Groups of tree-expanded series

We describe the proalgebraic groups represented by three Hopf algebras on planar binary trees previously introduced by the author and Christian Brouder in relation with the renormalization of quantum electrodynamics. Using two monoidal structures and a set-operad structure on planar binary trees, we show that these groups can be realized on formal series expanded over trees, and that the group laws are generalization of the multiplication and the composition of usual series in one variable. All the constructions are done in a general operad-theoretic setting, and then applied to the duplicial operad on trees.Comment: 30 pages; added references, to appear in J.Algebr

Renormalization of QED with planar binary trees

The renormalized photon and electron propagators are expanded over planar binary trees. Explicit recurrence solutions are given for the terms of these expansions. In the case of massless Quantum Electrodynamics (QED), the relation between renormalized and bare expansions is given in terms of a Hopf algebra structure. For massive quenched QED, the relation between renormalized and bare expansions is given explicitly.Comment: Uses feynmf package. 20 page

From quantum electrodynamics to posets of planar binary trees

This paper is a brief mathematical excursion which starts from quantum electrodynamics and leads to the Moebius function of the Tamari lattice of planar binary trees, within the framework of groups of tree-expanded series. First we recall Brouder's expansion of the photon and the electron Green's functions on planar binary trees, before and after the renormalization. Then we recall the structure of Connes and Kreimer's Hopf algebra of renormalization in the context of planar binary trees, and of their dual group of tree-expanded series. Finally we show that the Moebius function of the Tamari posets of planar binary trees gives rise to a particular series in this group.Comment: 13 page

Light Quark Spectroscopy Results from FOCUS and E687

Using the FOCUS spectrometer (experiments 687 and 831 at Fermilab) we confirm the existence of a diffractively photoproduced enhancement in $K^+K^-$ at 1750 \mevcc with nearly 100 times the statistics of previous experiments. We also observe a narrow dip structure at 1.9 GeV/c$^2$ in a study of diffractive photoproduction of the $3\pi^+3\pi^-$ final state.Comment: Uses epsfig and lnfprep (included). Five pages, three figures. Presented at the 31st International Conference On High Energy Physics (ICHEP 2002), 24-31 Jul 2002, Amsterdam, The Netherland

On the scalar nonet lowest in mass

The hypothesis that there exists a nonet of scalars mainly composed of a valence quark-antiquark pair and mixed according to near singlet-octet separation : f_0 (980) singlet, a_0^{+,0,-} (980), K^{* +,0}_0 (1430), \bar K^{* -,0}_0 (1430), f_0 (1500) octet, is put to further tests from the three body decays D^{\pm}, D_{s}^{\pm} -> PS^{\pm} pi^+ pi^- with PS^{\pm} = pi^{\pm}, K^{\pm}. The analysis of decay phases supports the singlet nature of f_0 (980).Comment: Talk (by P.M.) given at the QCD 02 9th International High-Energy Physics Conference in QuantumChromoDynamics (Montpellier 2-9th July 2002), 4 page

Complex amplitude phase motion in Dalitz plot heavy meson three body decay

We propose a method to determine the phase motion of a complex amplitude in three body heavy meson decays. We show that the phase variation of a complex amplitude can be directly revealed through the interference observed in the Dalitz Plot region where it crosses with a well established resonant state. This method could be applied to the decays \d3pi and $D^+\to K^-\pi^+\pi^+$, to determine whether the low mass states $\sigma$ and $\kappa$, suggested by E791, have phase motions compatible with resonances.Comment: To appear in Physics Letters