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

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

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

Dalitz plot analysis and branching fraction measurement of D+ and Ds+ -> pi+pi-pi+

Fermilab fixed target experiment E791 obtained a sample of $1172 \pm 61$ events of $D^+ \to \pi^- \pi^+ \pi^+$ and 848 $\pm 44$ events of $D_s^+ \to \pi^- \pi^+ \pi^+$ decays. We find respectively $B (D^+ \to \pi^- \pi^+ \pi^+) / B (D^+ \to K^- \pi^+ \pi^+) = 0.0311 \pm 0.0018 ^ {+0.0016}_{-0.0026}$ and $B(D_s^+ \to \pi^+ \pi^- \pi^+) / B(D_s^+ \to \phi \pi^+) = 0.245 \pm 0.028^{+0.019}_{-0.012}$. Using a coherent amplitude analysis to fit the Dalitz plot of the $D^+ \to \pi^- \pi^+ \pi^+$ decay, we find strong evidence for a scalar resonance of mass $478^{+24}_{-23} \pm 17$MeV/$c^2$ and width $324^{+42}_{-40} \pm 21$ MeV/$c^2$, compatible with what is expected for the isoscalar meson $\sigma$ >. The $D^+ \to \sigma(500) \pi^+$ fraction accounts for approximately half of all three-charged-pion decays of the $D^+$ . From the Dalitz plot analysis of the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay events, we find significant contributions from the channels $\rho^0(770)\pi^+$, $\rho^0(1450)\pi^+$, $f_0(980)\pi^+$, $f_2(1270)\pi^+$, and $f_0(1370)\pi^+$. We also present new measurement of the masses and widths of the isoscalar resonances $f_0(980)$ and $f_0(1370)$.Comment: 4 pages, 4 figures, talk presented in BEACH2000, Valencia, Spai

Noncommutative version of Borcherds' approach to quantum field theory

Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses its geometric meaning when Borcherds introduces a (graded) commutative normal product. We present a fully geometric version of Borcherds' quantization where the (external) tensor product plays the role of the normal product. We construct a noncommutative many-body Hopf algebra and a module over it which contains all the terms of the perturbative expansion and we quantize it to recover the expectation values of standard quantum field theory when the Hopf algebra fiber is (graded) cocommutative. This construction enables to the second quantize any theory described by a cocommutative Hopf algebra bundle.Comment: Frontiers of Fundamental Physics 14, Jul 2014, Marseille, Franc

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