Doubly Charmed Baryon Mass and Wave Function through a Random Walks Method

The mass and the wave function of doubly charmed Ξ_cc⁺⁺ (ccu) baryon are evaluated using Green Function Monte Carlo method to solve the three-body problem with Cornell potential. The mass of Ξ_cc⁺⁺ with spin 1/2 is in a good agreement with the LHCb value. Simulation of the wave function by random walks resulted in a configuration of the quark–diquark type. The radius of Ξ_cc⁺⁺ is much larger than the size needed for a large isospin splitting. The prediction for the Ω_cc mass is presented.     

Proc ess es e+ e− → cccc and e+ e− → J/ψ + gg at $$\sqrt s = 10.59 G eV$$

Experimental data obtained by the BELLE Collaboration for inclusive J/ψ production in the processes e⁺e^? → J/ψ + gg and e⁺e^? → J/ψ + cc are discussed. These data are compared with the predictions of perturbative QCD that were obtained by two methods, that which employs information about the J/ψ wave function and that which relies on the hypothesis of quark-hadron duality exclusively. Both computational methods yield results that disagree with the experimental data considerably. The dependence of the cross section for the process e⁺e^? → J/ψ + gg on the effective gluon mass is studied. The cross section for the production of doubly charmed baryons Ξ _cc ^* is estimated.     

Inclusive Production Λc in the e+e− - Annihilation

In the framework of the quark-diquark model of baryons, Λ_c can be considered as constituent c quark and ud diquark. In hadronizasion process baryon Λ_c can be produced from ud scalar diquark and c quark fragmentation. So in this work, in the lowest order of perturbative QCD, fragmentation functions c → Λ_c and ud → Λ_c are calculated and finally in the electron-positron annihilation in LEP, the inclusive cross section production of Λ_c is calculated about pole of z⁰.     

Spin dependent fragmentation functions for heavy flavor baryons and single heavy hyperon polarization

Spin dependent fragmentation functions for heavy flavor quarks to fragment into heavy baryons are carculated in a quark-diquark model. The production of intermediate spin 1/2 and 3/2 excited states is explicity included. Λ _b , Λ_c and Ξ _c production rate and polarization at LEP energies are calculated and, where possible, compared with experiment. A different approach, also relying on a heavy quark-diquark model, is proposed for the small momentum transfer inclusive production of polarized heavy flavor hyperons. The predicted Λ_c polarization is roughly in agreement with experiment.     

Properties of doubly heavy baryons in the relativistic quark model

Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.     

Production of triply charmed Ω<Subscript>ccc</Subscript> baryonsin <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

The total and differential cross sections for the production of triply charmed Ω_ccc baryons in e⁺e^? annihilation are calculated at the Z-boson pole.     

Isospin splittings of doubly heavy baryons

The SELEX Collaboration has reported a very large isospin splitting of doubly charmed baryons. We show that this effect would imply that the doubly charmed baryons are very compact. One intriguing possibility is that such baryons have a linear geometry Q–q–Q$Q\text{–}q\text{–}Q$ where the light quark q oscillates between the two heavy quarks Q  , analogous to a linear molecule such as carbon dioxide. However, using conventional arguments, the size of a heavy-light hadron is expected to be around 0.5 fm, much larger than the size needed to explain the observed large isospin splitting. Assuming the distance between two heavy quarks is much smaller than that between the light quark and a heavy one, the doubly heavy baryons are related to the heavy mesons via heavy quark–diquark symmetry. Based on this symmetry, we predict the isospin splittings for doubly heavy baryons including Ξ_cc${\Xi }_{cc}$, Ξ_bb${\Xi }_{bb}$ and Ξ_bc${\Xi }_{bc}$. The prediction for the Ξ_cc${\Xi }_{cc}$ is much smaller than the SELEX value. On the other hand, the Ξ_bb${\Xi }_{bb}$ baryons are predicted to have an isospin splitting as large as (6.3±1.7) MeV$(6.3\pm 1.7)\text{MeV}$. An experimental study of doubly bottomed baryons is therefore very important to better understand the structure of baryons with heavy quarks.     

