A computational approach to the Thompson group FF

Let $F$ denote the Thompson group with standard generators $A=x_0$, $B=x_1$. It is a long standing open problem whether $F$ is an amenable group. By a result of Kesten from 1959, amenability of $F$ is equivalent to $$(i)\qquad ||I+A+B||=3$$ and to $$(ii)\qquad ||A+A^{-1}+B+B^{-1}||=4,$$ where in both cases the norm of an element in the group ring $\mathbb{C} F$ is computed in $B(\ell^2(F))$ via the regular representation of $F$. By extensive numerical computations, we obtain precise lower bounds for the norms in $(i)$ and $(ii)$, as well as good estimates of the spectral distributions of $(I+A+B)^*(I+A+B)$ and of $A+A^{-1}+B+B^{-1}$ with respect to the tracial state $\tau$ on the group von Neumann Algebra $L(F)$. Our computational results suggest, that $$||I+A+B||\approx 2.95 \qquad ||A+A^{-1}+B+B^{-1}||\approx 3.87.$$ It is however hard to obtain precise upper bounds for the norms, and our methods cannot be used to prove non-amenability of $F$.Comment: appears in International Journal of Algebra and Computation (2015

The LAEX and NASA portals for CoRoT public data

* Aims. We describe here the main functionalities of the LAEX (Laboratorio de Astrofisica Estelar y Exoplanetas/Laboratory for Stellar Astrophysics and Exoplanets) and NASA portals for CoRoT Public Data. The CoRoT archive at LAEX was opened to the community in January 2009 and is managed in the framework of the Spanish Virtual Observatory. NStED (NASA Star and Exoplanet Database) serves as the CoRoT portal for the US astronomical community. NStED is a general purpose stellar and exoplanet archive with the aim of providing support for NASA planet finding and characterisation goals, and the planning and support of NASA and other space missions. CoRoT data at LAEX and NStED can be accessed at http://sdc.laeff.inta.es/corotfa/ and http://nsted.ipac.caltech.edu,respectively. * Methods. Based on considerable experience with astronomical archives, the aforementioned archives are designed with the aim of delivering science-quality data in a simple and efficient way. * Results. LAEX and NStED not only provide access to CoRoT Public Data but furthermore serve a variety of observed and calculated astrophysical data. In particular, NStED provides scientifically validated information on stellar and planetary data related to the search for and characterization of extrasolar planets, and LAEX makes any information from Virtual Observatory services available to the astronomical community.Comment: Accepted for publication in Astronomy & Astrophysic

Single neutral pion production by charged-current νˉμ\bar{\nu}_\mu interactions on hydrocarbon at ⟨Eν⟩=\langle E_\nu \rangle = 3.6 GeV

Single neutral pion production via muon antineutrino charged-current interactions in plastic scintillator (CH) is studied using the \minerva detector exposed to the NuMI low-energy, wideband antineutrino beam at Fermilab. Measurement of this process constrains models of neutral pion production in nuclei, which is important because the neutral-current analog is a background for $\bar{\nu}_e$ appearance oscillation experiments. The differential cross sections for $\pi^0$ momentum and production angle, for events with a single observed $\pi^0$ and no charged pions, are presented and compared to model predictions. These results comprise the first measurement of the $\pi^0$ kinematics for this process.Comment: 6 pages, 5 figures, submitted to Physics Letters

Measurement of Total and Differential Cross Sections of Neutrino and Antineutrino Coherent π±\pi^\pm Production on Carbon

Neutrino induced coherent charged pion production on nuclei, $\overline{\nu}_\mu A\to\mu^\pm\pi^\mp A$, is a rare inelastic interaction in which the four-momentum squared transfered to the nucleus is nearly zero, leaving it intact. We identify such events in the scintillator of MINERvA by reconstructing |t| from the final state pion and muon momenta and by removing events with evidence of energetic nuclear recoil or production of other final state particles. We measure the total neutrino and antineutrino cross sections as a function of neutrino energy between 2 and 20 GeV and measure flux integrated differential cross sections as a function of $Q^2$, $E_\pi$ and $\theta_\pi$. The $Q^2$ dependence and equality of the neutrino and anti-neutrino cross-sections at finite $Q^2$ provide a confirmation of Adler's PCAC hypothesis

First evidence of coherent K+K^{+} meson production in neutrino-nucleus scattering

Neutrino-induced charged-current coherent kaon production, $\nu_{\mu}A\rightarrow\mu^{-}K^{+}A$, is a rare, inelastic electroweak process that brings a $K^+$ on shell and leaves the target nucleus intact in its ground state. This process is significantly lower in rate than neutrino-induced charged-current coherent pion production, because of Cabibbo suppression and a kinematic suppression due to the larger kaon mass. We search for such events in the scintillator tracker of MINERvA by observing the final state $K^+$, $\mu^-$ and no other detector activity, and by using the kinematics of the final state particles to reconstruct the small momentum transfer to the nucleus, which is a model-independent characteristic of coherent scattering. We find the first experimental evidence for the process at $3\sigma$ significance.Comment: added ancillary file with information about the six kaon candidate

Measurement of Partonic Nuclear Effects in Deep-Inelastic Neutrino Scattering using MINERvA

The MINERvA collaboration reports a novel study of neutrino-nucleus charged-current deep inelastic scattering (DIS) using the same neutrino beam incident on targets of polystyrene, graphite, iron, and lead. Results are presented as ratios of C, Fe, and Pb to CH. The ratios of total DIS cross sections as a function of neutrino energy and flux-integrated differential cross sections as a function of the Bjorken scaling variable x are presented in the neutrino-energy range of 5 - 50 GeV. Good agreement is found between the data and predicted ratios, based on charged-lepton nucleus scattering, at medium x and low neutrino energies. However, the data rate appears depleted in the vicinity of the nuclear shadowing region, x < 0.1. This apparent deficit, reflected in the DIS cross-section ratio at high neutrino energy , is consistent with previous MINERvA observations and with the predicted onset of nuclear shadowing with the the axial-vector current in neutrino scattering