25,200 research outputs found
Anharmonic oscillator radiation process in a large cavity
We consider a particle represented by an anharmonic oscillator, coupled to an
environment (a field) modeled by an ensemble of anharmonic oscillators, the
whole system being confined in a cavity of diameter . Up to the first
perturbative order in the quartic interaction (interaction parameter
), we use the formalism of {\it dressed} states introduced in previous
publications, to obtain for a large cavity explicit -dependent
formulas for the particle radiation process. These formulas are obtained in
terms of the corresponding exact expressions for the linear case. We conclude
for the enhancement of the particle decay induced by the quartic interaction.Comment: LaTex, 4 pages, 1 figure, some misprints correcte
Time evolution of quantum systems in microcavities and in free space -- a non-perturbative approach
We consider a system consisting of a particle in the harmonic approximation,
having frequency , coupled to a scalar field inside a spherical
reflecting cavity of diameter . By introducing {\it dressed} coordinates we
define {\it dressed} states which allow a non-perturbative unified description
of the radiation process, for weak and strong coupling regimes. We perform a
study of the energy distribution in a small cavity, with the initial condition
that the particle is in the first excited state. In the {\it weak} coupling
regime, we conclude for the quasi-stability of the excited particle. For
instance, for a frequency of the order (in the visible red), starting from the initial condition
that the particle is in the first excited level, we find that for a cavity with
diameter , the probability that the particle be at
any time still in the first excited level, will be of the order of 97%. For
appropriate cavity dimensions, which are of the same order of those ensuring
stability for weak coupling, we ensure for strong coupling the complete decay
of the particle to the ground state in a small ellapsed time. Also we consider
briefly the effects of a quartic interaction up to first order in the
interaction parameter . We obtain for a large cavity an explicit
-dependent expression for the particle radiation process. This formula
is obtained in terms of the corresponding exact expression for the linear case
and we conclude for the enhancement of the particle decay induced by the
quartic interaction.Comment: 12 pages, 1 figure. LATE
in the SM and beyond
We study the decays (; )
in the Standard Model (SM) and in the effective field theory (EFT) description
of the weak charged current at low energy, both for polarized and unpolarized
, keeping the mass dependence. We clarify the discrepancy between two
previous SM calculations of the decay rate improving their precision. The
recent anomaly found in
could be checked using our precise prediction for the decays, which shall be measured analyzing already existing
data from the first generation B-factories. It is shown how measurements of the
di- mass distribution (with appropriate cuts) and -asymmetries are able
to reveal the corresponding lepton flavor violating (LFV) processes without
neutrinos in the final state.Comment: 5 pages, two figures, contribution to the Proceedings of the PhiPsi15
Workshop, Sep. 23-26, 2015, Hefei, China. To be published by the Journal of
University of Science and Technology of Chin
Lightlike sets with applications to the rigidity of null geodesic incompleteness
An important, if relatively less well known aspect of the singularity
theorems in Lorentzian Geometry is to understand how their conclusions fare
upon weakening or suppression of one or more of their hypotheses. Then,
theorems with modified concusions may arise, showing that those conclusions
will fail only in special cases, at least some of which may be described. These
are the so-called rigidity theorems, and have many important examples in the
especialized literature. In this paper, we prove rigidity results for
generalized plane waves and certain globally hyperbolic spacetimes in the
presence of maximal compact surfaces. Motivated by some general properties
appearing in these proofs, we develop the theory of lightlike sets, entities
similar to achronal sets, but more appropriate to deal with low-regularity null
submanifolds.Comment: 23 page
Five-body leptonic decays of muon and tau leptons
We study the five-body decays
and for within the Standard Model (SM) and in a general effective field
theory description of the weak interactions at low energies. We compute the
branching ratios and compare our results with two previous, mutually
discrepant, SM calculations. By assuming a general structure for the weak
currents we derive the expressions for the energy and angular distributions of
the three charged leptons when the decaying lepton is polarized, which will be
useful in precise tests of the weak charged current at Belle II. In these
decays, leptonic -odd correlations in triple products of spin and
momenta --which may signal time reversal violation in the leptonic sector-- are
suppressed by the tiny neutrino masses. Therefore, a measurement of such
-violating observables would be associated to neutrinoless lepton
flavor violating (LFV) decays, where this effect is not extremely suppressed.
