Six-quark Configurations Research Articles

Hidden Color and the b 1 Structure Function of the Deuteron

The $b_1$ structure function is an observable feature of a spin-1 system sensitive to non-nucleonic components of the target nuclear wave function. A simple model for hidden-color, six-quark configurations is proposed and found to give substantial contributions for values of $ x>0.2$. Good agreement with Hermes data is obtained. Predictions are made for an upcoming JLab experiment.

Pionic and hidden-color, six-quark contributions to the deuteron b1 structure function

The b1 deep-inelastic structure function is an observable feature of a spin-1 system that is sensitive to non-nucleonic components of the target nuclear wave function. The contributions of exchanged pions in the deuteron are estimated and found to be of measurable size for values of x of about 0.1. A simple model for a hidden-color, six-quark configuration (with only about 0.15% probability to exist in the deuteron) is proposed and found to give substantial contributions for values of x greater than about 0.2. Good agreement with the only existing (HERMES) data is obtained. Predictions are made for an upcoming JLab experiment. The Close and Kumano sum rule is investigated and found to be a useful guide to understanding various possible effects that may contribute.

Pionic and hidden-color, six-quark contributions to the deuteronb1structure function

The b1 structure function is an observable feature of a spin-1 system sensitive to non-nucleonic components of the target nuclear wave function. The contributions of exchanged pions in the deuteron are estimated and found to be of measurable size for small values of x. A simple model for a hidden-color, six-quark configurations (with~ 0.15% probability to exist in the deuteron) is proposed and found to give substantial contributions for values of x>0.2. Good agreement with Hermes data is obtained. Predictions are made for an upcoming JLab experiment. The Close & Kumano sum rule is investigated and found to be a useful guide to understanding various possible effects that may contribute.

Novel six-quark hidden-color dibaryon states in QCD

The recent observation of a hadronic resonance d⁎ in the proton–neutron system with isospin I=0 and spin-parity JP=3+ raises the possibility of producing other novel six-quark dibaryon configurations allowed by QCD. A dramatic example of an exotic six-quark color-singlet system is the charge Q=+4, isospin I=3, Iz=+3|uuuuuu〉 state which couples strongly to Δ+++Δ++. The width and decay properties of such six-quark resonances could be regarded as manifestations of “hidden-color” six-quark configurations, a first-principle prediction of QCD – SU(3)-color gauge theory for the deuteron distribution amplitude. Other implications and possible future experiments are discussed.

Baryon–Baryon Interactions S = 0, −1, −2, −3, −4

We review the extended-soft-core models ESC08, which at present are the most complete meson-exchange models for the baryon–baryon (BB) interactions. The ESC-model describes the nucleon–nucleon (NN), hyperon–nucleon (YN), and hyperon–hyperon (YY), in terms of meson-exchanges using (broken) SU(3,F)-symmetry. In this approach to baryon-baryon the dynamics is derived from (1) one-boson-exchanges (OBE), (2) two-meson-exchanges, and (3) meson-pair-exchanges, (4) multiple gluon-exchanges (MGE), and (5) quark-core effects. In the OBE-sector, special features are (a) the axial-vector meson potentials, and (b) the inclusion of a zero in the scalar- and axial- meson form-factors. Novel for the ESC08-versions is (a) the inclusion in MGE next to the pomeron the odderon-exchange, and (b) the analysis of possible (pronounced) effects of the appearance of forbidden six-quark configurations. With these ingredients a rather flexible dynamical model is constructed for the description of all BB-channels in the {8} × {8} SU(3,F)-representation. Namely, it appeared feasible to keep the meson coupling parameters of the model in accordance with the predictions of the quark-pair-creation model, with a clear dominance of the 3P0-mechanism. This is the case for the meson- and meson-pair-baryon coupling constants and the F/(F + D)-ratio’s as well. The NN, YN, and YY results for this model are excellent. This is marked in particular by the NN-results, namely \({\chi^2_{p.d.p.}}\) = 1.180, 1.135, and 1.085 for, respectively, ESC08a, ESC08b, and ESC08c. These fits were achieved with partial-wave independent meson-coupling parameters in a combined fit of the \({NN \oplus YN}\) -data, supplemented with information from G-matrix calculations of hypernuclei, e.g. \({B_\Lambda(^{6}_{\Lambda\Lambda}He)}\) from the Nagara-event, and an attractive Ξ-nucleus interaction. The special quark-core effects provide ample repulsion in the Σ+p(3S1, T = 3/2)- and ΣN(1S0, T = 1/2)-channels, in particular for ESC08a,b. The well depths (UΛ, UΣ, UΞ) correspond rather well with expectations from hypernuclei. Here, in ESC08c a universal repulsion, which we derived from multiple pomeron-exchange, is necessary. This at the same time gives both a very satisfactory nuclear saturation point as well as a description of the neutron star matter in the presence of hyperons for all ESC08-models. The requirement of a sizable Ξ-nucleus attraction leads to the prediction of an S = −2 deuteron-state in ΞN(3S1, T = 1) with EB ≈ 8.3 MeV. Also possible/likely are similar bound states for Ξ N(3S1, T = 0), Λ Ξ, Σ Ξ(3S1, T = 1/2, 3/2), and Ξ Ξ(1S0, T = 1).

