421 research outputs found
Fundamental representations and algebraic properties of biquaternions or complexified quaternions
The fundamental properties of biquaternions (complexified quaternions) are
presented including several different representations, some of them new, and
definitions of fundamental operations such as the scalar and vector parts,
conjugates, semi-norms, polar forms, and inner and outer products. The notation
is consistent throughout, even between representations, providing a clear
account of the many ways in which the component parts of a biquaternion may be
manipulated algebraically
Quaternion-Octonion SU(3) Flavor Symmetry
Starting with the quaternionic formulation of isospin SU(2) group, we have
derived the relations for different components of isospin with quark states.
Extending this formalism to the case of SU(3) group we have considered the
theory of octonion variables. Accordingly, the octonion splitting of SU(3)
group have been reconsidered and various commutation relations for SU(3) group
and its shift operators are also derived and verified for different iso-spin
multiplets i.e. I, U and V- spins.
Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices
PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and
models of strong and electroweak interaction
Quaternion Octonion Reformulation of Quantum Chromodynamics
We have made an attempt to develop the quaternionic formulation of Yang -
Mill's field equations and octonion reformulation of quantum chromo dynamics
(QCD). Starting with the Lagrangian density, we have discussed the field
equations of SU(2) and SU(3) gauge fields for both cases of global and local
gauge symmetries. It has been shown that the three quaternion units explain the
structure of Yang- Mill's field while the seven octonion units provide the
consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics
Octonion Quantum Chromodynamics
Starting with the usual definitions of octonions, an attempt has been made to
establish the relations between octonion basis elements and Gell-Mann \lambda
matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann
\lambda matrices of SU(3)symmetry and octonion basis elements. Consequently,
the quantum chromo dynamics (QCD) has been reformulated and it is shown that
the theory of strong interactions could be explained better in terms of
non-associative octonion algebra. Further, the octonion automorphism group
SU(3) has been suitably handled with split basis of octonion algebra showing
that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields
which are responsible for the existence of two gauge potentials respectively
associated with electric charge and magnetic monopole and supports well the
idea that the colored quarks are dyons
Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators
An attempt has been made to investigate the global SU(2) and SU(3) unitary
flavor symmetries systematically in terms of quaternion and octonion
respectively. It is shown that these symmetries are suitably handled with
quaternions and octonions in order to obtain their generators, commutation
rules and symmetry properties. Accordingly, Casimir operators for SU(2)and
SU(3) flavor symmetries are also constructed for the proper testing of these
symmetries in terms of quaternions and octonions
A straw drift chamber spectrometer for studies of rare kaon decays
We describe the design, construction, readout, tests, and performance of
planar drift chambers, based on 5 mm diameter copperized Mylar and Kapton
straws, used in an experimental search for rare kaon decays. The experiment
took place in the high-intensity neutral beam at the Alternating Gradient
Synchrotron of Brookhaven National Laboratory, using a neutral beam stop, two
analyzing dipoles, and redundant particle identification to remove backgrounds
Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions
In this paper, we reconsider the large-argument asymptotic expansions of the
Hankel, Bessel and modified Bessel functions and their derivatives. New
integral representations for the remainder terms of these asymptotic expansions
are found and used to obtain sharp and realistic error bounds. We also give
re-expansions for these remainder terms and provide their error estimates. A
detailed discussion on the sharpness of our error bounds and their relation to
other results in the literature is given. The techniques used in this paper
should also generalize to asymptotic expansions which arise from an application
of the method of steepest descents.Comment: 32 pages, 2 figures, accepted for publication in Acta Applicandae
Mathematica
Time-integrated luminosity recorded by the BABAR detector at the PEP-II e+e- collider
This article is the Preprint version of the final published artcile which can be accessed at the link below.We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e+e- collider at the ϒ(4S), ϒ(3S), and ϒ(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e+e-→e+e- and (for the ϒ(4S) only) e+e-→μ+μ- candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e+e-→e+e- and e+e-→μ+μ-, the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the ϒ(3S) and ϒ(2S) resonances, an additional uncertainty arises due to ϒ→e+e-X background. For data collected off the ϒ resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the ϒ(4S), 0.58% (0.72%) for the ϒ(3S), and 0.68% (0.88%) for the ϒ(2S).This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l’Energie Atomique and Institut National de Physique Nucléaire et de Physiquedes Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e Innovación (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A.P. Sloan Foundation (USA)
Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events
The - oscillation frequency has been measured with a sample of
23 million \B\bar B pairs collected with the BABAR detector at the PEP-II
asymmetric B Factory at SLAC. In this sample, we select events in which both B
mesons decay semileptonically and use the charge of the leptons to identify the
flavor of each B meson. A simultaneous fit to the decay time difference
distributions for opposite- and same-sign dilepton events gives ps.Comment: 7 pages, 1 figure, submitted to Physical Review Letter
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