Ground state heavy baryon production in a relativistic quark-diquark model

We use current-current interaction to calculate the fragmentation functions to describe the production of spin-1/2, spin-1/2$'$ and spin-3/2 baryons with massive constituents in a relativistic quark-diquark model. Our results are in their analytic forms and are applicable for singly, doubly and triply heavy baryons. We discuss the production of $\Omega_{bbc}$, $\Omega_{bcc}$ and $\Omega_{ccc}$ baryons in some detail. The results are satisfactorily compared with those obtained for triply heavy baryons calculated in a perturbative regime within reasonable values of the parameters involved.Comment: 8 pages, 4 figures. To appear in Phys. Rev.

Heavy quark fragmentation models

We discuss the process of quark fragmentation placing a particular emphasise on the change of the fragmentation spectrum due to kinematical effects when light quarks are replaced by heavy ones. After investigating different methods of data extraction, we compile the data on heavy quark fragmentation from various collaborations. These data are compared with various models of heavy quark fragmentation for charm and bottom quark fragmentation. In our comparison we first separate the fragmentation models into two categories in accordance with their behaviour at large values of the fragmentation parameter. Models that are in agreement with the dimensional counting rules have a softer behaviour than some popular models which axe not in agreement. This point is crucial in the case of heavier quarks. However, due to the large errors in experimental data, it is hard to make a firm judgement about the merits of these models. We study the spin properties of heavy quark fragmentation and obtain the fragmentation functions for different polarisation states. The fragmentation function for an unpolarised state is then taken to be a combination of the longitudinal and the transverse fragmentation functions. We also give a model in which the transverse momentum of the constituent quarks is taken into account. The effect of the increase in the constituent transverse momentum is to soften the fragmentation by a limited amount, since there is a small probabability that the constituents of a bound state will have a large relative momentum. Finally we give a rather detailed Monte Carlo study of the effect of different fragmentation models on the momentum spectrum of heavy mesons, and the final state leptons resulting from heavy quark production in hadron colliders at CERN and FNAL. We find that the effect on the lepton spectrum is more significant

Fragmentation Production of Omega_ccc and Omega_bbb Baryons

The Lambda baryons with a single heavy flavor which transfer the quark polarization, have been studied both theoretically and experimentally. The Xi's with two heavy constituents are well treated in quark-diquark model. In this work we study the production of triply heavy baryons in the perturbative QCD regime and calculate the fragmentation functions for Omega_ccc and Omega_bbb in the c and b quark fragmentation, respectively. We then obtain the total fragmentation probability and the average fragmentation parameter for each case.Comment: 10 pages, 2 figures, published at Phys. Lett. B 559 (2003) 239-244(errata corrected

An ivestigation of triply heavy baryon production at hadron colliders

The triply heavy baryons have a rather diverse mass range. While some of them possess considerable production rates at existing facilities, others need to be produced at future high energy colliders. Here we study the direct fragmentation production of the$\Omega_{ccc}$ and $\Omega_{bbb}$ baryons as the prototypes of triply heavy baryons at the hadron colliders with different $\sqrt{s}$. We present and compare the transverse momentum distributions of the differential cross sections, $p_T^{\rm min}$ distributions of total cross sections and the integrated total cross sections of these states at the RHIC, the Tevatron Run II and the CERN LHC.Comment: 9 pages, 5 figures, To appear in Nuclear Physics

Landau Levels as a Limiting Case of a Model with the Morse-Like Magnetic Field

We consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\vec{B}=-B_{0}e^{-\frac{2\pi}{a_{0}}x}\hat{k}$ with $B_{0}>0$ as a constant strength and $a_{0}$ as the width of the band. It is shown that the square integrable pure states realize representations of $su(1,1)$ algebra via the quantum number corresponding to the linear momentum in the $y$-direction. The energy of the states increases by decreasing the width $a_{0}$ while it is not changed by $B_{0}$. It is quadratic in terms of two quantum numbers, and the linear spectrum of the Landau levels is obtained as a limiting case of $a_{0}\rightarrow\infty$. All of the lowest states of the $su(1,1)$ representations minimize uncertainty relation and the minimizing of their second and third states is transformed to that of the Landau levels in the limit $a_{0}\rightarrow\infty$. The compact forms of the Barut-Girardello coherent states corresponding to $l$-representation of $su(1,1)$ algebra and their positive definite measures on the complex plane are also calculated

The Fermi motion contribution to J/\psi production at the hadron colliders

We investigate the relativistic Fermi motion effect in the case of $J/\psi$ production in various hadron colliders. A light-cone wave function is adopted to represent the $J/\psi$ final state. The change in the confinement parameter which sets a scale for the size of the final state, allows one to see the effect in an explicit manner. While the effect has considerable influence on the fragmentation probabilities and the differential cross sections, the total cross sections are essentially left unchanged. such a feature is in agreement with the momentum sum rule which the fragmentation functions should satisfy.Comment: 10 pages, 4 figures, to appear in Phys. Lett.

Direct Fragmentation of Quarkonia Including Fermi Motion Using Light-cone Wave Function

We investigate the effect of Fermi motion on the direct fragmentation of the $J/\psi$ and $\Upsilon$ states employing a light-cone wave function. Consistent with such a wave function we set up the kinematics of a heavy quark fragmenting into a quarkonia such that the Fermi motion of the constituents split into longitudinal as well as transverse direction and thus calculate the fragmentation functions for these states. In the framework of our investigation, we estimate that the fragmentation probabilities of $J/\psi$ and $\Upsilon$ may increase at least up to 14 percent when including this degree of freedom.Comment: 7 pages 5 figures Appeared in EPJC; Fig 1 and Appendix revise

Pion distribution amplitude from holographic QCD and the electromagnetic form factor F_pi(Q2)

The holographic QCD prediction for the pion distribution amplitude (DA) $\phi_{hol}(u)$ is used to compute the pion spacelike electromagnetic form factor $F_{\pi}(Q^2)$ within the QCD light-cone sum rule method. In calculations the pion's renormalon-based model twist-4 DA, as well as the asymptotic twist-4 DA are employed. Obtained theoretical predictions are compared with experimental data and with results of the holographic QCD

Production of Triply Heavy Baryons at LHC

Triply heavy baryons are very interesting hadrons to be explored for they provide particular information about strong interactions, hadron structures, and weak decays of heavy baryons. We calculate the hadronic production cross sections of the \Omega_{ccc} and the \Omega_{ccb}, which are dominated by the gg fusion subprocesses containing 4362 and 1454 Feynman diagrams, respectively. A method for generating and calculating tree level Feynman diagrams automatically is developed to deal with complicated processes containing so many diagrams. Our results show that 10^4-10^5 events of triply heavy baryons can be accumulated for 10 fb^{-1} integrated luminosity at LHC. Signatures of the triply heavy baryons are pointed out, with emphasis on the decay modes \Omega_{ccc} -> \Omega_{sss} + 3 \pi^+ and \Omega_{ccb} -> \Omega_{sss} + 3 \pi^+ +\pi^-. We conclude that it is quite promising to discover them at LHC.Comment: 32 pages, 7 figures, to appear in JHE