NIJMEGEN BARYON-BARYON INTERACTIONS FOR S = -1, -2 SYSTEMS

We present and discuss the most recent version of the extended-soft-core (ESC) interactions. The ESC-model describes the nucleon-nucleon ( NN ), hyperon-nucleon ( YN ), and hyperon-hyperon ( YY ), in terms of meson-exchanges using (broken) SUF(3)-symmetry. In this approach to baryon-baryon ( BB ) the dynamics is derived from (i) one-boson-exchanges (OBE), (ii) two-meson-exchanges (TME), and (iii) meson-pair-exchanges (MPE), (iv) gluon-exchanges, and (v) quark-core effects. In the OBE-sector, a special feature is the importance of the axial-vector meson potentials, and the inclusion of a zero in the scalar- and axial- meson form-factors. Novelties are the inclusion of (a) odderon-exchange, and (b) special pronounced effects of the appearance of forbidden six-quark configurations. With these ingredients, a rather flexible dynamical framework is constructed. Namely, it appeared feasible to keep the parameters of the model in reasonable accordance with the predictions of the 3P0 quark-pair-creation model (QPC). This is the case for the meson- and meson-pair-baryon coupling constants and the F/(F + D)-ratio's as well. The NN , YN , and YY results for this model are rather promising. In particular, we improved the ΛN spin-orbit interaction greatly by the inclusion of (a) the Brown, Downs, and Iddings anti-symmetric spin-orbit potentials, and (b) new corrections to the MPE-potentials. Also, the special quark-core effects provide ample repulsion in the Σ+p(3S1,T = 3/2)- and ΣN(1S0,T = 1/2)-channels. The new version of the ESC-model reported here will be referred to as ESC07 henceforth.

