite Temperature

The first lattice QCD numerical study of heavy quark-quark potentials at finite temperature is reported. Using the quenched approximation, we evaluate the color anti-symmetric and symmetric potentials.

Quadrupole and octupole softness in theN=Znucleus64Ge

Quadrupole and octupole softness in the even-even N=Z nucleus 64Ge is studied on the spherical shell model basis. We carry out the shell model calculation using the pairing plus quadrupole (QQ) plus octupole (OO) interaction with monopole corrections. It is shown that 64Ge is an unstable nucleus with respect to both the quadrupole and octupole deformations, which is consistent with the previous discussions predicting the gamma softness and octupole instability. It is demonstrated that proton-neutron part QpQn of the QQ interaction is important for the gamma softness or triaxiality.

Improvement of the extended [formula omitted] interaction by modifying the monopole field

The extended pairing plus QQ interaction with the J-independent isoscalar proton–neutron force as an average monopole field, which has succeeded in describing collective yrast states of N≈Z even- A nuclei, is improved. The improvement is accomplished by adding small monopole terms (relevant to spectroscopy) to the average monopole field (indispensable to the binding energy). This modification extends the applicability of the interaction to nuclei with N≈28 such as 48Ca, and moreover improves energy levels of nonyrast states. The modified interaction successfully describes not only even- A but also odd- A nuclei in the f 7/2 shell region. Results of exact shell model calculations in the model space ( f 7/2 , p 3/2 , p 1/2 ) (its usefulness has been demonstrated previously) are shown for A=47, 48, 49, 50 and 51 nuclei.

Single and Double Decay in N Z Nuclei

We study single and double β decay for N ≈ Z nuclei, using an extended P + QQ interaction with four force strengths. The Gamov-Teller (GT) transition is examined using the proton-neutron QRPA (pn-QRPA) in many j shells and using a single j shell model calculation. First, we calculate the single β-decay strength. The integrated strengths of N ≈ Z nuclei in the fp shell region are reproduced well by the pn-QRPA, although some quenching factor is necessary for several cases. The model accounts for the experimental observation that the GT strength increases with decreasing |N − Z|. The single j shell model calculation indicates that the GT strength becomes very large at N = Z. Second, we perform calculations for two-neutrino double β-decay transition strengths for 76 Ge and 82 Se. The results suggest fairly good applicability of the extended P + QQ interaction to single and double β decay.

3D–4D INTERLINKAGE OF qqq WAVE FUNCTIONS UNDER 3D SUPPORT FOR PAIRWISE BETHE–SALPETER KERNELS

Using the method of Green functions within the framework of a Bethe–Salpeter formalism characterized by a pairwise qq interaction under the Markov–Yukawa transversality principle (MYTP) which gives Lorentz-covariant 3D support to the BS kernel, the 4D BS amplitude for three identical spinless quarks is reconstructed from the corresponding 3D quantities which satisfy a fully connected 3D BSE. This result is a three-body generalization of a similar 3D–4D interlinkage for the corresponding two-body wave functions found earlier under identical conditions of a Lorentz-covariant 3D support to the corresponding BS kernel, ("CIA" for short), for the [Formula: see text] interaction. (The generalization from spinless to fermion quarks is straightforward). To set "CIA" for 3D kernel support in the context of contemporary approaches to the qqq baryon problem, a model scalar 4D qqq BSE with pairwise contact interactions simulating the NJL–Faddeev equations, is worked out fully and compared with the "CIA" vertex function which reduces exactly to the 4D NJL–Faddeev form in the limit of zero spatial range. This consistency check is part of a detailed accounting of the CIA vertex structure whose physical motivation stems from the role of spectroscopy when considered as an integral part of any QCD-motivated dynamical investigation.

The spin structure of the qq interaction and the mass spectra of bound systems: different versions of the 3-dimensional reductions of the Bethe-Salpeter equation

Bound q\bar q -systems are considered in the framework of three different versions of the 3-dimensional reduction of the Bethe-Salpeter equation, all having the correct one-body limit when one of the constituent quark masses tends to infinity, and in the framework of the Salpeter equation. The spin structure of confining qq interaction potential is taken in the form x\gamma_{1}^{0}\gamma_{2}^{0}+(1-x)I_{1}I_{2}, with 0 \leq x \leq 1. The problem of existence (nonexistence) of stable solutions of 3-dimensional relativistic equations for bound q\bar q systems is studied for different values of x from this interval. Some other aspects of this problem are discussed.

