6,900 research outputs found
Hadron Optics: Diffraction Patterns in Deeply Virtual Compton Scattering
We show that the Fourier transform of the Deeply Virtual Compton Scattering
(DVCS) amplitude with respect to the skewness variable at fixed
invariant momentum transfer squared provides a unique way to visualize the
structure of the target hadron in the boost-invariant longitudinal coordinate
space. The results are analogous to the diffractive scattering of a wave in
optics. As a specific example, we utilize the quantum fluctuations of a fermion
state at one loop in QED to obtain the behavior of the DVCS amplitude for
electron-photon scattering. We then simulate the wavefunctions for a hadron by
differentiating the above LFWFs with respect to and study the
corresponding DVCS amplitudes in light-front longitudinal space. In both cases
we observe that the diffractive patterns in the longitudinal variable conjugate
to sharpen and the positions of the first minima move in with
increasing momentum transfer. For fixed , higher minima appear at positions
which are integral multiples of the lowest minimum. Both these observations
strongly support the analogy with diffraction in optics.Comment: Some plots modified, clarifications and references adde
Scientific Argumentation as a Foundation for the Design of Inquiry-Based Science Instruction
Despite the attention that inquiry has received in science education research and policy, a coherent means for implementing inquiry in the classroom has been missing [1]. In recent research, scientific argumentation has received increasing attention for its role in science and in science education [2]. In this article, we propose that organizing a unit of instruction around building a scientific argument can bring inquiry practices together in the classroom in a coherent way. We outline a framework for argumentation, focusing on arguments that are central to science—arguments for the best explanation. We then use this framework as the basis for a set of design principles for developing a sequence of inquiry-based learning activities that support students in the construction of a scientific argument. We show that careful analysis of the argument that students are expected to build provides designers with a foundation for selecting resources and designing supports for scientific inquiry. Furthermore, we show that creating multiple opportunities for students to critique and refine their explanations through evidence-based argumentation fosters opportunities for critical thinking, while building science knowledge and knowledge of the nature of science
Extension dimensional approximation theorem
Let be a countable CW-complex and be upper
semicontinuous -valued mapping of a paracompact space to a
complete metric space . We prove that if is a C-space of extension
dimension \ed X \le [L], then admits single-valued graph approximations.
For our result implies well-known approximation theorem for
-valued mappings of -dimensional spaces. And for
our theorem implies a theorem of Ancel on approximations of -valued
mappings of C-spaces.Comment: 7 pages, final version, minor correction
Hurewicz theorem for extension dimension
We prove a new selection theorem for multivalued mappings of C-space. Using
this theorem we prove extension dimensional version of Hurewicz theorem for a
closed mapping of -space onto paracompact -space
: if for finite -complex we have \ed Y\le [M] and for every point
and every compactum with \ed Z\le [M] we have
\ed(f^{-1}(y)\times Z)\le [L] for some -complex , then \ed X\le [L]
Perturbative QCD and factorization of coherent pion photoproduction on the deuteron
We analyze the predictions of perturbative QCD for pion photoproduction on
the deuteron, gamma D -> pi^0 D, at large momentum transfer using the reduced
amplitude formalism. The cluster decomposition of the deuteron wave function at
small binding only allows the nuclear coherent process to proceed if each
nucleon absorbs an equal fraction of the overall momentum transfer.
Furthermore, each nucleon must scatter while remaining close to its mass shell.
Thus the nuclear photoproduction amplitude, M_{gamma D -> pi^0 D}(u,t),
factorizes as a product of three factors: (1) the nucleon photoproduction
amplitude, M_{gamma N_1 -> pi^0 N_1}(u/4,t/4), at half of the overall momentum
transfer, (2) a nucleon form factor, F_{N_2}(t/4), at half the overall momentum
transfer, and (3) the reduced deuteron form factor, f_d(t), which according to
perturbative QCD, has the same monopole falloff as a meson form factor. A
comparison with the recent JLAB data for gamma D -> pi^0 D of Meekins et al.
[Phys. Rev. C 60, 052201 (1999)] and the available gamma p -> pi^0 p data shows
good agreement between the perturbative QCD prediction and experiment over a
large range of momentum transfers and center of mass angles. The reduced
amplitude prediction is consistent with the constituent counting rule, p^11_T
M_{gamma D -> pi^0 D} -> F(theta_cm), at large momentum transfer. This is found
to be consistent with measurements for photon lab energies E_gamma > 3 GeV at
theta_cm=90 degrees and \elab > 10 GeV at 136 degrees.Comment: RevTeX 3.1, 17 pages, 6 figures; v2: incorporates minor changes as
version accepted by Phys Rev
Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei
A simple exact covariant model in which a scalar particle is modeled as a
bound state of two different particles is used to elucidate relativistic
aspects of electromagnetic form factors. The model form factor is computed
using an exact covariant calculation of the lowest-order triangle diagram and
shown to be the same as that obtained using light-front techniques. The meaning
of transverse density is explained using coordinate space variables, allowing
us to identify a true mean-square transverse size directly related to the form
factor. We show that the rest-frame charge distribution is generally not
observable because of the failure to uphold current conservation. Neutral
systems of two charged constituents are shown to obey the lore that the heavier
one is generally closer to the transverse origin than the lighter one. It is
argued that the negative central charge density of the neutron arises, in
pion-cloud models, from pions of high longitudinal momentum. The
non-relativistic limit is defined precisely and the ratio of the binding energy
to that of the mass of the lightest constituent is shown to govern the
influence of relativistic effects. The exact relativistic formula for the form
factor reduces to the familiar one of the three-dimensional Fourier transform
of a square of a wave function for a very limited range of parameters. For
masses that mimic the quark-di-quark model of the nucleon we find substantial
relativistic corrections for any value of . A schematic model of the
lowest s-states of nuclei is used to find that relativistic effects decrease
the form factor for light nuclei but increase the form factor for heavy nuclei.
Furthermore, these states are strongly influenced by relativity.Comment: 18 pages, 11 figure
Hadron Spin Dynamics
Spin effects in exclusive and inclusive reactions provide an essential new
dimension for testing QCD and unraveling hadron structure. Remarkable new
experiments from SLAC, HERMES (DESY), and the Jefferson Laboratory present many
challenges to theory, including measurements at HERMES and SMC of the single
spin asymmetries in pion electroproduction, where the proton is polarized
normal to the scattering plane. This type of single spin asymmetry may be due
to the effects of rescattering of the outgoing quark on the spectators of the
target proton, an effect usually neglected in conventional QCD analyses. Many
aspects of spin, such as single-spin asymmetries and baryon magnetic moments
are sensitive to the dynamics of hadrons at the amplitude level, rather than
probability distributions. I illustrate the novel features of spin dynamics for
relativistic systems by examining the explicit form of the light-front
wavefunctions for the two-particle Fock state of the electron in QED, thus
connecting the Schwinger anomalous magnetic moment to the spin and orbital
momentum carried by its Fock state constituents and providing a transparent
basis for understanding the structure of relativistic composite systems and
their matrix elements in hadronic physics. I also present a survey of
outstanding spin puzzles in QCD, particularly the double transverse spin
asymmetry A_{NN} in elastic proton-proton scattering, the J/psi to rho-pi
puzzle, and J/psi polarization at the Tevatron.Comment: Concluding theory talk presented at SPIN2001, the Third
Circum-Pan-Pacific Symposium on High Energy Physics, October, 2001, Beijin
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