12,039 research outputs found
Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory
I study an aspect of chiral perturbation theory (\chi PT) which enables one
to ``bridge'' different reactions. That is, an operator fixed in one of the
reactions can then be used to predict the other. For this purpose, I calculate
the partial wave amplitude for the p-wave pion production (pp\to pn\pi^+) using
the pion production operator from the lowest and the next nonvanishing orders.
The operator includes a contact operator whose coupling has been fixed using a
matrix element of a low-energy weak process (pp\to de^+\nu_e). I find that this
operator does not reproduce the partial wave amplitude extracted from
experimental data, showing that the bridging over the reactions with
significantly different kinematics is not necessarily successful. I study the
dependence of the amplitude on the various inputs such as the NN potential, the
\pi N\Delta coupling, and the cutoff. I argue the importance of a higher order
calculation. In order to gain an insight into a higher order calculation, I add
a higher order counter term to the operator used above, and fit the couplings
to both the low-energy weak process and the pion production. The energy
dependence of the partial wave amplitude for the pion production is described
by the operator consistently with the data. However, I find a result which
tells us to be careful about the convergence of the chiral expansion for the
pp\to pn\pi^+ reaction.Comment: 30 pages, 13 figures, figures changed, compacted tex
The Arason invariant of orthogonal involutions of degree 12 and 8, and quaternionic subgroups of the Brauer group
Using the Rost invariant for torsors under Spin groups one may define an
analogue of the Arason invariant for certain hermitian forms and orthogonal
involutions. We calculate this invariant explicitly in various cases, and use
it to associate to every orthogonal involution with trivial discriminant and
trivial Clifford invariant over a central simple algebra of even co-index a
cohomology class of degree 3 with coefficients. This invariant
is the double of any representative of the Arason invariant; it vanishes
when the algebra has degree at most 10, and also when there is a quadratic
extension of the center that simultaneously splits the algebra and makes the
involution hyperbolic. The paper provides a detailed study of both invariants,
with particular attention to the degree 12 case, and to the relation with the
existence of a quadratic splitting field.Comment: A mistake pointed out by A. Sivatski in Section 5.3 has been
corrected in the new version of this preprin
Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties
An orthogonal involution on a central simple algebra , after
scalar extension to the function field of the Severi--Brauer
variety of , is adjoint to a quadratic form over
, which is uniquely defined up to a scalar factor. Some
properties of the involution, such as hyperbolicity, and isotropy up to an
odd-degree extension of the base field, are encoded in this quadratic form,
meaning that they hold for the involution if and only if they hold for
. As opposed to this, we prove that there exists non-totally
decomposable orthogonal involutions that become totally decomposable over
, so that the associated form is a Pfister form. We
also provide examples of nonisomorphic involutions on an index algebra that
yield similar quadratic forms, thus proving that the form does not
determine the isomorphism class of , even when the underlying algebra
has index . As a consequence, we show that the invariant for
orthogonal involutions is not classifying in degree , and does not detect
totally decomposable involutions in degree , as opposed to what happens for
quadratic forms
Schooling effects and earnings of French University graduates: school quality matters, but choice of discipline matters more
Our aim in this article is to study the relation between earnings of French universities graduates and some characteristics of their universities. We exploit data from the Céreq's "Génération 98" survey, enriched with information on university characteristics primarily from the ANETES (yearbook of French institutions of higher education). We employ multilevel modeling, enabling us to take advantage of the natural hierarchy in our separate datasets, and thus to identify, and even to measure potential effects of institutional quality. Since we take into account many individual students characteristics, we are able to obtain an income hierarchy among the different disciplines : students who graduated in science, economics or management obtain the highest earnings. Below them, we and students who graduated in law, political science, communication or language and literature, while the ones who graduated in social studies earn the lowest incomes. On the institutional level, we need two significant quality effects : the rest is from the socioeconomic composition of the university's student population, and the second effect is from the university's network in the job market. These last two results remain stable when we examine subsamples of universities according to their dominant teaching fields, except for universities that are particularly concentrated in science.Demand for schooling, educational economics, human capital, salaries wage differentials, school choice
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