Microscopic analysis of collective states in neutron-deficient doubly even xenon isotopes.

The low-lying collective states of xenon isotopes are studied by means of the boson expansion theory. The microscopic Hamiltonian is comprised of the self-consistent QQ interaction with higher-order (three- and four-body) terms, monopole- and quadrupole-pairing interactions in addition to the spherical limit of the Nilsson Hamiltonian. It is shown that the difficulty of weak strengths of the monopole-pairing interaction in this region, indicated by Rohozi\ifmmode \acute{n}\else \'{n}\fi{}ski et al., can be naturally remedied by including the quadrupole-pairing interactions.

A QCD calculation of the interaction of quarkonium with nuclei

The interaction of quarkonium with nuclei is studied in the mQ→∞ limit of QCD, where the binding energy is found to be exactly computable. The dominant contribution to the interaction is from two-gluon operators. The forward matrix elements of these two-gluon operators can be determined from the QCD scale anomaly, and from deep inelastic scattering. We apply our results to the υ and Jψ treating the QQ interaction as purely coulombic. We find the υ binds in nuclear matter with a binding energy of a few MeV, while for the Jψ binding is of order 10 MeV. For the Jψ in particular we expect confinement effects to produce large corrections to this result.

Self-consistent mean-field wavefunctions of nucleon and delta for the cranked Chiral soliton bag

The mean-field equations of the chiral soliton bag model are solved numerically on a full three-dimensional grid by solving the corresponding finite difference equations self-consistently. The spherical hedgehog configuration is found to be the ground state even if deformation degrees of freedom for all fields are allowed for. Individual states describing the nucleon and the delta resonance are obtained using the cranking formalism in isospace. The classical instability of the pion field, which occurs as soon as the angular frequency is larger than the pion mass, is taken into account by an explicit treatment of the asymptotic meson tails for smaller frequencies. A comparison with the perturbative approach used by other authors is given. As an alternative approach we present calculations for baryon states built up from single-quark states of sharp spin and isospin coupled to the corresponding total quantum numbers. As a consequence of the wrong spin-isospin dependence of the short-range qq interaction mediated by the chiral meson fields a negative mass splitting between nucleon and delta is found. Implications on other approaches are discussed.

Long-distance Lienard-Wiechert potentials and qq-bar spin dependence.

The long-range spin dependence of the qq interaction is considered in a model in which the confining potential is required to be the static limit of retarded scalar and vector potentials analogous to the Lienard-Wiechert potentials of classical electrodynamics. A generalization of Darwin's method is used to obtain the corresponding Hamiltonian. The long-distance spin-dependent interaction is found to be determined completely by only two potentials: namely, the static scalar and vector potentials. This is to be compared with the four potentials required in Eichten and Feinberg's general formulation. Two different solutions are allowed by Gromes's theorem. In one, the scalar potential can be linear; in the other, it must be logarithmic.

A variational calculation for Γ and ξfamilies

The authors consider the non-relativistic approach to the Gamma and xi families by solving the Schrodinger equation through the variational method. A truncated basis of harmonic-oscillator wavefunctions is used as the trial function. They study two kinds of phenomenological potentials for the qq interaction and fit the parameters by analysing the 1 3S1 and 2 3S1 states. They also calculate hadronic, leptonic and electric dipole transition widths for these bb and tt systems.

Microscopic calculation of IBM parameters by using intrinsic states

The overlaps between intrinsic fermionic and bosonic wave functions are required to be the same. This provides relations between fermion and boson variables. These relations are used in conjunction with an OAI procedure for intrinsic states to map the shell-model space operators onto their equivalent boson space operators. As an example, a QQ interaction is mapped.

Charmonium chi states: Radiative and hadronic widths, spin of the gluon

The dipole sum rules, used earlier to give upper and lower bounds for the radiative transitions for χ→γψ and so estimate the hadronic widths of the χ state, are re-examined with more general assumptions about the QQ interaction, namely the presence of spin—spin, spin—orbit, and tensor forces. The lower and upper bounds for a specific J value are now explicitly force dependent. In fact, a useful lower bound can be established only for the J = 2 state. The inferred radiative rates and estimates of hadronic width, based on new data, are similar to those given earlier by the author. The improved presicion of the data affords a test of the spin of the gluon, within conventional QCD assumptions. The inferred ratio of hadronic widths Γ h (0 ++)/ Γ h (2 ++) = 5.5 +14 - 3 is in agreement with the ratio 15:4 expected from spin 1 and in disagreement with the ratio 125:2 for scalar gluons.