Phenomenology of a light scalar: the dilaton

We make use of the language of non-linear realizations to analyze electro-weak symmetry breaking scenarios in which a light dilaton emerges from the breaking of a nearly conformal strong dynamics, and compare the phenomenology of the dilaton to that of the well motivated light composite Higgs scenario. We argue that -- in addition to departures in the decay/production rates into massless gauge bosons mediated by the conformal anomaly -- characterizing features of the light dilaton scenario (as well as other scenarios admitting a light CP-even scalar not directly related to the breaking of the electro-weak symmetry) are off-shell events at high invariant mass involving two longitudinally polarized vector bosons and a dilaton, and tree-level flavor violating processes. Accommodating both electro-weak precision measurements and flavor constraints appears especially challenging in the ambiguous scenario in which the Higgs and the dilaton fields strongly mix. We show that warped higgsless models of electro-weak symmetry breaking are explicit and tractable realizations of this limiting case. The relation between the naive radion profile often adopted in the study of holographic realizations of the light dilaton scenario and the actual dynamical dilaton field is clarified in the Appendix.Comment: 21 page

On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2

For an integer $k\geq 2$, let $\{F^{(k)}_{n} \}_{n\geq 0}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ having at least two presentations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$

Precision measurement of the rotational energy-level structure of the three-electron molecule He2+_2^+

The term values of all rotational levels of the $^4$He${_2}^+\,X^+\,^2\Sigma_u^+\,(\nu^+=0)$ ground vibronic state with rotational quantum number $N^+\le 19$ have been determined with an accuracy of 8 x 10$^{-4}$ cm$^{-1}$ ($\sim{25}$ MHz) by MQDT-assisted Rydberg spectroscopy of metastable He$_2^*$. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveal discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm$^{-1}$ ($\sim{2.1}$ GHz) at $N^+=19$.Comment: 11 pages, 6 figure

The Role of Social Security in Household Decisions: Var Estimates of Saving and Fertility Behaviour in Germany

Estimating saving and fertility simultaneously by the VAR method, we find that social security cover has a positive effect on household saving, and a negative effect on fertility. In Germany, as in other countries where the hypothesis was tested, social security is thus good for growth. A possible explanation for this unconventional finding is that compulsory saving in the form of pension contributions tends to displace intra-family transfers, rather than asset formation. However, the negative effect of social security on fertility tends to erode the system’s own contributory base, because it reduces the number of future contributors. That is one of the reasons why, in Germany as elsewhere, pay-as-you-go pension systems tend to be financially unstable. To some extent, this is counteracted by child-related benefits, which tend to encourage fertility, but the effect appears to be weak.

Cooling flows and quasars: different aspects of the same phenomenon? I. Concepts

We present a new class of solutions for the gas flows in elliptical galaxies containing massive central black holes (BH). Modified King model galaxies are assumed. Two source terms operate: mass loss from evolving stars, and a secularly declining heating by SNIa. Relevant atomic physical processes are modeled in detail. Like the previous models investigated by Ciotti et al. (1991), these new models first evolve through three consecutive evolutionary stages: wind, outflow, and inflow. At this point the presence of the BH alters dramatically the subsequent evolution, because the energy emitted by the BH can heat the surrounding gas to above virial temperatures, causing the formation of a hot expanding central bubble. Short and strong nuclear bursts of radiation are followed by longer periods during which the X-ray galaxy emission comes from the coronal gas (Lx). The range and approximate distribution spanned by Lx are found to be in accordance with observations of X-ray early type galaxies. Moreover, although high accretion rates occur during bursting phases when the central BH has a luminosity characteristic of QSOs, the total mass accreted is very small when compared to that predicted by stationary cooling-flow solutions and computed masses are in accord with putative BH nuclear masses. In the bursting phases Lx is low and the surface brightness profile is very low compared to pre-burst or to cooling flow models. We propose that these new models, while solving some long-standing problems of the cooling flow scenario, can provide a unified description of QSO-like objects and X-ray emitting elliptical galaxies, these being the same objects observed at two different evolutionary phases.Comment: 10 pages, ApJ LaTeX, plus 5 .eps figures and TeX-macro aasms4.sty - revised version - in press on ApJ Letter