1,353 research outputs found
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 at 1750
\mevcc with nearly 100 times the statistics of previous experiments.
We also observe a narrow dip structure at 1.9 GeV/c in a study of
diffractive photoproduction of the 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 , to
determine whether the low mass states and , suggested by E791,
have phase motions compatible with resonances.Comment: To appear in Physics Letters
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