4,450 research outputs found
Unbounded B-Fredholm operators on Hilbert spaces
This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index 0 is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties of the powers Tm of a closed B-Fredholm operator and we establish a spectral mapping theorem
Thermal Field Theory in a wire: Applications of Thermal Field Theory methods to the propagation of photons in a one-dimensional plasma
We apply the Thermal Field Theory (TFT) methods to study the propagation of
photons in a plasma wire, that is, a system in which the electrons are confined
to a one-dimensional tube or wire, but are otherwise free. We find the
appropriate expression for the photon \emph{free-field} propagator in such a
medium, and write down the dispersion relation in terms of the free-field
propagator and the photon self-energy. The self-energy is then calculated in
the one-loop approximation and the corresponding dispersion relation is
determined and studied in some detail. Our work differs from previous work on
this subject in that we do not adopt any specific electronic wave functions in
the coordinates that are transverse to the idealized wire, or rely on
particular features of the electronic structure. We treat the electrons as a
free gas of particles, constrained to move in one dimension, but otherwise in a
model-independent way only following the rules of TFT adapted to the situation
at hand. For the appropriate conditions of the plasma the \emph{static
approximation} can be employed and the dispersion relation reduces to the
results obtained in previous works, but the formula that we obtain is valid
under more general conditions, including those in which the static
approximation is not valid. In particular, the dispersion relation has several
branches, which are not revealed if the static approximation is used. The
dispersion relations obtained reproduce several unique features of these
systems that have been observed in recent experiments.Comment: 17 pages Revised and extended discussion of the dispersion relation
Coherent pion production off nuclei at T2K and MiniBooNE energies revisited
As a result of a new improved fit to old bubble chamber data of the dominant
axial C_5^A nucleon-to-Delta form factor, and due to the relevance of this form
factor for neutrino induced coherent pion production, we re-evaluate our model
predictions in Phys. Rev. D79, 013002 (2009) for different observables of the
latter reaction. Central values for the total cross sections increase by 20% to
30%, while differential cross sections do not change their shape appreciably.
Furthermore, we also compute the uncertainties on total, differential and flux
averaged cross sections induced by the errors in the determination of C_5^A.
Our new results turn out to be compatible within about 1 sigma with the former
ones. Finally, we stress the existing tension between the recent experimental
determination of the sigma(CC coh \pi^+)/sigma(NC coh \pi^0) ratio by the
SciBooNE Collaboration and the theoretical predictions.Comment: 6 latex pages, 1 table, 2 figures. Shortened versio
: Confronting theory and lattice simulations
We consider a recent -matrix analysis by Albaladejo {\it et al.}, [Phys.\
Lett.\ B {\bf 755}, 337 (2016)] which accounts for the and
coupled--channels dynamics, and that successfully describes the
experimental information concerning the recently discovered .
Within such scheme, the data can be similarly well described in two different
scenarios, where the is either a resonance or a virtual state. To
shed light into the nature of this state, we apply this formalism in a finite
box with the aim of comparing with recent Lattice QCD (LQCD) simulations. We
see that the energy levels obtained for both scenarios agree well with those
obtained in the single-volume LQCD simulation reported in Prelovsek {\it et
al.} [Phys.\ Rev.\ D {\bf 91}, 014504 (2015)], making thus difficult to
disentangle between both possibilities. We also study the volume dependence of
the energy levels obtained with our formalism, and suggest that LQCD
simulations performed at several volumes could help in discerning the actual
nature of the intriguing state
Non-universal gravitational couplings of neutrinos in matter
When neutrinos travel through a normal matter medium, the electron neutrinos
couple differently to gravity compared to the other neutrinos, due to the
presence of electrons in the medium and the absence of the other charged
leptons. The matter-induced gravitational couplings of the neutrinos under such
conditions are calculated and their contribution to the neutrino index of
refraction in the presence of a gravitational potential is determined.Comment: Latex, 10 page
Nuclear effects on lepton polarization in charged-current quasielastic neutrino scattering
We use a correlated local Fermi gas (LFG) model, which accounts also for long
distance corrections of the RPA type and final-state interactions, to compute
the polarization of the final lepton in charged-current quasielastic neutrino
scattering. The present model has been successfully used in recent studies of
inclusive neutrino nucleus processes and muon capture. We investigate the
relevance of nuclear effects in the particular case of polarization in
tau-neutrino induced reactions for several kinematics of relevance for neutrino
oscillation experiments.Comment: 13 pages, 8 figure
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