346 research outputs found
Relativistic effects in electromagnetic nuclear responses in the quasi-elastic delta region
A new non-relativistic expansion in terms of the nucleon's momentum inside
nuclear matter of the current for isobar electro-excitation from the nucleon is
performed. Being exact with respect to the transferred energy and momentum,
this yields new current operators which retain important aspects of relativity
not taken into account in the traditional non-relativistic reductions. The
transition current thus obtained differs from the leading order of the
traditional expansion by simple multiplicative factors. These depend on the
momentum and energy transfer and can be easily included together with
relativistic kinematics in non-relativistic, many-body models of isobar
electro-excitation in nuclei. The merits of the new current are tested by
comparing with the unexpanded electromagnetic nuclear responses in the isobar
peak computed in a relativistic Fermi gas framework. The sensitivity of the
relativistic responses to the isobar's magnetic, electric and Coulomb form
factors and the finite width of the isobar is analyzed.Comment: 26 pages plus 6 figure
Making Almost Commuting Matrices Commute
Suppose two Hermitian matrices almost commute (). Are they close to a commuting pair of Hermitian matrices, ,
with ? A theorem of H. Lin
shows that this is uniformly true, in that for every there exists
a , independent of the size of the matrices, for which almost
commuting implies being close to a commuting pair. However, this theorem does
not specify how depends on . We give uniform bounds relating
and . We provide tighter bounds in the case of block
tridiagonal and tridiagonal matrices and a fully constructive method in that
case. Within the context of quantum measurement, this implies an algorithm to
construct a basis in which we can make a {\it projective} measurement that
approximately measures two approximately commuting operators simultaneously.
Finally, we comment briefly on the case of approximately measuring three or
more approximately commuting operators using POVMs (positive operator-valued
measures) instead of projective measurements.Comment: 22 pages; tighter bounds; Note: fixed mistake in proof pointed out by
Filonov and Kachkovski
Delta-isobar relativistic meson exchange currents in quasielastic electron scattering
We study the role of the -isobar current on the response functions
for high energy inclusive quasielastic electron scattering from nuclei. We
consider a general Lagrangian which is compatible with contact invariance and
perform a fully relativistic calculation in first-order perturbation theory for
one-particle emission. The dependence of the responses upon off-shell
parametrizations is analyzed and found to be mild. A discussion of scaling
behaviour and a comparison with various non-relativistic approaches are also
presented.Comment: 26 pages, 9 figures; one page of text added; corrected errors in eq
Neutrino masses from higher than d=5 effective operators
We discuss the generation of small neutrino masses from effective operators
higher than dimension five, which open new possibilities for low scale see-saw
mechanisms. In order to forbid the radiative generation of neutrino mass by
lower dimensional operators, extra fields are required, which are charged under
a new symmetry. We discuss this mechanism in the framework of a two Higgs
doublet model. We demonstrate that the tree level generation of neutrino mass
from higher dimensional operators often leads to inverse see-saw scenarios in
which small lepton number violating terms are naturally suppressed by the new
physics scale. Furthermore, we systematically discuss tree level
generalizations of the standard see-saw scenarios from higher dimensional
operators. Finally, we point out that higher dimensional operators can also be
generated at the loop level. In this case, we obtain the TeV scale as new
physics scale even with order one couplings.Comment: 22 pages, 3 figures, 2 tables. Some references adde
Neutrino masses in with adjoint flavons
We present a supersymmetric model for neutrino masses
and mixings that implements the seesaw mechanism by means of the heavy SU(2)
singlets and triplets states contained in three adjoints of SU(5). We discuss
how Abelian symmetries can naturally yield non-hierarchical light
neutrinos even when the heavy states are strongly hierarchical, and how it can
also ensure that --parity arises as an exact accidental symmetry. By
assigning two flavons that break to the adjoint representation of
SU(5) and assuming universality for all the fundamental couplings, the
coefficients of the effective Yukawa and Majorana mass operators become
calculable in terms of group theoretical quantities. There is a single free
parameter in the model, however, at leading order the structure of the light
neutrinos mass matrix is determined in a parameter independent way.Comment: 16 pages, 9 figures. Included contributions to neutrino masses from
the triplet states contained in the three adjoints of SU(5
On perfect fluid models in non-comoving observational spherical coordinates
We use null spherical (observational) coordinates to describe a class of
inhomogeneous cosmological models. The proposed cosmological construction is
based on the observer past null cone. A known difficulty in using inhomogeneous
models is that the null geodesic equation is not integrable in general. Our
choice of null coordinates solves the radial ingoing null geodesic by
construction. Furthermore, we use an approach where the velocity field is
uniquely calculated from the metric rather than put in by hand. Conveniently,
this allows us to explore models in a non-comoving frame of reference. In this
frame, we find that the velocity field has shear, acceleration and expansion
rate in general. We show that a comoving frame is not compatible with expanding
perfect fluid models in the coordinates proposed and dust models are simply not
possible. We describe the models in a non-comoving frame. We use the dust
models in a non-comoving frame to outline a fitting procedure.Comment: 8 pages, 1 figure. To appear in Phys.Rev.
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