1,546 research outputs found
Efficient numerical diagonalization of hermitian 3x3 matrices
A very common problem in science is the numerical diagonalization of
symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be
too inefficient if the number of matrices is large, we study several
alternatives. We consider optimized implementations of the Jacobi, QL, and
Cuppen algorithms and compare them with an analytical method relying on
Cardano's formula for the eigenvalues and on vector cross products for the
eigenvectors. Jacobi is the most accurate, but also the slowest method, while
QL and Cuppen are good general purpose algorithms. The analytical algorithm
outperforms the others by more than a factor of 2, but becomes inaccurate or
may even fail completely if the matrix entries differ greatly in magnitude.
This can mostly be circumvented by using a hybrid method, which falls back to
QL if conditions are such that the analytical calculation might become too
inaccurate. For all algorithms, we give an overview of the underlying
mathematical ideas, and present detailed benchmark results. C and Fortran
implementations of our code are available for download from
http://www.mpi-hd.mpg.de/~globes/3x3/ .Comment: 13 pages, no figures, new hybrid algorithm added, matches published
version, typo in Eq. (39) corrected; software library available at
http://www.mpi-hd.mpg.de/~globes/3x3
Hadron Helicity Violation in Exclusive Processes: Quantitative Calculations in Leading Order QCD
We study a new mechanism for hadronic helicity flip in high energy hard
exclusive reactions. The mechanism proceeds in the limit of perfect chiral
symmetry, namely without any need to flip a quark helicity. The fundamental
feature of the new mechanism is the breaking of rotational symmetry of the hard
collision by a scattering plane in processes involving independent quark
scattering. We show that in the impulse approximation there is no evidence for
of the helicity violating process as the energy or momentum transfer is
increased over the region 1 GeV^2 < Q^2 < 100 GeV^2. In the asymptotic region
Q^2> 1000 GeV^2, a saddle point approximation with doubly logarithmic accuracy
yields suppression by a fraction of power of Q^2. ``Chirally--odd" exclusive
wave functions which carry non--zero orbital angular momentum and yet are
leading order in the high energy limit, play an important role.Comment: uuencoded LaTeX file (21 pages) and PostScript figure
Transversity GPD in photo- and electroproduction of two vector mesons
The chiral-odd generalized parton distribution (GPD), or transversity GPD, of
the nucleon can be accessed experimentally through the photo- or
electroproduction of two vector mesons on a polarized nucleon target,
\gamma^(*) N --> \rho_1 \rho_2 N', where \rho_1 is produced at large transverse
momentum, \rho_2 is transversely polarized, and the mesons are separated by a
large rapidity gap. We predict the cross section for this process for both
transverse and longitudinal \rho_{2} production. To this end we propose a model
for the transversity GPD H_T(x,\xi,t), and give an estimate of the relative
sizes of the transverse and longitudinal \rho_{2} cross sections. We show that
a dedicated experiment at high energy should be able to measure the
transversity content of the proton.Comment: 15 pages, 9 figures. Extended discussion of experimental prospects in
the conclusions. Version to appear in EPJ
Hard exclusive reactions and hadron structure
The generalized Bjorken regime of exclusive reactions opens new ways to
explore the hadron structure. We shortly review the present status of this
domain where generalized parton distributions, generalized distribution
amplitudes and transition distribution amplitudes describe various aspects of
confinement physics.Comment: 7 pages LATEX, 5 figures, invited talk at the Vth Conference on
Hadronic Physics held at ICTP, Trieste, Italy, May 200
Exclusive production of pentaquarks in the scaling regime
We investigate two exclusive reactions with a Theta+ pentaquark in the final
state: electroproduction of a K meson on the nucleon, and K+ scattering on a
neutron target producing a lepton pair. These reactions offer unique
opportunities to investigate the structure of pentaquark baryons at parton
level. We discuss the generalized parton distributions for the N --> Theta+
transition and give the leading order amplitude for these processes in the
Bjorken regime.Comment: 5 pages in LATEX, 1 .eps figure, talk at the Baryons04 Conference,
October 25-29, 2004, Palaiseau, Franc
Multiple-Scattering Series For Color Transparency
Color transparency CT depends on the formation of a wavepacket of small
spatial extent. It is useful to interpret experimental searches for CT with a
multiple scattering scattering series based on wavepacket-nucleon scattering
instead of the standard one using nucleon-nucleon scattering. We develop
several new techniques which are valid for differing ranges of energy. These
techniques are applied to verify some early approximations; study new forms of
the wave-packet-nucleon interaction; examine effects of treating wave packets
of non-zero size; and predict the production of 's in electron scattering
experiments.Comment: 26 pages, U.Wa. preprint 40427-23-N9
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