Gluon Mass, Glueballs and Gluonic Mesons

We review the phenomenological and theoretical evidences for dynamical gluon mass generation and the main features of the glueball spectrum in (pure gauge) Yang-Mills theories. The mixing between glueball and conventional $\bar q q$ states in $f_0$ scalar mesons is discussed. For pseudoscalar mesons, the inclusion of the glue field in an effective low energy theory is presented leading to a third isoscalar $\eta''$ partner of the $\eta$ and $\eta'$. Branching ratios for processes involving $\eta''$ are given and, when available, compatible with data for $\eta(1405)$.Comment: 9 pages, 6 figures. Contribution for the workshop "The many faces of QCD", 1-5 Nov 2010, Ghent, Belgiu

On the Chacteristic Numbers of Voting Games

This paper deals with the non-emptiness of the stability set for any proper voting game.We present an upper bound on the number of alternatives which guarantees the non emptiness of this solution concept. We show that this bound is greater than or equal to the one given by Le Breton and Salles [6] for quota games.voting game, core, stability set

The Physics of Glueballs

Glueballs are particles whose valence degrees of freedom are gluons and therefore in their description the gauge field plays a dominant role. We review recent results in the physics of glueballs with the aim set on phenomenology and discuss the possibility of finding them in conventional hadronic experiments and in the Quark Gluon Plasma. In order to describe their properties we resort to a variety of theoretical treatments which include, lattice QCD, constituent models, AdS/QCD methods, and QCD sum rules. The review is supposed to be an informed guide to the literature. Therefore, we do not discuss in detail technical developments but refer the reader to the appropriate references.Comment: Invited review for Int. J. Mod. Phys. E, 32 pages, 12 figures, 8 table

Glueball phenomenology and the relativistic flux tube model

The relativistic flux tube model is an effective description of confined quarks and gluons in which the confining interaction is carried by the flux tube, a Nambu-Goto string. We first show that the relativistic flux tube model can be applied to glueballs seen as bound states of transverse constituent gluons. After a comparison of that approach with usual spinless Salpeter Hamiltonians, we compute glueball masses and decay widths. Comments about the $\eta$-$\eta'$-pseudosclar glueball problem, the glueball--Pomeron conjecture, and finite-temperature effects are finally given. We also point out the existence of a duality between open- and closed-flux tube models of glueballs.Comment: v2: References added and changes in sec.

Speed of coming down from infinity for birth and death processes

We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, we firstly determine the behavior of the successive hitting times of large integers. We put in light two different regimes depending on whether the mean time for the process to go from $n+1$ to $n$ is negligible or not compared to the mean time to reach $n$ from infinity. In the first regime, the coming down from infinity is very fast and the convergence is weak. In the second regime, the coming down from infinity is gradual and a law of large numbers and a central limit theorem for the hitting times sequence hold. By an inversion procedure, we deduce that the process is a.s. equivalent to a non-increasing function when the time goes to zero. Our results are illustrated by several examples including applications to population dynamics and population genetics. The particular case where the death rate varies regularly is studied in details.Comment: 30 pages. arXiv admin note: text overlap with arXiv:1310.740

Hybrid meson masses and the correlated Gaussian basis

We revisited a model for charmonium hybrid meson with a magnetic gluon [Yu. S. Kalashnikova and A. V. Nefediev, Phys. Rev. D {\bf 77}, 054025 (2008)] and improved the numerical calculations. These improvements support the hybrid meson interpretation of X(4260). Within the same model, we computed the hybrid meson mass with an electric gluon which is resolved to be lighter. Relativistic effects and coupling channels decreased also the mass.Comment: 9 pages, 20 figures ; accepted for publication in Phys. Rev.

On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates

A classical problem in the power index literature is to design a voting mechanism such as the distribution of power of the different players is equal (or closer) to a pre established target. This tradition is especially popular when considering two tiers voting mechanisms: each player votes in his own jurisdiction to designate a delegate for the upper tier; and the question is to assign a certain number of mandates for each delegate according the population of the jurisdiction he or she represents. Unfortunately, there exist several measures of power, which in turn imply different distributions of the mandates for the same pre established target. The purposes of this paper are twofold: first, we calculate the probability that the two most important power indices, the Banzhaf index and the Shapley-Shubik index, lead to the same voting rule when the target is the same. Secondly, we determine which index on average comes closer to the pre established target.Banzhaf, Shapley-Shubik, power indices