Constrained Orthogonal Polynomials

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study of density fluctuations in centrifuges. We give explicit properties of such polynomial sets, generalizing Laguerre and Legendre polynomials. The nature of the dimension 1 subspace completing such sets is described. A numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure

Antisymmetrization of a Mean Field Calculation of the T-Matrix

The usual definition of the prior(post) interaction $V(V^\prime )$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector ${\cal A}$ must be included in the definition of the transition operator, $T\equiv V^\prime{\cal A}+V^\prime{\cal A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14

Phenomenological discussion of B→PVB\to P V decays in QCD improved factorization approach

Trying a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorization, we find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. This failure reflects the difficulty to accommodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B}^0\to\rho^+ \pi^-$, which is predicted very small by QCD factorization. Proposing a fit with QCD factorization complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly.Comment: 8 pages, 2 figures (requires epsfig, psfrag),talk presented at the XXXVIIIth Rencontres de Moriond: Electroweak Interactions and Unified Theories,Les Arcs, France, March 15-22, 2003. To be published in the Proceeding