PCAC and the Deficit of Forward Muons in pi^+ Production by Neutrinos

The K2K experiment, using a fine-grained detector in a neutrino beam of energy $\sim 1.3 \mathrm{GeV}$ has observed two-track events that can be interpreted as a coherent reaction $\nu_\mu + \N \to \mu^- + \N + \pi^+ (\N = \rm{C}^{12})$ or an incoherent process $\nu_\mu + (p,n) \to \mu^- + \pi^+ + (p,n)$, the final nucleon being unobserved. The data show a significant deficit of forward-going muons in the interval $Q^2 \lesssim 0.1 \rm{GeV}^2$, where a sizeable coherent signal is expected. We attempt an explanantion of this effect, using a PCAC formula that includes the effect of the non-vanishing muon mass. A suppression of about 25 % is caused by a destructive interference of the axial vector and pseudoscalar (pion-exchange) amplitudes. The incoherent background is also reduced by 10 - 15 %. As a consequence the discrepancy between theory and observation is significantly reduced.Comment: 4 pages including 1 figure, changes in abstract and text; version to appear in Phys.Lett.

Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.Comment: 2

On the steady states of the spherically symmetric Einstein-Vlasov system

Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they can be multi-peaked, we give numerical evidence and a partial proof for the conjecture that the Buchdahl inequality $\sup_{r > 0} 2 m(r)/r < 8/9$, $m(r)$ the quasi-local mass, holds for all such steady states--both isotropic {\em and} anisotropic--, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state--both isotropic {\em and} anisotropic--the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe

Examining collusion and voting biases between countries during the Eurovision song contest since 1957

The Eurovision Song Contest (ESC) is an annual event which attracts millions of viewers. It is an interesting activity to examine since the participants of the competition represent a particular country's musical performance that will be awarded a set of scores from other participating countries based upon a quality assessment of a performance. There is a question of whether the countries will vote exclusively according to the artistic merit of the song, or if the vote will be a public signal of national support for another country. Since the competition aims to bring people together, any consistent biases in the awarding of scores would defeat the purpose of the celebration of expression and this has attracted researchers to investigate the supporting evidence for biases. This paper builds upon an approach which produces a set of random samples from an unbiased distribution of score allocation, and extends the methodology to use the full set of years of the competition's life span which has seen fundamental changes to the voting schemes adopted. By building up networks from statistically significant edge sets of vote allocations during a set of years, the results display a plausible network for the origins of the culture anchors for the preferences of the awarded votes. With 60 years of data, the results support the hypothesis of regional collusion and biases arising from proximity, culture and other irrelevant factors in regards to the music which that alone is intended to affect the judgment of the contest.Comment: to be published in JASS

Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a scalar field, subject to the Vlasov and wave equations respectively. The spacetime is future geodesically complete in the special case of plane symmetry with only a scalar field. Causal geodesics are also shown to be future complete for homogeneous solutions of the Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.Comment: 14 page

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.Comment: 16 page

Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system

Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.Comment: 12 page