In 1984 Poland proposed that lattice and continuum hard-core fluids are characterized by a singularity on the negative fugacity axis with an exponent, here called φ(d), that is universal, depending only on the dimensionality d. We show that this singularity can be identified with the Yang–Lee edge singularity in d dimensions, which occurs on a locus of complex chemical potential above a gas-liquid or binary fluid critical point (or in pure imaginary magnetic fields above a ferromagnetic Curie point) and, hence, with directed lattice animals in d+1 dimensions and isotropic lattice animals or branched polymers in d+2 dimensions. It follows that φ=3/2 for d≥6 while power series in ε=6−d can be derived for φ(d) and for the associated correction-to-scaling exponent θ(d) with θ(1)=1 and θ(2)=5/6. By examining the two-component primitive penetrable sphere model for d=1 and d=∞ and long series for the binary Gaussian-molecule mixture (GMM) for all d, we conclude that the universality of φ(d) and θ(d) extends to continuum fluid mixtures with hard and soft repulsive cores [the GMM having Mayer f functions of the form −exp(−r2/r20)]. The new estimates φ(3)=1.0877(25) and θ(3)=0.622(12) are obtained with similar results for d=4 and 5.

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Quark and gluon spin densities in a proton are phenomenologically parametrized based on the European Muon Collaboration (EMC) data and on some plausible theoretical arguments. Four different characteristic values of gluon and sea polarizations suggested by various theoretical conjectures are considered. The sea polarization in a proton is probed by measuring the spin-spin asymmetry AE in the Drell-Yan process, while the helicity asymmetry AIL in direct photon production at high p, is employed to test the gluon spin content. Helicity asymmetries in both processes are quite sizable. AZ is positive and of order lo-' if the sea is polarized opposite to the proton spin, as suggested by the EMC data. However, even in the absence of the sea polarization at the EMC energies, we find A?; to be large and negative. Experimental measurements of A P~ and ALL together will not only provide a clean probe of sea and gluon polarizations, but also test whether the combination As -(a,/4r)AG inferred from the EMC data is valid, i.e., whether gluons contribute to the spin-dependent structure function gj'(x, e2) via the triangular anomaly.

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