Abstract:
We present a detailed analysis of the use of heavy quark fragmentation into heavy hadrons for testing the heavy quark effective theory through comparison of the measured fragmentation parameters of the $c$ and $b$ quarks. Our analysis is entirely model independent. We interpret the known perturbative evolution in a way useful for exploiting heavy quark symmetry at low energy. We first show consistency with perturbative QCD scaling for measurements done solely with $c$ quarks. We then apply the perturbative analysis and the heavy quark expansion to relate measurements from ARGUS and LEP. We place bounds on a nonperturbative quark mass suppressed parameter, and compare the values for the $b$ and $c$ quarks. We find consistency with the heavy quark expansion but fairly sizable QCD uncertainties. We also suggest that one might reduce the systematic uncertainty in the result by not extrapolating to low $z$.

Abstract:
We calculate the spin density matrix of the hadron $h$ created via quark fragmentation in the process $e^-e^+ \to q\bar q \to h + X$. In the case of $h=\Lambda$ the experimental data could possibly elucidate the problem of $s$-quark contribution to the spin of the $\Lambda$-hyperon, to be compared with the case of the proton (``spin crisis''). Generally we find that for hadrons with spin 1/2 the parton description, using only probabilities, works much better than for vector particles, since in the former case the non diagonal matrix elements of the hadron spin density matrix are suppressed by a small factor $p_T/(z\sqrt s)$, where $p_T$ is the hadron transverse momentum inside the jet.

Abstract:
Quark-quark double scattering in eA DIS and its contribution to quark and anti-quark fragmentation functions are investigated with the generalized factorization of the relevant twist-four processes in pQCD. It is shown that the resulting modifications to quark and anti-quark fragmentation functions are different. While the numerical size of these effects cannot be determined from pQCD, the structure of our result leads to a number of qualitative predictions for the relative size of the effect for different hadrons. These qualitative predictions agree with the multiplicity ratios for positive and negative hadrons as observed by HERMES.

Abstract:
The study of quark jets in e+e- reactions at LEP has demonstrated that the hadronisation process is reproduced well by the Lund string model. However, our understanding of gluon fragmentation is less complete. In this study enriched quark and gluon jet samples of different purities are selected in three-jet events from hadronic decays of the Z collected by the DELPHI experiment in the LEP runs during 1994 and 1995. The leading systems of the two kinds of jets are defined by requiring a rapidity gap and their sum of charges is studied. An excess of leading systems with total charge zero is found for gluon jets in all cases, when compared to Monte Carlo Simulations with JETSET (with and without Bose-Einstein correlations included) and ARIADNE. The corresponding leading systems of quark jets do not exhibit such an excess. The influence of the gap size and of the gluon purity on the effect is studied and a concentration of the excess of neutral leading systems at low invariant masses (<~ 2 GeV/c^2) is observed, indicating that gluon jets might have an additional hitherto undetected fragmentation mode via a two-gluon system. This could be an indication of a possible production of gluonic states as predicted by QCD.

Abstract:
Charm and bottom mesons and baryons are incorporated into a low energy chiral Lagrangian. Interactions of the heavy hadrons with light octet Goldstone bosons are studied in a framework which represents a synthesis of chiral perturbation theory and the heavy quark effective theory. The differential decay rate for the semileptonic process $\LBzero \to \Sigma_c^{++} + e^- + \bar{\nu}_e + \pi^-$ is calculated at the zero recoil point using this hybrid formalism.

Abstract:
We discuss the fragmentation of a heavy quark to a baryon containing two heavy quarks of mass $m_Q\gg\Lambda_{\rm QCD}$. In this limit the heavy quarks first combine perturbatively into a compact diquark with a radius small compared to $1/\Lambda_{\rm QCD}$, which interacts with the light hadronic degrees of freedom exactly as does a heavy antiquark. The subsequent evolution of this $QQ$ diquark to a $QQq$ baryon is identical to the fragmentation of a heavy antiquark to a meson. We apply this analysis to the production of baryons of the form $ccq$, $bbq$, and $bcq$.

Abstract:
After a brief review on how heavy quark symmetry constraints the helicity fragmentation probabilities for a heavy quark hadronizes into heavy-light hadrons, we present a heavy quark fragmentation model to extract the value for the Falk-Peskin probability $w_{3/2}$ describing the fragmentation of a heavy quark into a heavy-light meson whose light degrees of freedom have angular momentum ${3 \over 2}$. We point out that this probability depends on the longitudinal momentum fraction $z$ of the meson and on its transverse momentum $p_\bot$ relative to the jet axis. In this model, the light degrees of freedom prefer to have their angular momentum aligned transverse to, rather than along, the jet axis. Implications for the production of excited heavy mesons, like $D^{**}$ and $B^{**}$, are briefly discussed.

Abstract:
Experimental data, theoretical ideas and models concerning jet fragmentation and the hadronization process are reviewed, concentrating on the following topics: factorization and small-x resummation of fragmentation functions, hadronization models, single-particle yields and spectra in Z decay, comparisons between quark and gluon jets, current and target fragmentation in deep inelastic scattering, heavy quark fragmentation, Bose-Einstein correlations and WW fragmentation.

Abstract:
Multiple scattering, induced radiative energy loss and modified fragmentation functions of a heavy quark in nuclear matter are studied within the framework of generalized factorization in perturbative QCD. Modified heavy quark fragmentation functions and energy loss are derived in detail with illustration of the mass dependencies of the Landau-Pomeranchuk-Migdal interference effects and heavy quark energy loss. Due to the quark mass dependence of the gluon formation time, the nuclear size dependencies of nuclear modification of the heavy quark fragmentation function and heavy quark energy loss are found to change from a linear to a quadratic form when the initial energy and momentum scale are increased relative to the quark mass. The radiative energy loss of the heavy quark is also significantly suppressed due to limited cone of gluon radiation imposed by the mass. Medium modification of the heavy quark fragmentation functions is found to be limited to the large $z$ region due to the form of heavy quark fragmentation functions in vacuum.

Abstract:
In this paper we prove factorization of fragmentation function in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. We use the background field method of QCD in a pure gauge in path integral approach to prove factorization of fragmentation function in non-equilibrium QCD. Our proof is valid in any arbitrary gauge fixing parameter $\alpha$. This may be relevant to study hadron production from quark-gluon plasma at high energy heavy-ion colliders at RHIC and LHC.