Status of understanding the YN/YY-interactions Meson-exchange viewpoint

We analyze and discuss the extended-soft-core models ESC04 and ESC08, which at present are the most complete meson-exchange models for the baryon-baryon interactions. The ESC-model describes the nucleon-nucleon (NN), hyperon-nucleon (YN), and hyperon-hyperon (YY), in terms of meson-exchanges using (broken) S U F ( 3 ) -symmetry. In this approach to baryon-baryon (BB) the dynamics is derived from (i) one-boson-exchanges (OBE), (ii) two-meson-exchanges (TME), and (iii) meson-pair-exchanges (MPE), (iv) gluon-exchanges, and (v) quark-core effects. In the OBE-sector, special features are the importance of the axial-vector meson potentials, and the inclusion of a zero in the scalar- and axial-meson form-factors. Novel for the ESC08-versions is the inclusion of (a) odderon-exchange, and (b) special pronounced effects of the appearance of forbidden six-quark configurations. With these ingredients a rather flexible dynamical framework is constructed. Namely, it appeared feasible to keep the parameters of the model in reasonable accordance with the predictions of the P 0 3 quark-pair-creation model (QPC), although in ESC08a,b a certain admixture of S 1 3 quark-pair creation is present. This is the case for the meson- and meson-pair-baryon coupling constants and the F / ( F + D ) -ratio's as well. The NN, YN, and YY results for this model are excellent. This is marked in particularly by the NN-results, namely χ p . d . p . 2 = 1.180 and 1.135 for respectively ESC08a and ESC08b. Also, we improved the Λ N spin-orbit interaction greatly by the inclusion of (a) the Brown, Downs, and Iddings anti-symmetric spin-orbit potentials, and (b) new corrections to the MPE-potentials. Also, the special quark-core effects provide ample repulsion in the Σ + p ( S 1 3 , T = 3 / 2 ) - and Σ N ( S 0 1 , T = 1 / 2 ) -channels.

Superfast Quarks in the Nuclear Medium

We discuss the studies of superfast quarks as a new method in probing high-density fluctuations in the nuclear medium. Kinematical as well as dynamical aspects of probing such fluctuations are discussed. Several theoretical models are considered which are based on significantly different underlying picture of high density nuclear fluctuations that generate superfast quarks with x B j > 1 . First, is the convolution model in which it is assumed that fast quarks originate from the nucleon which is in short-range NN correlation. In the second model it is assumed that 2N system is collapsed into the six-quark configuration from which the superfast quark is produced. The third approach considers a situation in which the high density fluctuation is not yet a six-quark system and the superfast quark is generated due to hard exchange of a single gluon between two partons, one from each nucleon. This represents an intermediate stage between the first two models and may correspond to the scenario of evolution of 2N system into six-quark configuration. We compare the predictions of all three models and discuss the feasibility of their experimental verification.

Inclusive neutral-pion production in dC and dCu interactions at a momentum of 4.5 GeV/. per nucleon

The cross sections for inclusive neutral-pion production in the reactions d + C → π 0 + x and d + Cu → π 0 + x at a momentum of 4.5 GeV/c per nucleon were measured over the kinematical region specified by the inequalities Θπ≤16° and E π≥2 GeV (in the laboratory frame). From the ratio of the cross sections for neutral-pion generation on carbon and copper nuclei, the exponent n in the parametrization Ed 3 σ/d 3 p ∼ A is obtained as a function of the cumulative number X in the range 0.6 ≤ X ≤ 1.8 and as a function of the square of the transverse momentum in the range 0.04 ≤ P t 2 ≤ 0.40 (GeV/c)2. The probabilities of the formation of six-quark configurations in the D, 4He, and 12C nuclei are estimated. The double-differential cross section for the reaction d + C → π 0 + x is determined for the first time by using a data sample containing more than 40 000 neutral pions.

Pionic decay of a possibled′dibaryon and the short-rangeNNinteraction

We study the pionic decay of a possible dibaryon d' --> N N \pi in the microscopic quark shell model. The initial d' dibaryon wave function (J^P=0^-, T=0) consists of one 1\hbar\omega six-quark shell-model s^5p[51]_X configuration. The most important final six-quark configurations s^6[6]_X, s^4p^2[42]_X and (s^4p^2-s^52s)[6]_X are properly projected onto the NN channel. The final state NN interaction is investigated by means of two phase-equivalent - but off-shell different - potential models. We demonstrate that the decay width \Gamma_d' depends strongly on the short-range behavior of the NN wave function. In addition, the width \Gamma_d' is very sensitive to the mass and size of the d' dibaryon. For dibaryon masses slightly above the experimentally suggested value M_d'=2.065 GeV, we obtain a pionic decay width of \Gamma_d' = 0.18 - 0.32 MeV close to the experimental value \Gamma_d' = 0.5 MeV.

