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

Conformal Symmetry and Pion Form Factor: Soft and Hard Contributions

We discuss a constraint of conformal symmetry in the analysis of the pion form factor. The usual power-law behavior of the form factor obtained in the perturbative QCD analysis can also be attained by taking negligible quark masses in the nonperturbative quark model analysis, confirming the recent AdS/CFT correspondence. We analyze the transition from soft to hard contributions in the pion form factor considering a momentum-dependent dynamical quark mass from a nonnegligible constituent quark mass at low momentum region to a negligible current quark mass at high momentum region. We find a correlation between the shape of nonperturbative quark distribution amplitude and the amount of soft and hard contributions to the pion form factor.Comment: 7 pages, 6 figures, extensively revised, to appear in Phys. Rev.

Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture

By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy-bound property and nilpotent periodicity property, satisfy the $\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the conjugacy-bound for relatively hyperbolic groups and compute the cyclic cohomology of the $\ell^1$-algebra of any discrete group.Comment: 32 pages, 2 figures; added an appendix also by C. Ogl

Generalizing smoothness constraints from discrete samples

We study how certain smoothness constraints, for example, piecewise continuity, can be generalized from a discrete set of analog-valued data, by modifying the error backpropagation, learning algorithm. Numerical simulations demonstrate that by imposing two heuristic objectives — (1) reducing the number of hidden units, and (2) minimizing the magnitudes of the weights in the network — during the learning process, one obtains a network with a response function that smoothly interpolates between the training data