Near-threshold Z-pair production in the semi-phenomenological model of unstable particles

Near-threshold production of neutral boson pairs is considered within the framework of the model of unstable particles with smeared mass. The results of calculations are in good agreement with LEP II data and Monte-Carlo simulations.Comment: 7 pages, 2 figure

Nonperturbative and spin effects in the central exclusive production of tensor χc(2+)\chi_c(2^+) meson

We discuss central exclusive production (CEP) of the tensor $\chi_c(2^{+})$ meson in proton-(anti)proton collisions at Tevatron, RHIC and LHC energies. The amplitude for the process is derived within the $k_t$-factorisation approach. Differential and total cross sections are calculated for several unintegrated gluon distributions (UGDFs). We compare exclusive production of all charmonium states $\chi_c(0^+),\,\chi_c(1^+)$ and $\chi_c(2^+)$. Equally good description of the recent Tevatron data is achieved both with Martin-Ryskin phenomenological UGDF and UGDF based on unified BFKL-DGLAP approach. Unlike for Higgs production, the main contribution to the diffractive amplitude of heavy quarkonia comes from nonperturbative region of gluon transverse momenta Q_{\perp}<1\,\GeV. At $y \approx$ 0, depending on UGDF we predict the contribution of $\chi_c(1^+,2^+)$ to the $J/\Psi + \gamma$ channel to be comparable or larger than that of the $\chi_c(0^+)$ one. This is partially due to a significant contribution from lower polarization states $\lambda=0$ for $\chi_c(1^+)$ and $\lambda=0,\,\pm 1$ for $\chi_c(2^+)$ meson. Corresponding theoretical uncertainties are discussed.Comment: 18 pages, 12 figures, discrepancies with Durham group results clarified, numerics corrected, basic conclusions unchanged, acknowledgements adde

Extended F_4-buildings and the Baby Monster

The Baby Monster group B acts naturally on a geometry E(B) with diagram c.F_4(t) for t=4 and the action of B on E(B) is flag-transitive. It possesses the following properties: (a) any two elements of type 1 are incident to at most one common element of type 2, and (b) three elements of type 1 are pairwise incident to common elements of type 2 iff they are incident to a common element of type 5. It is shown that E(B) is the only (non-necessary flag-transitive) c.F_4(t)-geometry, satisfying t=4, (a) and (b), thus obtaining the first characterization of B in terms of an incidence geometry, similar in vein to one known for classical groups acting on buildings. Further, it is shown that E(B) contains subgeometries E(^2E_6(2)) and E(Fi22) with diagrams c.F_4(2) and c.F_4(1). The stabilizers of these subgeometries induce on them flag-transitive actions of ^2E_6(2):2 and Fi22:2, respectively. Three further examples for t=2 with flag-transitive automorphism groups are constructed. A complete list of possibilities for the isomorphism type of the subgraph induced by the common neighbours of a pair of vertices at distance 2 in an arbitrary c.F_4(t) satisfying (a) and (b) is obtained.Comment: to appear in Inventiones Mathematica

Automorphisms of necklaces and sandpile groups

We introduce a group naturally acting on aperiodic necklaces of length $n$ with two colours using the 1--1 correspondences between aperiodic necklaces and irreducible polynomials over the field \F_2 of two elements. We notice that this group is isomorphic to the quotient group of non-degenerate circulant matrices of size $n$ over that field modulo a natural cyclic subgroup. Our groups turn out to be isomorphic to the sandpile groups for a special sequence of directed graphs.Comment: 12 pages, several tables, no picture