Algebriac technique in the quark-cluster approach to NN interaction

The nucleon-nucleon interaction at short range is analyzed in terms of six-quark configurations on a base of numerical solutions of modified RGM equations. It is shown that in low partial waves L=0,1 the wave function of the system has a two-channel structure: the N N channel and the inner six-quark state (“bag”). Starting from this analysis a simple phenomenological model of N N interaction at intermediate energies is proposed.

The nucleon-nucleon potential in the chromodielectric soliton model: Statics.

We study the nucleon-nucleon interaction in the framework of the chromodielectric soliton model (CDM). Here, the long-range parts of the non-Abelian gluon self-interactions are assumed to give rise to a color-dielectric function which is parametrized in terms of an effective scalar background field. The six-quark system is confined in a deformed mean field through an effective nonlinear interaction between the quarks and the scalar field. The CDM is covariant, respects chiral invariance, leads to absolute color confinement, and is free of the spurious long-range van der Waals forces which trouble nonrelativistic investigations employing a confining potential. Six-quark molecular-type configurations are generated as a function of deformation and their energies are evaluated in a coupled channel analysis. By using molecular states instead of cluster model wave functions, all important six-quark configurations are properly taken into account. The corresponding Hamiltonian includes the effective interaction between the quarks and the scalar background field and quark-quark interactions generated through one gluon exchange treated in Coulomb gauge. When evaluating the gluonic propagators, the inhomogeneity and deformation of the dielectric medium are taken into account. Results for the adiabatic nucleon-nucleon potential are presented, and the various contributions are discussed. Finally, an outlook is given on how, in the next stage of our investigation, dynamical effects will be incorporated by employing the generator coordinate method.

Exclusive process 2H(e,e'p)N* as a tool for investigation of the quark structure of the deuteron.

The exclusive $^{2}\mathrm{H}$(e,e'p)${\mathit{N}}^{\mathrm{*}}$ process at CEBAF energies, with the missing mass coincidence technique, offers the opportunity to reveal the baryon-baryon (BB) composition of the deuteron and to reconstruct the deuteron six-quark wave function. As an example, we project out two different kinds of currently discussed six-quark functions into various BB channels including such baryons as n, p, \ensuremath{\Delta}, N(1440), N(1520), and N(1535). Spectroscopic factors and momentum distributions are calculated using the nonrelativistic quark model. The results are that the \ensuremath{\Delta}\ensuremath{\Delta} component in the deuteron is almost entirely connected with the six-quark configuration ${\mathit{s}}^{6}$ while the channels with N(1440), N(1520), and N(1535) display the configuration ${\mathit{s}}^{4}$${\mathit{p}}^{2}$.

O( alpha s2) mass contributions to the H dibaryon in a truncated bag model.

The $H$ dibaryon is a color-singlet flavor-singlet spinless six-quark configuration. We discuss aspects of its Fock-space wave vector in the quark model and discuss construction of diquark state vectors as well. We then address the general issue of computing higher-order contributions to mass. A formalism is developed, and calculations are carried out in a truncated bag model. Mass contributions to both diquark systems and the $H$ dibaryon are computed to $O({\ensuremath{\alpha}}_{s}^{2})$.

Measurements of the deuteron and proton magnetic form factors at large momentum transfers.