Fragmentation production of Ωccc baryons at LHC energies

Within the nonrelativistic quark-diquark model for heavy baryons, the fragmentation functions for the transitions of a c-quark and a doubly charmed vector diquark into an Ω_ccc baryon are calculated in the leading order of perturbative QCD. The cross section for Ω _ccc production in high-energy hadron interactions is estimated. It is assumed that Ω_ccc baryons are formed via the fragmentation of a c quark or a vector (cc) diquark produced in the partonic subprocesses gg → c $\bar c$ , q $\bar q$ → c $\bar c$ , gg → (cc)+ $\bar c$ + $\bar c$ , and q $\bar q$ → (cc)+ $\bar c$ + $\bar c$ .     

Nonperturbative parton distributions and the proton spin problem

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q² = 10 (GeV/c)². Applying the same model to the proton spin problem one obtains Σ₃ = 0.18 for the same Q².     

Diquark Fragmentation Contribution in Λ<Subscript><Emphasis Type="Italic">b</Emphasis></Subscript> Production

In the framework of the quark-diquark model of baryons, Λ _b can be considered as b constituent quark an ud constituent diquark. In this study, we investigate the effect ud scalar diquark fragmentation into Λ _b , therefor we calculate frgmentation functions of b quark and ud diquark into Λ _b baryon through the use of perturbative QCD. In the next stage, throuth the use of the obtained fragmentation functions, we calculate the total fragmentation probabilities and average fragmentation parameters for b→Λ _b and u d→Λ _b . Finally, the inclusive cross section of Λ _b baryon in electron-positron annihilation in ALEPH experiment is calculated with regard to ud diquark fragmentation contribution.     

A measurement of ∧ and Ξ<Superscript>−</Superscript> polarization in inclusive production by Σ<Superscript>−</Superscript> of 340 GeV/c in C and Cu targetsof 340 GeV/c in C and Cu targets

We have measured the polarization of ∧ and Ξ^? hyperons produced inclusively by a Σ^? beam of 340 GeV/c momentum in nuclear targets, using samples of 9.5 million ∧ decays and 880000 Ξ^? decays. The large statistics allowed a two-dimensional analysis as functions ofx _F andp _t . The polarization w.r.t. the production normal is mainly positive for ∧ and negative for Ξ^?. The positive sign of the ∧ polarization is opposite to predictions. Atp _t >1 Gev/c, the ∧ polarization decreases to zero or even negative values, in sharp contrast to the plateau abovep _t <1 GeV/c observed in inclusive ∧ production by protons. No such effect is observed for the Ξ^? polarization, and its sign is as expected.     

Quark-hadron duality and production of charmonia and doubly charmed baryons in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> anninhilation

The cross sections for the production of charmonia and doubly charmed baryons in e ⁺ e ^? annihilation at an interaction energy of \(\sqrt s \) = 10.6 GeV are predicted under the assumption of quark—hadron duality. The method used is shown to remove some contradictions between experimental data and perturbative QCD.     

Charm contribution to the proton structure function in deep-inelastic <Emphasis Type="Italic">ep</Emphasis> scattering at the HERA collider

The structure function F ₂ ^c is evaluated within the charm-production model based on perturbative QCD. The results are compared with H1 and ZEUS data obtained at the HERA collider. It is shown that, for D*-meson production, the spectator mechanism, which is independent of the flavors of the hadronic-remnant quarks, comes into play for p _T >10 GeV and that, in calculating charm production in the kinematical domain studied at the HERA collider, it is not necessary to take into account the evolution of the c-quark distribution in the initial-state hadron.     

Heavy-quark production in p $$\bar p$$ collisions and unintegrated gluon distributions

The inclusive production of heavy (c and b) quarks in high-energy p\(\bar p\) collisions are considered within the semihard approach in QCD. The dependence of the cross section for heavy-quark production, σ(p_T>p _T ^min ), on unintegrated gluon distributions is studied. The results of this consideration are compared with experimental data obtained by the D0 and CDF Collaborations at Tevatron.     

