Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].     

Polarization density matrix forZ decay intoWff' with generalZWW couplings

We give the polarization density matrix ofZ andW for the decay processZ ⁰→Wff' with generalZWW couplings. The matrix elements are expressed in terms of kinematical invariants so that they can be readily used in \(p\bar p \to Z^0 W\) as well. Using these formulas, we analyze the possibilities of probing theZWW couplings through the decay of polarizedZ ⁰.