Measurements of the deuteron elastic magnetic structure function B(${\mathit{Q}}^{2}$) are reported at squared four-momentum transfer values 1.20\ensuremath{\le}${\mathit{Q}}^{2}$\ensuremath{\le}2.77 (GeV/c${)}^{2}$. Also reported are values for the proton magnetic form factor ${\mathit{G}}_{\mathit{M}\mathit{p}}$(${\mathit{Q}}^{2}$) at 11 ${\mathit{Q}}^{2}$ values between 0.49 and 1.75 (GeV/c${)}^{2}$. The data were obtained using an electron beam of 0.5 to 1.3 GeV. Electrons backscattered near 180\ifmmode^\circ\else\textdegree\fi{} were detected in coincidence with deuterons or protons recoiling near 0\ifmmode^\circ\else\textdegree\fi{} in a large solid-angle double-arm spectrometer system. The data for B(${\mathit{Q}}^{2}$) are found to decrease rapidly from ${\mathit{Q}}^{2}$=1.2 to 2 (GeV/c${)}^{2}$, and then rise to a secondary maximum around ${\mathit{Q}}^{2}$=2.5 (GeV/c${)}^{2}$. Reasonable agreement is found with several different models, including those in the relativistic impulse approximation, nonrelativistic calculations that include meson-exchange currents, isobar configurations, and six-quark configurations, and one calculation based on the Skyrme model. All calculations are very sensitive to the choice of deuteron wave function and nucleon form factor parametrization. The data for ${\mathit{G}}_{\mathit{M}\mathit{p}}$(${\mathit{Q}}^{2}$) are in good agreement with the empirical dipole fit.

Nuclear force with an ultra short range attraction

The authors propose an ultra short range attraction in the nucleon-nucleon potential to imitate some qualitative features of the quark model. A modified version of the Reid soft core potential is presented. It is proved to be capable of describing the physical observables of the deuteron as well as the original Reid soft core potential. The probability of the six-quark configuration of the two-nucleon system can be defined and a good estimate for this probability can be obtained.

SU(3)F breaking in the 10∗F and 8F dibaryon multiplets

Abstract Certain positive-parity dibaryon channels, corresponding to multiplets of spin-flavor (J, F) = (0, 1), (2, 8 ) and (3, 10 ∗ ) , are expected, on qualitative grounds, to support six-quark configurations lying below super-allowed (fall apart) decay thresholds, in the SU(3)F symmetry limit. In view of the significant lowering of color magnetic (hyperfine) attraction induced by the breaking of this symmetry in the first of these multiplets (the well-known H channel) we investigate the effect of symmetry breaking on the remaining candidate dibaryon channels. While the (3, 10∗) is found to be largely unaffected, hyperfine binding is decreased in the (2, 8) multiplet, dramatically so for the least strange members of the multiplet.

Classification and construction of six-quark basis states from parity eigenfunctions for N-N processes.

Six-quark configurations relevant to N-N scattering and bound states are constructed from parity eigenfunctions which can be obtained from any static independent particle model. The two lowest, one even and one odd, parity orbitals are considered. In the (TS)=(10) and (01) sectors, there are 16 orthogonal color-singlet configurations of various orbital-spin-isospin symmetries; there are 7 in the (00) and 25 in the (11) sectors. The results obtained here are compared with the cluster model approach for single particle s states in each cluster. In that model, certain ${p}^{n}$${s}^{6\mathrm{\ensuremath{-}}n}$ components disappear from the wave function in the zero-separation limit, whereas the parity eigenfunction representation preserves a symmetry between even and odd parity states (with respect to the center of mass). Furthermore, cluster model configurations have been limited to three-quark clusters, which also limits the number of basis states. It is demonstrated here how parity eigenfunctions can be constructed from cluster model functions, and utilized to build the ``missing'' basis states.

A dynamical model for the six-quark admixture in the deuteron state

The coexistence problem of the six-quark and two-nucleon components in the deuteron state is studied within a dynamical model based on the quark cluster theory. The mixing probability of the (0s) 6 six-quark configuration in the deuteron is estimated to be about 2.4%. The physical consequences of this large admixture and also the relation with the conventional deuteron picture are examined in detail.

Properties of six-quark clusters in the topological chiral soliton model

The energy and bag radius of a six-quark configuration are obtained from a topological chiral soliton model. The calculation shows that three and six quark systems in this model behave much as those in the MIT bag model.