We also study the backgrounds that the SM five-lepton lepton decays constitute
to searches of LFV decays. Searches at high
values of the invariant mass of the pair look the most
convenient way to overcome the background.Comment: 40 pages, 6 figures, extended discussion of results in the case of
the effective lagrangian approach; other minor corrections/modifications are
adde
Phase transition effects on the dynamical stability of hybrid neutron stars
We study radial oscillations of hybrid non-rotating neutron stars composed by
a quark matter core and hadronic external layers. At first, we physically
deduce the junction conditions that should be imposed between two any phases in
these systems when perturbations take place. Then we compute the oscillation
spectrum focusing on the effects of slow and rapid phase transitions at the
quark-hadron interface. We use a generic MIT bag model for quark matter and a
relativistic mean field theory for hadronic matter. In the case of rapid
transitions at the interface we find a general relativistic version of the
reaction mode which has similar properties as its classical counterpart. We
also show that the usual static stability condition , where is the central density of a star whose total mass
is , remains always true for rapid transitions but breaks down in general
for slow transitions. In fact, for slow transitions we find that the frequency
of the fundamental mode can be a real number (indicating stability) even for
some branches of stellar models that verify . Thus, when secular instabilities are suppressed, as expected below some
critical stellar rotation rate, it would be possible the existence of twin or
even triplet stars with the same gravitational mass but different radii, with
one of the counterparts having . We explore
some astrophysical consequences of these results.Comment: 14 pages, 15 figures. Minor changes. Version accepted for publication
in Ap
Some remarks on conformal symmetries and Bartnik's splitting conjecture
Inspired by the results in a recent paper by G. Galloway and C. Vega (see
arXiv:1712.00785), we investigate a number of geometric consequences of the
existence of a timelike conformal Killing vector field on a globally hyperbolic
spacetime with compact Cauchy hypersurfaces, especially in connection with the
so-called Bartnik's splitting conjecture. In particular we give a complementary
result to the main theorem in Galloway and Vega's paper.Comment: The proof of Theorem 1.6 had a gap in the previous version which is
now fixed. This version also includes other minor change
Hausdorff closed limits and the causal boundary of globally hyperbolic spacetimes with timelike boundary
We show that when a spacetime is globally
hyperbolic with (possibly empty) smooth timelike boundary , a
metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff
himself in the 1950's in set theory, can be advantageously adopted on the
Geroch-Kronheimer-Penrose causal completion of M, retaining essentially all the
good properties of previous topologies in this ambient. In particular, we show
that if the globally hyperbolic spacetime admits a conformal boundary,
defined in such broad terms as to include all the standard examples in the
literature, then the latter is homeomorphic to the causal boundary endowed with
the CLT. We also discuss how our recent proposal arXiv:1807.00152 for a
definition of null infinity using only causal boundaries can be translated when
using the CLT, simplifying a number of technical aspects in the pertinent
definitions. In a more technical vein, in the appendix we discuss the
relationship of the CLT with the more generally applicable (but not always
Hausdorff) chronological topology, and show that they coincide exactly in those
cases when the latter happens to be Hausdorff.Comment: 38 page
Renormalization of the baryon axial vector current in large-N_c chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking
The baryon axial vector current is computed at one-loop order in large-N_c
baryon chiral perturbation theory, where N_c is the number of colors. Loop
graphs with octet and decuplet intermediate states are systematically
incorporated into the analysis and the effects of the decuplet-octet mass
difference and SU(3) flavor symmetry breaking are accounted for. As expected,
large-N_c cancellations between different one-loop graphs are observed as a
consequence of the large-N_c spin-flavor symmetry of QCD baryons. Fitting our
analytical formulas against experimental data on baryon semileptonic decays and
the strong decays of decuplet baryons, a detailed numerical analysis regarding
the determination of the basic parameters of large-N_c baryon chiral
perturbation theory as well as the extraction of the baryon axial vector
couplings is performed. The large-N_c baryon chiral perturbation theory
predictions are in very good agreement both with the expectations from the
1/N_c expansion and with the experimental data.Comment: 33 pages, 1 figur
Rigidity of geodesic completeness in the Brinkmann class of gravitational wave spacetimes
We consider restrictions placed by geodesic completeness on spacetimes
possessing a null parallel vector field, the so-called Brinkmann spacetimes.
This class of spacetimes includes important idealized gravitational wave models
in General Relativity, namely the plane-fronted waves with parallel rays, or
pp-waves, which in turn have been intensely and fruitfully studied in the
mathematical and physical literatures for over half a century. More concretely,
we prove a restricted version of a conjectural analogue for Brinkmann
spacetimes of a rigidity result obtained by M.T. Anderson for stationary
spacetimes. We also highlight its relation with a long-standing 1962 conjecture
by Ehlers and Kundt. Indeed, it turns out that the subclass of Brinkmann
spacetimes we consider in our main theorem is enough to settle an important
special case of the Ehlers-Kundt conjecture in terms of the well known class of
Cahen-Wallach spaces.Comment: Second version including new references, some extra motivation on the
Introduction and Propositions 2.2, 2.4 and Remark 2.5. 17 page
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