Determination of the angular and energy dependence of hard constituent scattering from π0 pair events at the CERN intersecting storage rings

We present data on proton-proton collisions, obtained at the CERN Intersecting Storage Rings, in which two roughly back-to-back π⁰'s of high transverse momentum (p_T) were produced. The angular distribution of the dipion axis relative to the collision axis is found to be independent of both the effective mass m of the dipion system and the centre-of-mass energy √s of the proton-proton collision. The cross-sections $\text{d}\text{σ}\text{d}\text{m}$ at the values of √s satisfy a scaling law of the form $\text{d}\text{σ}\text{d}\text{m}\text{=}\text{G(x)}\text{m}{}^{\mathrm{n}}\text{,}\text{where}\text{x = m(π}{}^0\text{, π}{}^0\text{)//trs}\text{and}\text{n = 6.5 ± 0.5}$. We show from our data that the leading π⁰ carries most of the momentum of the scattered parton. Given this fact, the axis of the dipion system follows closely the direction of the scattered constituents, and we exploit this to determine the angular dependence of the hard-scattering subprocess. We also compare our data with the lowest order QCD predictions using structure functions as determined in deep-inelastic scattering and fragmentation functions from electron-positron annihilation.     

High pT π0 production from αα and αp collisions at the CERN ISR

The invariant cross sections for π⁰ meson production in alpha—alpha and alpha—proton collisions at the ISR were meas- ured up to transverse momenta of $\text{7}\text{GeV}\text{c}$ and $\text{8}\text{GeV}\text{c}$, respectively. These measurements are compared with π⁰ production in pp collisions at the same values of $\text{s}\text{/}$nucleon, and the variation of the nuclear A-dependence with p_T is determined.     

Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions

We study the differential-delay equation x′(t) = ?αf(x(t–1)), where α is a positive parameter and f is an odd function which decays like x^?r at infinity. In particular, we consider the case r ? 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions. Our results disprove a conjecture of R. D. Nussbaum.