Energy spectra and energy correlations in the decayH→ZZ→μ+μ−μ+μ−

It is shown that in the sequential decay $H \to ZZ \to (f_1 \bar f_1 ) + (f_2 \bar f_2 )$ , the energy distribution of the final state particles provides a simple and powerful test of theHZZ vertex. For a standard Higgs boson, the energy spectrum of any final fermion, in the rest frame ofH, is predicted to be dΓ/dx～1+β⁴?2(x?1)², with $\beta = \sqrt {1 - 4m_Z^2 /m_H^2 } $ and 1?β≤x=4E/m _H ≤1+β. By contrast, the spectrum for a pseudoscalar Higgs is dΓ/dx～β²+(x?1)². There are characteristic energy correlations betweenf ₁ andf ₂ and betweenf ₁ andf ₂. These considerations are applied to the “gold-plated” reactionH→ZZ→μ⁺μ^?μ⁺μ^?, including possible effects ofCP-violation in theHZZ coupling. Our formalism also yields the energy spectra and correlations of leptons in the decay $H \to W^ + W^ - \to l^ + v_l l^ - \bar v_l $ .     

Group algebras whose units satisfy a group identity

Let be the group algebra of a torsion group over an infinite field . Let be the group of units of . We prove that if satisfies a group identity, then satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.

     

Constructing free subgroups of integral group ring units

Let be an arbitrary group. It is proved that if contains a bicyclic unit , then is a nonabelian free subgroup of invertible elements.

     

Precipitation-redispersion of cerium oxide nanoparticles with poly(acrylic acid): toward stable dispersions

We exploit a precipitation-redispersion mechanism for complexation of short chain polyelectrolytes with cerium oxide nanoparticles to extend their stability ranges. As synthesized, cerium oxide sols at pH 1.4 consist of monodisperse cationic nanocrystalline particles having a hydrodynamic diameter of 10 nm and a molecular weight of 400 000 g mol(-1). We show that short chain uncharged poly(acrylic acid) at low pH when added to a cerium oxide sols leads to macroscopic precipitation. As the pH is increased, the solution spontaneously redisperses into a clear solution of single particles with an anionic poly(acrylic acid) corona. The structure and dynamics of cerium oxide nanosols and their hybrid polymer-inorganic complexes in solution are investigated by static and dynamic light scattering, X-ray scattering, and chemical analysis. Quantitative analysis of the redispersed sol gives rise to an estimate of 40-50 polymer chains per particle for stable suspension. This amount represents 20% of the mass of the polymer-nanoparticle complexes. This complexation adds utility to the otherwise unstable cerium oxide dispersions by extending the range of stability of the sols in terms of pH, ionic strength, and concentration.