How to search for doubly charmed baryons and tetraquarks

Possible experimental searches of doubly charmed baryons and tetraquarks at fixed target experiments with high energy hadron beams and a high intensity spectrometer are considered here. The baryons are:Ξ _cc ⁺ (ccd),Ξ _cc ⁺⁺ (ccu), andΩ _cc ⁺ (ccs); and the tetraquark is T (ccūd). Estimates are given of masses, lifetimes, internal structure, production cross sections, decay modes, branching ratios, and yields. Experimental requirements are given for optimizing the signal and minimizing the backgrounds. This paper is designed as an experimental and theoretical review. It may therefore be of assistance in the planning for a future state-of-the-art high statistics charm experiment, in the spirit of the aims of the recent CHARM2000 workshop.     

Pentaquark search in the NA49 experiment

The NA49 experiment has found narrow peaks in the Ξ^? π ^?, Ξ^? π ⁺ (and antiparticle) spectra at 1862 MeV/c ². These states were identified with the predicted pentaquark cascades. We have searched for other decay channels of the pentaquark cascades. No signal was observed in the ΛK ^? and ΛK _S ⁰ spectra. Based on systematic inconsistencies in the experimental values of the reported Θ⁺, we tried to look for other possible pentaquark states, but observed no signal beyond statistical fluctuations.     

Leading-particle effects in the spectra of Λc and \bar \Lambda _c produced in Σ− p, pp, and π − p interactions

The spectra of leading and nonleading charmed baryons (Λ_c and $\bar \Lambda _c$ ) and the asymmetries between these spectra measured in Σ^? A, π ^? A, and pA collisions at p _L =600 GeV/c in the E781 experiment are simultaneously described within the framework of the Quark-Gluon String Model (QGSM). It is shown that the charmed baryon spectra can be fitted by QGSM curves calculated with the parameter of diquark fragmentation, $a_f^{\Lambda _c } = 0.006$ . It was found in this experiment that the asymmetry between the spectra of Λ_c and $\bar \Lambda _c$ in π ^? A collisions is of nonzero value. It might be described in our model only assuming that the string junction is transferred from target proton into the kinematical region of pion projectile fragmentation.     

Dark matter from the SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on the SU(4) and SU(2)×SU(2) symmetry groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the fourth generation of fermions are the same as those of the ordinary-matter fermions in the first three generations except for the family charge of the SU(4)_F group: F=(1/3, 1/3, 1/3, ?1), where F=1/3 for fermions of ordinary matter and F=?1 for the fourth-generation fermions. The difference in F does not allow mixing between ordinary and fourth-generation fermions. Because of the conservation of the Fcharge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the fourth generation. As a result, the excess n _B of baryons over antibaryons leads to the excess n_4ν=N?N? of neutrinos over antineutrinos in the fourth generation with n_4ν=n _B . This massive neutrino may form nonbaryonic dark matter. In principle, the mass density of the fourth neutrino n_4νm _N in the Universe can make the main contribution to dark matter, since the lower bound on the neutrino mass m _N from the data on decay of the Z bosons is m _N <m _Z /2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude higher than allowed by observations. This inconsistency may be avoided by nonconservation of the F charge.     

Excited state mass spectra of doubly heavy $$\Xi $$ baryons

In this paper, the mass spectra are obtained for doubly heavy \(\Xi \) baryons, namely, \(\Xi _{cc}^{+}\), \(\Xi _{cc}^{++}\), \(\Xi _{bb}^{-}\), \(\Xi _{bb}^{0}\), \(\Xi _{bc}^{0}\) and \(\Xi _{bc}^{+}\). These baryons consist of two heavy quarks (cc, bb, and bc) with a light (d or u) quark. The ground, radial, and orbital states are calculated in the framework of the hypercentral constituent quark model with Coulomb plus linear potential. Our results are also compared with other predictions, thus, the average possible range of excited states masses of these \(\Xi \) baryons can be determined. The study of the Regge trajectories is performed in (n, \(M^{2}\)) and (J, \(M^{2}\)) planes and their slopes and intercepts are also determined. Lastly, the ground state magnetic moments of these doubly heavy baryons are also calculated.