Another look at anomalous J/Psi suppression in Pb+Pb collisions at P/A = 158 GeV/c

A new data presentation is proposed to consider anomalous $J/\Psi$ suppression in Pb + Pb collisions at $P/A=158$ GeV/c. If the inclusive differential cross section with respect to a centrality variable is available, one can plot the yield of J/Psi events per Pb-Pb collision as a function of an estimated squared impact parameter. Both quantities are raw experimental data and have a clear physical meaning. As compared to the usual J/Psi over Drell-Yan ratio, there is a huge gain in statistical accuracy. This presentation could be applied advantageously to many processes in the field of nucleus-nucleus collisions at various energies.Comment: 6 pages, 5 figures, submitted to The European Physical Journal C; minor revisions for final versio

Arithmeticity vs. non-linearity for irreducible lattices

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, such as for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page

A lattice in more than two Kac--Moody groups is arithmetic

Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group over a local field and $\Gamma$ is an arithmetic lattice. This relies on the following alternative which is satisfied by any irreducible lattice provided n is at least 2: either $\Gamma$ is an S-arithmetic (hence linear) group, or it is not residually finite. In that case, it is even virtually simple when the ground field is large enough. More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther

The Bs -> Ds pi and Bs -> Ds K selections

The decay channels Bs->Dspi and Bs->DsK will be used to extract the physics parameters $\Delta m_s$, $\Delta\Gamma_s$ and $\gamma + \phi_s$. Simulation studies based on Monte Carlo samples produced in 2004 and 2005 show that a total of 140k Bs->Dspi and 6.2k Bs->DsK events are expected to be triggered, reconstructed and selected in $2fb^{-1}$ of data ($10^7s$ of data taking at a luminosity of 2\times 10^{32}\unit{cm^{-2}s^{-1}}). The combinatorial background-over-signal ratio originating from inclusive bb events is expected to be $B/S Dspi whereas, for Bs->DsK, the limit is$B/S < 0.18~\at~90\%$~CL

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n

The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.Comment: LaTeX, 3 figures, 12 page

The algorithm for FIR corrections of the VELO analogue links and its performance

The data from the VELO front-end is sent to the ADCs on the read-out board over a serial analogue link. Due imperfections in the link, inter-symbol cross talk occurs between adjacent time-bins in the transfer. This is corrected by an FIR filter implemented in the pre-processing FPGA locacted on the read-out board. This note reports on a method to determine the coefficients for the filter using date taken in-situ. Simulations are presented that show the performance of the methods as it is implemented in the LHCb read-out board. The effectiveness of the algorithm is demonstrated by the improvements in tracking performance on beam test data it brings

Reduction and approximation in gyrokinetics

The gyrokinetics formulation of plasmas in strong magnetic fields aims at the elimination of the angle associated with the Larmor rotation of charged particles around the magnetic field lines. In a perturbative treatment or as a time-averaging procedure, gyrokinetics is in general an approximation to the true dynamics. Here we discuss the conditions under which gyrokinetics is either an approximation or an exact operation in the framework of reduction of dynamical systems with symmetryComment: 15 pages late

Modular Lie algebras and the Gelfand-Kirillov conjecture

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.Comment: 20 page

Berry phase in homogeneous K\"ahler manifolds with linear Hamiltonians

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of {\em classical} objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.Comment: LaTeX fil