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 $L$. Up to the first perturbative order in the quartic interaction (interaction parameter $\lambda$), we use the formalism of {\it dressed} states introduced in previous publications, to obtain for a large cavity explicit $\lambda$-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 $\bar{\omega}$, coupled to a scalar field inside a spherical reflecting cavity of diameter $L$. 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 $\bar{\omega}$ of the order $\bar{\omega}\sim 4.00\times 10^{14}/s$ (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 $L\sim 1.0\times 10^{-6}m$, 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 $\lambda$. We obtain for a large cavity an explicit $\lambda$-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

L → l l′ l′ νl νLL\,\to\, l\, l'\, l'\, \nu_l\, \nu_L in the SM and beyond

We study the $L\to l l' l' \nu_l \nu_L$ decays ($L=\tau,\mu$; $l,l'=\mu,e$) 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 $L$, keeping the $l,l'$ mass dependence. We clarify the discrepancy between two previous SM calculations of the decay rate improving their precision. The recent $3.5\,\sigma$ anomaly found in $\tau\to e \gamma\bar{\nu}_e\nu_\tau$ could be checked using our precise prediction for the $\tau\to e e e \bar{\nu}_e\nu_\tau$ decays, which shall be measured analyzing already existing data from the first generation B-factories. It is shown how measurements of the di-$l'$ mass distribution (with appropriate cuts) and $T$-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 $\mu^- \to e^- e^+ e^- \nu_{\mu} \bar{\nu}_{e}$ and $\tau^- \to \ell^- \ell'^+\ell'^-\nu_{\tau}\bar{\nu}_{\ell}$ for $\ell, \ell'=e, \mu$ 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 $\mathbf{T}$-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 $\mathbf{T}$-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 $L^- \to \ell^- \ell'^+\ell'^-$ decays. Searches at high values of the invariant mass of the $\ell'^+\ell'^-$ 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 $\partial M/\partial \rho_c\geq 0$, where $\rho_c$ is the central density of a star whose total mass is $M$, 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 $\partial M/\partial \rho_c \leq 0$. 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 $\partial M/\partial \rho_c \leq 0$. 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 $\mathcal{M}(=M \cup \partial M)$ is globally hyperbolic with (possibly empty) smooth timelike boundary $\partial M$, 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 $M$ 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