Chiral-Odd and Spin-Dependent Quark Fragmentation Functions and their Applications

We define a number of quark fragmentation functions for spin-0, -1/2 and -1 hadrons, and classify them according to their twist, spin and chirality. As an example of their applications, we use them to analyze semi-inclusive deep-inelastic scattering on a transversely polarized nucleon.Comment: 19 pages in Plain TeX, MIT CTP #221

Quark Orbital-Angular-Momentum Distribution in the Nucleon

We introduce gauge-invariant quark and gluon angular momentum distributions after making a generalization of the angular momentum density operators. From the quark angular momentum distribution, we define the gauge-invariant and leading-twist quark {\it orbital} angular momentum distribution $L_q(x)$. The latter can be extracted from data on the polarized and unpolarized quark distributions and the off-forward distribution $E(x)$ in the forward limit. We comment upon the evolution equations obeyed by this as well as other orbital distributions considered in the literature.Comment: 8 pages, latex, no figures, minor corrections mad

Lorentz Symmetry and the Internal Structure of the Nucleon

To investigate the internal structure of the nucleon, it is useful to introduce quantities that do not transform properly under Lorentz symmetry, such as the four-momentum of the quarks in the nucleon, the amount of the nucleon spin contributed by quark spin, etc. In this paper, we discuss to what extent these quantities do provide Lorentz-invariant descriptions of the nucleon structure.Comment: 6 pages, no figur

Implications of Color Gauge Symmetry For Nucleon Spin Structure

We study the chromodynamical gauge symmetry in relation to the internal spin structure of the nucleon. We show that 1) even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element; 2) the evolution equations for the gluon spin take very different forms in the Feynman and axial gauges, but yield the same leading behavior in the asymptotic limit; 3) the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the light-cone gauge. We define a new gluon orbital angular momentum distribution $L_g(x)$ which {\it is} an experimental observable and has a simple scale evolution. However, its physical interpretation makes sense only in the light-cone gauge just like the gluon helicity distribution $\Delta g(x)$y.Comment: Minor corrections are made in the tex

Positivity Constraints for Spin-Dependent Parton Distributions

We derive new positivity constraints on the spin-dependent structure functions of the nucleon. These model independent results reduce conside\-rably their domain of allowed values, in particular for the chiral-odd parton distribution $h_1 (x)$.Comment: 8 pages,CPT-94/P.3059,LaTex,3 fig available on cpt.univ-mrs.fr directory pub/preprints/94/fundamental-interactions/94-P.305

Electronic transport in a Cantor stub waveguide network

We investigate theoretically, the character of electronic eigenstates and transmission properties of a one dimensional array of stubs with Cantor geometry. Within the framework of real space re-normalization group (RSRG) and transfer matrix methods we analyze the resonant transmission and extended wave-functions in a Cantor array of stubs, which lack translational order. Apart from resonant states with high transmittance we unravel a whole family of wave-functions supported by such an array clamped between two-infinite ordered leads, which have an extended character in the RSRG scheme, but, for such states the transmission coefficient across the lead-sample-lead structure decays following a power-law as the system grows in size. This feature is explained from renormalization group ideas and may lead to the possibility of trapping of electronic, optical or acoustic waves in such hierarchical geometries

Off-Forward Parton Distributions in 1+1 Dimensional QCD

We use two-dimensional QCD as a toy laboratory to study off-forward parton distributions (OFPDs) in a covariant field theory. Exact expressions (to leading order in $1/N_C$) are presented for OFPDs in this model and are evaluated for some specific numerical examples. Special emphasis is put on comparing the $x>\zeta$ and $x<\zeta$ regimes as well as on analyzing the implications for the light-cone description of form factors.Comment: Revtex, 6 pages, 4 figure

Glueball Spin

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is reexamined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This can be compared to the electromagnetic charge/monopole system, where the quantization of the field angular momentum places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of this operator under some simplifying assumptions.Comment: 11 pages, 0 figures; added references and some discussio

Helicity-Flip Off-Foward Parton Distributions of the Nucleon

We identify quark and gluon helicity-flip distributions defined between nucleon states of unequal momenta. The evolution of these distributions with change of renormalization scale is calculated in the leading-logarithmic approximation. The helicity-flip gluon distributions do not mix with any quark distribution and are thus a unique signature of gluons in the nucleon. Their contribution to the generalized virtual Compton process is obtained both in the form of a factorization theorem and an operator product expansion. In deeply virtual Compton scattering, they can be probed through distinct angular dependence of the cross section.Comment: a few corrections made, references change